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Уважаемые коллеги,<br>
<br>
На заседании Ученого совета в пятницу 18 декабря будут заслушаны 2
доклада:<br>
<br>
1) <u>А. М. Дюгаев</u>, П. Д. Григорьев<br>
<font size="+1"><b>Основное состояние квантовой частицы в
потенциальном поле. Моделирование потенциалов методом обратной
задачи</b> (посвящается памяти А. Шабата)</font><br>
<br>
<div class="abstract tex">
Исследуется решение уравнения Шредингера для основного состояния
частицы в потенциальном поле. Так как волновые функции основного
состояния не имеют узлов, оказывается возможным однозначно
определить потенциалы разных типов. Выяснилось, что для широкого
круга модельных потенциалов энергия основного состояния равна
нулю. Более того, нулевой уровень может быть единственным уровнем
на границе сплошного спектра. Рассмотрены потенциалы типа
«воронок», имеющие монотонную зависимость от координат, для случая
одного, двух и трех измерений. В одномерном случае интересны
потенциалы «инстантонного» типа с двумя точками равновесия
частицы. Для кулоновского потенциала энергия основного состояния
устойчива к его экранировке, как на больших, так и на малых
расстояниях. Найдены двухсолитонные решения нелинейного уравнения
Шредингера. Аргументирована эффективность предлагаемого «метода
обратной задачи» для исследования решений дифференциальных
уравнений.
<br>
Обнаружен широкий класс потенциалов, для которых энергия основного
состояния стационарна при трансляциях волновой функции для
размерности d=1,2,3. Для размерности d=1 эти функции известны из
теории нелинейных уравнений. Приводятся примеры нелинейных
уравнений с нулевой энергией основного состояния. Исследуются
функции, локализованные на сфере, и потенциалы типа воронок.
</div>
<br>
<br>
2) <u>А. М. Дюгаев</u>, П.Д. Григорьев (короткий доклад)<br>
<font size="+1"><b>Параметр порядка и теплоемкость сверхпроводящих
гранул</b></font><br>
<br>
<div class="abstract tex">
Определены термодинамические свойства сверхпроводящих гранул с
малым параметром <span class="MathJax"
id="MathJax-Element-1-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><mo>=</mo><msub><mi>ε</mi><mn>0</mn></msub><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-1" style="width: 3.839em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 4.332em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1004.33em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-2"><span class="mi"
id="MathJax-Span-3" style="font-family:
MathJax_Math; font-style: italic;">δ<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.007em;"></span></span><span
class="mo" id="MathJax-Span-4" style="font-family:
MathJax_Main; padding-left: 0.278em;">=</span><span
class="msubsup" id="MathJax-Span-5"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 0.895em;
height: 0px;"><span style="position: absolute;
clip: rect(3.312em, 1000.43em, 4.212em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-6"
style="font-family: MathJax_Math; font-style:
italic;">ε</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.466em;"><span class="mn" id="MathJax-Span-7"
style="font-size: 70.7%; font-family:
MathJax_Main;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="texatom" id="MathJax-Span-8"><span
class="mrow" id="MathJax-Span-9"><span class="mo"
id="MathJax-Span-10" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mi" id="MathJax-Span-11" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-12" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.005em;"></span></span></nobr></span>,
где <span class="MathJax" id="MathJax-Element-2-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ε</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-13" style="width: 0.856em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.923em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.329em,
1000.92em, 1.373em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-14"><span
class="msubsup" id="MathJax-Span-15"><span
style="display: inline-block; position: relative;
width: 0.895em; height: 0px;"><span
style="position: absolute; clip: rect(3.312em,
1000.43em, 4.212em, -1000em); top: -3.977em;
left: 0em;"><span class="mi"
id="MathJax-Span-16" style="font-family:
MathJax_Math; font-style: italic;">ε</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.466em;"><span class="mn" id="MathJax-Span-17"
style="font-size: 70.7%; font-family:
MathJax_Main;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.208em;
border-left: 0px solid; width: 0px; height: 0.668em;"></span></span></nobr></span>
– расстояние между уровнями размерного квантования, <span
class="MathJax" id="MathJax-Element-3-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-18" style="width: 0.998em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.136em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.312em,
1001.13em, 2.426em, -1000em); top: -2.202em; left: 0em;"><span
class="mrow" id="MathJax-Span-19"><span class="mi"
id="MathJax-Span-20" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-21" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.202em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.072em;
border-left: 0px solid; width: 0px; height: 0.73em;"></span></span></nobr></span>
– температура перехода в сверхпроводящее состояние объемного
образца. Показано, что параметр порядка <span class="MathJax"
id="MathJax-Element-4-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-22" style="width: 2.063em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.344em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1002.25em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-23"><span class="mi"
id="MathJax-Span-24" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-25" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-26" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-27" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span> не
обращается в ноль при <span class="MathJax"
id="MathJax-Element-5-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>></mo><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-28" style="width: 2.844em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.196em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em,
1003.19em, 2.526em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-29"><span class="mi"
id="MathJax-Span-30" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-31" style="font-family:
MathJax_Main; padding-left: 0.278em;">></span><span
class="mi" id="MathJax-Span-32" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">T<span style="display: inline-block;
overflow: hidden; height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-33" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.098em;
border-left: 0px solid; width: 0px; height: 0.756em;"></span></span></nobr></span>
и даже проходит через минимум при <span class="MathJax"
id="MathJax-Element-6-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>≈</mo><mi>e</mi><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-34" style="width: 3.2em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.622em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em,
1003.62em, 2.497em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-35"><span class="mi"
id="MathJax-Span-36" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-37" style="font-family:
MathJax_Main; padding-left: 0.278em;">≈</span><span
class="mi" id="MathJax-Span-38" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">e</span><span class="mi"
id="MathJax-Span-39" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-40" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.072em;
border-left: 0px solid; width: 0px; height: 0.73em;"></span></span></nobr></span>;
причем <span class="MathJax" id="MathJax-Element-7-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mi>e</mi><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mn>0</mn><mo
stretchy="false">)</mo><mo>≈</mo><msup><mi>δ</mi><mrow
class="MJX-TeXAtom-ORD"><mn>1</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-41" style="width: 7.745em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 8.807em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.166em,
1008.81em, 2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-42"><span class="mi"
id="MathJax-Span-43" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-44" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-45" style="font-family:
MathJax_Math; font-style: italic;">e</span><span
class="mi" id="MathJax-Span-46" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-47" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-48" style="font-family:
MathJax_Main;">)</span><span class="texatom"
id="MathJax-Span-49"><span class="mrow"
id="MathJax-Span-50"><span class="mo"
id="MathJax-Span-51" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mi" id="MathJax-Span-52" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-53" style="font-family:
MathJax_Main;">(</span><span class="mn"
id="MathJax-Span-54" style="font-family:
MathJax_Main;">0</span><span class="mo"
id="MathJax-Span-55" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-56" style="font-family:
MathJax_Main; padding-left: 0.278em;">≈</span><span
class="msubsup" id="MathJax-Span-57"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 1.639em;
height: 0px;"><span style="position: absolute;
clip: rect(3.047em, 1000.45em, 4.2em, -1000em);
top: -3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-58" style="font-family:
MathJax_Math; font-style: italic;">δ<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.007em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.503em;"><span class="texatom"
id="MathJax-Span-59"><span class="mrow"
id="MathJax-Span-60"><span class="mn"
id="MathJax-Span-61" style="font-size:
70.7%; font-family: MathJax_Main;">1</span><span
class="texatom" id="MathJax-Span-62"><span
class="mrow" id="MathJax-Span-63"><span
class="mo" id="MathJax-Span-64"
style="font-size: 70.7%; font-family:
MathJax_Main;">/</span></span></span><span
class="mn" id="MathJax-Span-65"
style="font-size: 70.7%; font-family:
MathJax_Main;">2</span></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.131em;"></span></span></nobr></span>,
а в точке перехода <span class="MathJax"
id="MathJax-Element-8-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mn>0</mn><mo
stretchy="false">)</mo><mo>≈</mo><msup><mi>δ</mi><mrow
class="MJX-TeXAtom-ORD"><mn>1</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>4</mn></mrow></msup></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-66" style="width: 7.319em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 8.31em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.166em,
1008.31em, 2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-67"><span class="mi"
id="MathJax-Span-68" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-69" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-70" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-71" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-72" style="font-family:
MathJax_Main;">)</span><span class="texatom"
id="MathJax-Span-73"><span class="mrow"
id="MathJax-Span-74"><span class="mo"
id="MathJax-Span-75" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mi" id="MathJax-Span-76" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-77" style="font-family:
MathJax_Main;">(</span><span class="mn"
id="MathJax-Span-78" style="font-family:
MathJax_Main;">0</span><span class="mo"
id="MathJax-Span-79" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-80" style="font-family:
MathJax_Main; padding-left: 0.278em;">≈</span><span
class="msubsup" id="MathJax-Span-81"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 1.639em;
height: 0px;"><span style="position: absolute;
clip: rect(3.047em, 1000.45em, 4.2em, -1000em);
top: -3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-82" style="font-family:
MathJax_Math; font-style: italic;">δ<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.007em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.503em;"><span class="texatom"
id="MathJax-Span-83"><span class="mrow"
id="MathJax-Span-84"><span class="mn"
id="MathJax-Span-85" style="font-size:
70.7%; font-family: MathJax_Main;">1</span><span
class="texatom" id="MathJax-Span-86"><span
class="mrow" id="MathJax-Span-87"><span
class="mo" id="MathJax-Span-88"
style="font-size: 70.7%; font-family:
MathJax_Main;">/</span></span></span><span
class="mn" id="MathJax-Span-89"
style="font-size: 70.7%; font-family:
MathJax_Main;">4</span></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.131em;"></span></span></nobr></span>.
Параметр <span class="MathJax" id="MathJax-Element-9-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo><mo>≫</mo><msub><mi>ε</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-90" style="width: 4.194em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 4.759em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1004.76em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-91"><span class="mi"
id="MathJax-Span-92" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-93" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-94" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-95" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-96" style="font-family:
MathJax_Main; padding-left: 0.278em;">≫</span><span
class="msubsup" id="MathJax-Span-97"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 0.895em;
height: 0px;"><span style="position: absolute;
clip: rect(3.312em, 1000.43em, 4.212em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-98"
style="font-family: MathJax_Math; font-style:
italic;">ε</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.466em;"><span class="mn" id="MathJax-Span-99"
style="font-size: 70.7%; font-family:
MathJax_Main;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.005em;"></span></span></nobr></span>
в широкой области температур <span class="MathJax"
id="MathJax-Element-10-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>></mo><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-100" style="width: 2.844em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.196em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em,
1003.19em, 2.526em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-101"><span class="mi"
id="MathJax-Span-102" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-103" style="font-family:
MathJax_Main; padding-left: 0.278em;">></span><span
class="mi" id="MathJax-Span-104" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">T<span style="display: inline-block;
overflow: hidden; height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-105" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.098em;
border-left: 0px solid; width: 0px; height: 0.756em;"></span></span></nobr></span>,
например, <span class="MathJax" id="MathJax-Element-11-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mo
stretchy="false">(</mo><mi>e</mi><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>ε</mi><mn>0</mn></msub><mo>∼</mo><msup><mi>δ</mi><mrow
class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-106" style="width: 7.177em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 8.168em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.166em,
1008.17em, 2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-107"><span class="mi"
id="MathJax-Span-108" style="font-family:
MathJax_Main;">Δ</span><span class="mo"
id="MathJax-Span-109" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-110" style="font-family:
MathJax_Math; font-style: italic;">e</span><span
class="mi" id="MathJax-Span-111" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-112" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-113" style="font-family:
MathJax_Main;">)</span><span class="texatom"
id="MathJax-Span-114"><span class="mrow"
id="MathJax-Span-115"><span class="mo"
id="MathJax-Span-116" style="font-family:
MathJax_Main;">/</span></span></span><span
class="msubsup" id="MathJax-Span-117"><span
style="display: inline-block; position: relative;
width: 0.895em; height: 0px;"><span
style="position: absolute; clip: rect(3.312em,
1000.43em, 4.212em, -1000em); top: -3.977em;
left: 0em;"><span class="mi"
id="MathJax-Span-118" style="font-family:
MathJax_Math; font-style: italic;">ε</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.466em;"><span class="mn" id="MathJax-Span-119"
style="font-size: 70.7%; font-family:
MathJax_Main;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-120" style="font-family:
MathJax_Main; padding-left: 0.278em;">∼</span><span
class="msubsup" id="MathJax-Span-121"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 2.189em;
height: 0px;"><span style="position: absolute;
clip: rect(3.047em, 1000.45em, 4.2em, -1000em);
top: -3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-122" style="font-family:
MathJax_Math; font-style: italic;">δ<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.007em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.503em;"><span class="texatom"
id="MathJax-Span-123"><span class="mrow"
id="MathJax-Span-124"><span class="mo"
id="MathJax-Span-125" style="font-size:
70.7%; font-family: MathJax_Main;">−</span><span
class="mn" id="MathJax-Span-126"
style="font-size: 70.7%; font-family:
MathJax_Main;">1</span><span
class="texatom" id="MathJax-Span-127"><span
class="mrow" id="MathJax-Span-128"><span
class="mo" id="MathJax-Span-129"
style="font-size: 70.7%; font-family:
MathJax_Main;">/</span></span></span><span
class="mn" id="MathJax-Span-130"
style="font-size: 70.7%; font-family:
MathJax_Main;">2</span></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.131em;"></span></span></nobr></span>.
<br>
</div>
Определена температурная зависимость избыточной теплоемкости гранул
<span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mi>C</mi><mo>=</mo><mo
stretchy="false">[</mo><msub><mi>C</mi><mi>S</mi></msub><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo><mo>−</mo><msub><mi>C</mi><mi>N</mi></msub><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo><mo
stretchy="false">]</mo><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>C</mi><mi>N</mi></msub><mo
stretchy="false">(</mo><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-131" style="width: 12.433em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 14.134em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1014.04em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-132"><span class="mi"
id="MathJax-Span-133" style="font-family:
MathJax_Main;">Δ</span><span class="mi"
id="MathJax-Span-134" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.045em;"></span></span><span
class="mo" id="MathJax-Span-135" style="font-family:
MathJax_Main; padding-left: 0.278em;">=</span><span
class="mo" id="MathJax-Span-136" style="font-family:
MathJax_Main; padding-left: 0.278em;">[</span><span
class="msubsup" id="MathJax-Span-137"><span
style="display: inline-block; position: relative;
width: 1.246em; height: 0px;"><span style="position:
absolute; clip: rect(3.059em, 1000.76em, 4.212em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-138"
style="font-family: MathJax_Math; font-style:
italic;">C<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.045em;"></span></span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.823em; left:
0.715em;"><span class="mi" id="MathJax-Span-139"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">S<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.023em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-140" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-141" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-142" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-143" style="font-family:
MathJax_Main; padding-left: 0.222em;">−</span><span
class="msubsup" id="MathJax-Span-144"
style="padding-left: 0.222em;"><span style="display:
inline-block; position: relative; width: 1.418em;
height: 0px;"><span style="position: absolute; clip:
rect(3.059em, 1000.76em, 4.212em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-145" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.045em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.715em;"><span class="mi" id="MathJax-Span-146"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">N<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.06em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-147" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-148" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-149" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-150" style="font-family:
MathJax_Main;">]</span><span class="texatom"
id="MathJax-Span-151"><span class="mrow"
id="MathJax-Span-152"><span class="mo"
id="MathJax-Span-153" style="font-family:
MathJax_Main;">/</span></span></span><span
class="msubsup" id="MathJax-Span-154"><span
style="display: inline-block; position: relative;
width: 1.418em; height: 0px;"><span style="position:
absolute; clip: rect(3.059em, 1000.76em, 4.212em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-155"
style="font-family: MathJax_Math; font-style:
italic;">C<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.045em;"></span></span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.715em;"><span class="mi" id="MathJax-Span-156"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">N<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.06em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-157" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-158" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-159" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-160" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span>, где <span
class="MathJax" id="MathJax-Element-13-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>S</mi></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-161" style="width: 1.14em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.278em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.076em, 1001.28em,
1.377em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-162"><span class="msubsup"
id="MathJax-Span-163"><span style="display:
inline-block; position: relative; width: 1.246em;
height: 0px;"><span style="position: absolute; clip:
rect(3.059em, 1000.76em, 4.212em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-164" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.045em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.823em; left:
0.715em;"><span class="mi" id="MathJax-Span-165"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">S<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.023em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.212em;
border-left: 0px solid; width: 0px; height: 0.895em;"></span></span></nobr></span>
и <span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>N</mi></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-166" style="width: 1.282em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.42em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.076em, 1001.42em,
1.357em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-167"><span class="msubsup"
id="MathJax-Span-168"><span style="display:
inline-block; position: relative; width: 1.418em;
height: 0px;"><span style="position: absolute; clip:
rect(3.059em, 1000.76em, 4.212em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-169" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.045em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.715em;"><span class="mi" id="MathJax-Span-170"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">N<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.06em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.194em;
border-left: 0px solid; width: 0px; height: 0.877em;"></span></span></nobr></span>
– теплоемкость сверхпроводящей и нормальной фаз. При низких T
теплоемкость гранул не зависит от их размера. При <span
class="MathJax" id="MathJax-Element-15-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>−</mo><mo>></mo><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-171" style="width: 3.555em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.977em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em, 1003.97em,
2.568em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-172"><span class="mi"
id="MathJax-Span-173" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-174" style="font-family:
MathJax_Main;">−</span><span class="mo"
id="MathJax-Span-175" style="font-family:
MathJax_Main; padding-left: 0.278em;">></span><span
class="mi" id="MathJax-Span-176" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">T<span style="display: inline-block;
overflow: hidden; height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-177" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.135em;
border-left: 0px solid; width: 0px; height: 0.793em;"></span></span></nobr></span>
<span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mi>C</mi><mo
stretchy="false">(</mo><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo
stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>2</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>π</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-178" style="width: 8.526em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 9.659em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1009.56em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-179"><span class="mi"
id="MathJax-Span-180" style="font-family:
MathJax_Main;">Δ</span><span class="mi"
id="MathJax-Span-181" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.045em;"></span></span><span
class="mo" id="MathJax-Span-182" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-183" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-184" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-185" style="font-family:
MathJax_Main;">)</span><span class="mo"
id="MathJax-Span-186" style="font-family:
MathJax_Main; padding-left: 0.278em;">=</span><span
class="mi" id="MathJax-Span-187" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">A</span><span class="mo"
id="MathJax-Span-188" style="font-family:
MathJax_Main;">(</span><span class="mn"
id="MathJax-Span-189" style="font-family:
MathJax_Main;">1</span><span class="mo"
id="MathJax-Span-190" style="font-family:
MathJax_Main; padding-left: 0.222em;">−</span><span
class="mn" id="MathJax-Span-191" style="font-family:
MathJax_Main; padding-left: 0.222em;">2</span><span
class="texatom" id="MathJax-Span-192"><span
class="mrow" id="MathJax-Span-193"><span class="mo"
id="MathJax-Span-194" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mi" id="MathJax-Span-195" style="font-family:
MathJax_Math; font-style: italic;">π<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.003em;"></span></span><span
class="mo" id="MathJax-Span-196" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span>, где <span
class="MathJax" id="MathJax-Element-17-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-197" style="width: 0.714em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.781em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.273em, 1000.76em,
2.415em, -1000em); top: -2.202em; left: 0em;"><span
class="mrow" id="MathJax-Span-198"><span class="mi"
id="MathJax-Span-199" style="font-family:
MathJax_Math; font-style: italic;">A</span></span><span
style="display: inline-block; width: 0px; height:
2.202em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.063em;
border-left: 0px solid; width: 0px; height: 0.755em;"></span></span></nobr></span>
– скачок теплоемкости объемного образца. В области <span
class="MathJax" id="MathJax-Element-18-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>></mo><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-200" style="width: 2.844em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.196em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em, 1003.19em,
2.526em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-201"><span class="mi"
id="MathJax-Span-202" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-203" style="font-family:
MathJax_Main; padding-left: 0.278em;">></span><span
class="mi" id="MathJax-Span-204" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">T<span style="display: inline-block;
overflow: hidden; height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-205" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.098em;
border-left: 0px solid; width: 0px; height: 0.756em;"></span></span></nobr></span>
<span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mi>C</mi><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-206" style="width: 2.702em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.054em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1002.96em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-207"><span class="mi"
id="MathJax-Span-208" style="font-family:
MathJax_Main;">Δ</span><span class="mi"
id="MathJax-Span-209" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.045em;"></span></span><span
class="mo" id="MathJax-Span-210" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-211" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-212" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span> зависит
только от параметра <span class="MathJax"
id="MathJax-Element-20-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>l</mi><mi>n</mi><mo
stretchy="false">(</mo><mi>T</mi><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>T</mi><mi>c</mi><mo
stretchy="false">)</mo><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msup><mi>δ</mi><mrow
class="MJX-TeXAtom-ORD"><mn>1</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-213" style="width: 7.035em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 7.955em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.166em, 1007.96em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-214"><span class="mi"
id="MathJax-Span-215" style="font-family:
MathJax_Math; font-style: italic;">z<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.003em;"></span></span><span
class="mo" id="MathJax-Span-216" style="font-family:
MathJax_Main; padding-left: 0.278em;">=</span><span
class="mi" id="MathJax-Span-217" style="font-family:
MathJax_Math; font-style: italic; padding-left:
0.278em;">l</span><span class="mi"
id="MathJax-Span-218" style="font-family:
MathJax_Math; font-style: italic;">n</span><span
class="mo" id="MathJax-Span-219" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-220" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="texatom" id="MathJax-Span-221"><span
class="mrow" id="MathJax-Span-222"><span class="mo"
id="MathJax-Span-223" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mi" id="MathJax-Span-224" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-225" style="font-family:
MathJax_Math; font-style: italic;">c</span><span
class="mo" id="MathJax-Span-226" style="font-family:
MathJax_Main;">)</span><span class="texatom"
id="MathJax-Span-227"><span class="mrow"
id="MathJax-Span-228"><span class="mo"
id="MathJax-Span-229" style="font-family:
MathJax_Main;">/</span></span></span><span
class="msubsup" id="MathJax-Span-230"><span
style="display: inline-block; position: relative;
width: 1.639em; height: 0px;"><span style="position:
absolute; clip: rect(3.047em, 1000.45em, 4.2em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-231"
style="font-family: MathJax_Math; font-style:
italic;">δ<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.007em;"></span></span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.503em;"><span class="texatom"
id="MathJax-Span-232"><span class="mrow"
id="MathJax-Span-233"><span class="mn"
id="MathJax-Span-234" style="font-size:
70.7%; font-family: MathJax_Main;">1</span><span
class="texatom" id="MathJax-Span-235"><span
class="mrow" id="MathJax-Span-236"><span
class="mo" id="MathJax-Span-237"
style="font-size: 70.7%; font-family:
MathJax_Main;">/</span></span></span><span
class="mn" id="MathJax-Span-238"
style="font-size: 70.7%; font-family:
MathJax_Main;">2</span></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.283em;
border-left: 0px solid; width: 0px; height: 1.131em;"></span></span></nobr></span>;
при <span class="MathJax" id="MathJax-Element-21-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>></mo><mn>1</mn></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-239" style="width: 1.992em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.273em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.394em, 1002.2em,
2.526em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-240"><span class="mi"
id="MathJax-Span-241" style="font-family:
MathJax_Math; font-style: italic;">z<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.003em;"></span></span><span
class="mo" id="MathJax-Span-242" style="font-family:
MathJax_Main; padding-left: 0.278em;">></span><span
class="mn" id="MathJax-Span-243" style="font-family:
MathJax_Main; padding-left: 0.278em;">1</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.098em;
border-left: 0px solid; width: 0px; height: 0.746em;"></span></span></nobr></span>
<span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mi>C</mi><mo>=</mo><mn>3</mn><mrow
class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mo
stretchy="false">(</mo><mn>2</mn><msup><mi>π</mi><mn>2</mn></msup><msup><mi>z</mi><mn>2</mn></msup><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-244" style="width: 6.325em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 7.173em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.226em, 1007.08em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-245"><span class="mi"
id="MathJax-Span-246" style="font-family:
MathJax_Main;">Δ</span><span class="mi"
id="MathJax-Span-247" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.045em;"></span></span><span
class="mo" id="MathJax-Span-248" style="font-family:
MathJax_Main; padding-left: 0.278em;">=</span><span
class="mn" id="MathJax-Span-249" style="font-family:
MathJax_Main; padding-left: 0.278em;">3</span><span
class="texatom" id="MathJax-Span-250"><span
class="mrow" id="MathJax-Span-251"><span class="mo"
id="MathJax-Span-252" style="font-family:
MathJax_Main;">/</span></span></span><span
class="mo" id="MathJax-Span-253" style="font-family:
MathJax_Main;">(</span><span class="mn"
id="MathJax-Span-254" style="font-family:
MathJax_Main;">2</span><span class="msubsup"
id="MathJax-Span-255"><span style="display:
inline-block; position: relative; width: 1.052em;
height: 0px;"><span style="position: absolute; clip:
rect(3.333em, 1000.57em, 4.201em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-256" style="font-family:
MathJax_Math; font-style: italic;">π<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.003em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.624em;"><span class="mn" id="MathJax-Span-257"
style="font-size: 70.7%; font-family:
MathJax_Main;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="msubsup" id="MathJax-Span-258"><span
style="display: inline-block; position: relative;
width: 0.947em; height: 0px;"><span style="position:
absolute; clip: rect(3.322em, 1000.47em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-259"
style="font-family: MathJax_Math; font-style:
italic;">z<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.003em;"></span></span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.519em;"><span class="mn" id="MathJax-Span-260"
style="font-size: 70.7%; font-family:
MathJax_Main;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-261" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.079em;"></span></span></nobr></span>.
Медленная логарифмическая зависимость <span class="MathJax"
id="MathJax-Element-23-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi
mathvariant="normal">Δ</mi><mi>C</mi><mo
stretchy="false">(</mo><mi>T</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-262" style="width: 2.702em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.054em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1002.96em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-263"><span class="mi"
id="MathJax-Span-264" style="font-family:
MathJax_Main;">Δ</span><span class="mi"
id="MathJax-Span-265" style="font-family:
MathJax_Math; font-style: italic;">C<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.045em;"></span></span><span
class="mo" id="MathJax-Span-266" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-267" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-268" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span> может
быть экспериментально обнаружена при <span class="MathJax"
id="MathJax-Element-24-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>∼</mo><mn>2</mn><mi>T</mi><mi>c</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-269" style="width: 3.271em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.693em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.383em, 1003.69em,
2.497em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-270"><span class="mi"
id="MathJax-Span-271" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mo" id="MathJax-Span-272" style="font-family:
MathJax_Main; padding-left: 0.278em;">∼</span><span
class="mn" id="MathJax-Span-273" style="font-family:
MathJax_Main; padding-left: 0.278em;">2</span><span
class="mi" id="MathJax-Span-274" style="font-family:
MathJax_Math; font-style: italic;">T<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.12em;"></span></span><span
class="mi" id="MathJax-Span-275" style="font-family:
MathJax_Math; font-style: italic;">c</span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.072em;
border-left: 0px solid; width: 0px; height: 0.73em;"></span></span></nobr></span>.
<div class="abstract tex"><br>
<br>
</div>
Доклады будут сопровождаться онлайн-трансляцией в Zoom. ID и пароль
те же, что и для предыдущих трансляций:<a
class="moz-txt-link-freetext"
href="https://zoom.us/j/93947383544?pwd=QnU4VGVuYVBlSlJSeHBkTlp4QW9HZz09"><br>
</a><a class="moz-txt-link-freetext"
href="https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09">https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09</a><br>
Meeting ID: 968 9936 4518<br>
Пароль: 250319<br>
<br>
<br>
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