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Уважаемые сотрудники ИТФ,<br>
<br>
На заседании Ученого совета ИТФ в пятницу 26 октября будут заслушаны
2 доклада:<br>
<br>
1) A. S. Ioselevich, <u>N. S. Peshcherenko</u><br>
<b>Non-Born effects in scattering of electrons in clean
quasi-one-dimensional conductors</b><br>
<br>
<div class="abstract tex">
Quasi-one-dimensional systems demonstrate Van Hove singularities
in the density of states <span class="MathJax"
id="MathJax-Element-1-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ν</mi><mi>F</mi></msub></math>"
role="presentation"><nobr><span class="math" id="MathJax-Span-1"
style="width: 0.927em; display: inline-block;"><span
style="display: inline-block; position: relative; width:
0.994em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.34em, 1000.99em,
1.357em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-2"><span class="msubsup"
id="MathJax-Span-3"><span style="display:
inline-block; position: relative; width: 1.001em;
height: 0px;"><span style="position: absolute;
clip: rect(3.323em, 1000.46em, 4.208em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-4"
style="font-family: STIXGeneral; font-style:
italic;">ν</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.47em;"><span class="mi" id="MathJax-Span-5"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">F<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.024em;"></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: 0.645em;"></span></span></nobr></span>
and the resistivity <span class="MathJax"
id="MathJax-Element-2-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math>"
role="presentation"><nobr><span class="math" id="MathJax-Span-6"
style="width: 0.43em; display: inline-block;"><span
style="display: inline-block; position: relative; width:
0.497em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.903em,
1000.46em, 2.975em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-7"><span class="mi"
id="MathJax-Span-8" style="font-family: STIXGeneral;
font-style: italic;">ρ</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.243em;
border-left: 0px solid; width: 0px; height: 0.693em;"></span></span></nobr></span>,
occurring when the Fermi level <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>E</mi></math>"
role="presentation"><nobr><span class="math" id="MathJax-Span-9"
style="width: 0.572em; display: inline-block;"><span
style="display: inline-block; position: relative; width:
0.639em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.691em,
1000.64em, 2.77em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-10"><span class="mi"
id="MathJax-Span-11" style="font-family:
STIXGeneral; font-style: italic;">E<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.023em;"></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.063em;
border-left: 0px solid; width: 0px; height: 0.7em;"></span></span></nobr></span>
crosses a bottom <span class="MathJax"
id="MathJax-Element-4-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>N</mi></msub></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-12" style="width: 1.069em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.207em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.128em,
1001.21em, 1.368em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-13"><span
class="msubsup" id="MathJax-Span-14"><span
style="display: inline-block; position: relative;
width: 1.2em; height: 0px;"><span style="position:
absolute; clip: rect(3.111em, 1000.63em, 4.19em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-15"
style="font-family: STIXGeneral; font-style:
italic;">E<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
style="position: absolute; top: -3.827em; left:
0.611em;"><span class="mi" id="MathJax-Span-16"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">N<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.042em;"></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: -0.204em;
border-left: 0px solid; width: 0px; height: 0.841em;"></span></span></nobr></span>
of some subband of transverse quantization. We demonstrate that
the character of smearing of the singularities crucially depends
on the concentration of impurities. There is a crossover
concentration <span class="MathJax" id="MathJax-Element-5-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mi>c</mi></msub><mo>∝</mo><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>λ</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-17" style="width: 2.915em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.267em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.654em,
1003.14em, 2.959em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-18"><span
class="msubsup" id="MathJax-Span-19"><span
style="display: inline-block; position: relative;
width: 0.889em; height: 0px;"><span
style="position: absolute; clip: rect(3.323em,
1000.47em, 4.199em, -1000em); top: -3.977em;
left: 0em;"><span class="mi"
id="MathJax-Span-20" style="font-family:
STIXGeneral; font-style: italic;">n</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.5em;"><span class="mi" id="MathJax-Span-21"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">c</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-22" style="font-family:
STIXGeneral; padding-left: 0.313em;">∝</span><span
class="texatom" id="MathJax-Span-23"
style="padding-left: 0.313em;"><span class="mrow"
id="MathJax-Span-24"><span class="mo"
id="MathJax-Span-25" style="font-family:
STIXVariants;">|</span></span></span><span
class="mi" id="MathJax-Span-26" style="font-family:
STIXGeneral; font-style: italic;">λ</span><span
class="texatom" id="MathJax-Span-27"><span
class="mrow" id="MathJax-Span-28"><span class="mo"
id="MathJax-Span-29" style="font-family:
STIXVariants;">|</span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.229em;
border-left: 0px solid; width: 0px; height: 0.899em;"></span></span></nobr></span>,
<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>λ</mi><mo>≪</mo><mn>1</mn></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-30" style="width: 2.205em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.486em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.666em,
1002.38em, 2.796em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-31"><span class="mi"
id="MathJax-Span-32" style="font-family:
STIXGeneral; font-style: italic;">λ</span><span
class="mo" id="MathJax-Span-33" style="font-family:
STIXGeneral; padding-left: 0.313em;">≪</span><span
class="mn" id="MathJax-Span-34" style="font-family:
STIXGeneral; padding-left: 0.313em;">1</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.085em;
border-left: 0px solid; width: 0px; height: 0.745em;"></span></span></nobr></span>
being the dimensionless amplitude of scattering. For <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>n</mi><mo>≫</mo><msub><mi>n</mi><mi>c</mi></msub></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-35" style="width: 2.56em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.912em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.812em,
1002.91em, 2.928em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-36"><span class="mi"
id="MathJax-Span-37" style="font-family:
STIXGeneral; font-style: italic;">n</span><span
class="mo" id="MathJax-Span-38" style="font-family:
STIXGeneral; padding-left: 0.313em;">≫</span><span
class="msubsup" id="MathJax-Span-39"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.889em;
height: 0px;"><span style="position: absolute;
clip: rect(3.323em, 1000.47em, 4.199em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-40"
style="font-family: STIXGeneral; font-style:
italic;">n</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.5em;"><span class="mi" id="MathJax-Span-41"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">c</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.201em;
border-left: 0px solid; width: 0px; height: 0.732em;"></span></span></nobr></span>
the singularities are simply rounded at <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>ε</mi><mo>≡</mo><mi>E</mi><mo>−</mo><msub><mi>E</mi><mi>N</mi></msub><mo>∼</mo><msup><mi>τ</mi><mrow
class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-42" style="width: 6.609em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 7.457em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.503em,
1007.46em, 2.93em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-43"><span class="mi"
id="MathJax-Span-44" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="mo" id="MathJax-Span-45" style="font-family:
STIXGeneral; padding-left: 0.313em;">≡</span><span
class="mi" id="MathJax-Span-46" style="font-family:
STIXGeneral; font-style: italic; padding-left:
0.313em;">E<span style="display: inline-block;
overflow: hidden; height: 1px; width: 0.023em;"></span></span><span
class="mo" id="MathJax-Span-47" style="font-family:
STIXGeneral; padding-left: 0.25em;">−</span><span
class="msubsup" id="MathJax-Span-48"
style="padding-left: 0.25em;"><span style="display:
inline-block; position: relative; width: 1.2em;
height: 0px;"><span style="position: absolute;
clip: rect(3.111em, 1000.63em, 4.19em, -1000em);
top: -3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-49" style="font-family:
STIXGeneral; font-style: italic;">E<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
style="position: absolute; top: -3.827em; left:
0.611em;"><span class="mi" id="MathJax-Span-50"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">N<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.042em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-51" style="font-family:
STIXGeneral; padding-left: 0.313em;">∼</span><span
class="msubsup" id="MathJax-Span-52"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 1.394em;
height: 0px;"><span style="position: absolute;
clip: rect(3.336em, 1000.43em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-53"
style="font-family: STIXGeneral; font-style:
italic;">τ<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.016em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.481em;"><span class="texatom"
id="MathJax-Span-54"><span class="mrow"
id="MathJax-Span-55"><span class="mo"
id="MathJax-Span-56" style="font-size:
70.7%; font-family: STIXGeneral;">−</span><span
class="mn" id="MathJax-Span-57"
style="font-size: 70.7%; font-family:
STIXGeneral;">1</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:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.204em;
border-left: 0px solid; width: 0px; height: 1.006em;"></span></span></nobr></span>
– the Born scattering rate.
For <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>n</mi><mo>≪</mo><msub><mi>n</mi><mi>c</mi></msub></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-58" style="width: 2.56em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.912em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.812em,
1002.91em, 2.928em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-59"><span class="mi"
id="MathJax-Span-60" style="font-family:
STIXGeneral; font-style: italic;">n</span><span
class="mo" id="MathJax-Span-61" style="font-family:
STIXGeneral; padding-left: 0.313em;">≪</span><span
class="msubsup" id="MathJax-Span-62"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.889em;
height: 0px;"><span style="position: absolute;
clip: rect(3.323em, 1000.47em, 4.199em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-63"
style="font-family: STIXGeneral; font-style:
italic;">n</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.5em;"><span class="mi" id="MathJax-Span-64"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">c</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.201em;
border-left: 0px solid; width: 0px; height: 0.732em;"></span></span></nobr></span>
the non-Born effects in scattering become essential, despite <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>λ</mi><mo>≪</mo><mn>1</mn></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-65" style="width: 2.205em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.486em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.666em,
1002.38em, 2.796em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-66"><span class="mi"
id="MathJax-Span-67" style="font-family:
STIXGeneral; font-style: italic;">λ</span><span
class="mo" id="MathJax-Span-68" style="font-family:
STIXGeneral; padding-left: 0.313em;">≪</span><span
class="mn" id="MathJax-Span-69" style="font-family:
STIXGeneral; padding-left: 0.313em;">1</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.085em;
border-left: 0px solid; width: 0px; height: 0.745em;"></span></span></nobr></span>.
The peak of the resistivity is split: for <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>ε</mi><mo>></mo><mn>0</mn></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-70" 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(1.668em,
1002.25em, 2.794em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-71"><span class="mi"
id="MathJax-Span-72" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="mo" id="MathJax-Span-73" style="font-family:
STIXGeneral; padding-left: 0.313em;">></span><span
class="mn" id="MathJax-Span-74" style="font-family:
STIXGeneral; padding-left: 0.313em;">0</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.084em;
border-left: 0px solid; width: 0px; height: 0.741em;"></span></span></nobr></span>
there is a broad maximum at <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>ε</mi><mo>∝</mo><msup><mi>λ</mi><mn>2</mn></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-75" style="width: 2.347em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.628em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.503em,
1002.63em, 2.786em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-76"><span class="mi"
id="MathJax-Span-77" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="mo" id="MathJax-Span-78" style="font-family:
STIXGeneral; padding-left: 0.313em;">∝</span><span
class="msubsup" id="MathJax-Span-79"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.887em;
height: 0px;"><span style="position: absolute;
clip: rect(3.086em, 1000.43em, 4.206em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-80"
style="font-family: STIXGeneral; font-style:
italic;">λ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.458em;"><span class="mn" id="MathJax-Span-81"
style="font-size: 70.7%; font-family:
STIXGeneral;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.077em;
border-left: 0px solid; width: 0px; height: 0.879em;"></span></span></nobr></span>.
For <span class="MathJax" id="MathJax-Element-13-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi><mo><</mo><mn>0</mn></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-82" 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(1.668em,
1002.25em, 2.794em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-83"><span class="mi"
id="MathJax-Span-84" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="mo" id="MathJax-Span-85" style="font-family:
STIXGeneral; padding-left: 0.313em;"><</span><span
class="mn" id="MathJax-Span-86" style="font-family:
STIXGeneral; padding-left: 0.313em;">0</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.084em;
border-left: 0px solid; width: 0px; height: 0.741em;"></span></span></nobr></span>
there is a deep minimum at <span class="MathJax"
id="MathJax-Element-14-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>ε</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mo>∝</mo><msup><mi>n</mi><mn>2</mn></msup><mo>≪</mo><msup><mi>λ</mi><mn>2</mn></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-87" style="width: 5.117em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 5.753em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.503em,
1005.75em, 2.959em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-88"><span
class="texatom" id="MathJax-Span-89"><span
class="mrow" id="MathJax-Span-90"><span class="mo"
id="MathJax-Span-91" style="font-family:
STIXVariants;">|</span></span></span><span
class="mi" id="MathJax-Span-92" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="texatom" id="MathJax-Span-93"><span
class="mrow" id="MathJax-Span-94"><span class="mo"
id="MathJax-Span-95" style="font-family:
STIXVariants;">|</span></span></span><span
class="mo" id="MathJax-Span-96" style="font-family:
STIXGeneral; padding-left: 0.313em;">∝</span><span
class="msubsup" id="MathJax-Span-97"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.929em;
height: 0px;"><span style="position: absolute;
clip: rect(3.323em, 1000.47em, 4.199em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-98"
style="font-family: STIXGeneral; font-style:
italic;">n</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.5em;"><span class="mn" id="MathJax-Span-99"
style="font-size: 70.7%; font-family:
STIXGeneral;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-100" style="font-family:
STIXGeneral; padding-left: 0.313em;">≪</span><span
class="msubsup" id="MathJax-Span-101"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.887em;
height: 0px;"><span style="position: absolute;
clip: rect(3.086em, 1000.43em, 4.206em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-102"
style="font-family: STIXGeneral; font-style:
italic;">λ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.458em;"><span class="mn" id="MathJax-Span-103"
style="font-size: 70.7%; font-family:
STIXGeneral;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.229em;
border-left: 0px solid; width: 0px; height: 1.031em;"></span></span></nobr></span>.
The behaviour of <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>ρ</mi></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-104" style="width: 0.43em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.497em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.903em,
1000.46em, 2.975em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-105"><span class="mi"
id="MathJax-Span-106" style="font-family:
STIXGeneral; font-style: italic;">ρ</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.243em;
border-left: 0px solid; width: 0px; height: 0.693em;"></span></span></nobr></span>
below the minimum depends on the sign of <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>λ</mi></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-107" style="width: 0.43em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.426em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.666em, 1000.4em,
2.786em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-108"><span class="mi"
id="MathJax-Span-109" style="font-family:
STIXGeneral; font-style: italic;">λ</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.077em;
border-left: 0px solid; width: 0px; height: 0.736em;"></span></span></nobr></span>.
In case of repulsion <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>ρ</mi></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-110" style="width: 0.43em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.497em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.903em,
1000.46em, 2.975em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-111"><span class="mi"
id="MathJax-Span-112" style="font-family:
STIXGeneral; font-style: italic;">ρ</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.243em;
border-left: 0px solid; width: 0px; height: 0.693em;"></span></span></nobr></span>
monotonically grows with <span class="MathJax"
id="MathJax-Element-18-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>ε</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-113" style="width: 0.927em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.065em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.654em,
1000.94em, 2.959em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-114"><span
class="texatom" id="MathJax-Span-115"><span
class="mrow" id="MathJax-Span-116"><span
class="mo" id="MathJax-Span-117"
style="font-family: STIXVariants;">|</span></span></span><span
class="mi" id="MathJax-Span-118" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="texatom" id="MathJax-Span-119"><span
class="mrow" id="MathJax-Span-120"><span
class="mo" id="MathJax-Span-121"
style="font-family: STIXVariants;">|</span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.229em;
border-left: 0px solid; width: 0px; height: 0.899em;"></span></span></nobr></span>
and saturates for <span class="MathJax"
id="MathJax-Element-19-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>ε</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mo>≫</mo><msup><mi>λ</mi><mn>2</mn></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-122" style="width: 3.129em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.551em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.503em,
1003.55em, 2.959em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-123"><span
class="texatom" id="MathJax-Span-124"><span
class="mrow" id="MathJax-Span-125"><span
class="mo" id="MathJax-Span-126"
style="font-family: STIXVariants;">|</span></span></span><span
class="mi" id="MathJax-Span-127" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="texatom" id="MathJax-Span-128"><span
class="mrow" id="MathJax-Span-129"><span
class="mo" id="MathJax-Span-130"
style="font-family: STIXVariants;">|</span></span></span><span
class="mo" id="MathJax-Span-131" style="font-family:
STIXGeneral; padding-left: 0.313em;">≫</span><span
class="msubsup" id="MathJax-Span-132"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.887em;
height: 0px;"><span style="position: absolute;
clip: rect(3.086em, 1000.43em, 4.206em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-133"
style="font-family: STIXGeneral; font-style:
italic;">λ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.458em;"><span class="mn" id="MathJax-Span-134"
style="font-size: 70.7%; font-family:
STIXGeneral;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.229em;
border-left: 0px solid; width: 0px; height: 1.031em;"></span></span></nobr></span>.
In case of attraction <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>ρ</mi></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-135" style="width: 0.43em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.497em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.903em,
1000.46em, 2.975em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-136"><span class="mi"
id="MathJax-Span-137" style="font-family:
STIXGeneral; font-style: italic;">ρ</span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.243em;
border-left: 0px solid; width: 0px; height: 0.693em;"></span></span></nobr></span>
has sharp maximum at <span class="MathJax"
id="MathJax-Element-21-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>ε</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mo>∝</mo><msup><mi>λ</mi><mn>2</mn></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-138" style="width: 2.915em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.267em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.503em,
1003.27em, 2.959em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-139"><span
class="texatom" id="MathJax-Span-140"><span
class="mrow" id="MathJax-Span-141"><span
class="mo" id="MathJax-Span-142"
style="font-family: STIXVariants;">|</span></span></span><span
class="mi" id="MathJax-Span-143" style="font-family:
STIXGeneral; font-style: italic;">ε</span><span
class="texatom" id="MathJax-Span-144"><span
class="mrow" id="MathJax-Span-145"><span
class="mo" id="MathJax-Span-146"
style="font-family: STIXVariants;">|</span></span></span><span
class="mo" id="MathJax-Span-147" style="font-family:
STIXGeneral; padding-left: 0.313em;">∝</span><span
class="msubsup" id="MathJax-Span-148"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 0.887em;
height: 0px;"><span style="position: absolute;
clip: rect(3.086em, 1000.43em, 4.206em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-149"
style="font-family: STIXGeneral; font-style:
italic;">λ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -4.34em; left:
0.458em;"><span class="mn" id="MathJax-Span-150"
style="font-size: 70.7%; font-family:
STIXGeneral;">2</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.229em;
border-left: 0px solid; width: 0px; height: 1.031em;"></span></span></nobr></span>.
The latter feature is due to resonant scattering by
quasistationary bound states that inevitably arise just below the
bottom of each subband for any attracting impurity.
<span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mi>ε</mi><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><mo>∝</mo><msup><mi>λ</mi><mn>2</mn></msup></math>"
role="presentation"><nobr><span class="math"
id="MathJax-Span-138" style="width: 2.915em; display:
inline-block;"></span></nobr></span>
<br>
</div>
<br>
<br>
2) М. В. Фейгельман, В. Е. Кравцов
<br>
<b>Электрон-фононная теплопередача в изоляторах Андерсона</b><br>
<br>
<div class="abstract tex">
Построена теория электрон-фононной передачи энергии в изоляторах
Андерсона с большой длиной локализации. Показано, что
температурная зависимость этой величины прямо связана с
корреляционной функцией локальных плотностей состояний электронов.
Эта корреляционная функция содержит степенной рост на малых
энергиях вследствие фрактальной структуры волновых функций, а
также вследствие Моттовского механизма резонансных пар. Это
приводит к значительному усилению теплопередачи (по сравнению с
предсказаниями стандартной теории для грязных металлов) находится
в согласии с экспериментами на слабо диэлектрических пленках
оксида индия.
</div>
</body>
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