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<div class="moz-cite-prefix">В разосланном несколько минут назад
письме была допущена ошибка:<br>
<br>
В пятницу 6 октября будет заслушано 2 доклада одного и того же
докладчика:<br>
<br>
11:30 Коллоквиум<br>
Sergej Flach (Institute for Basic Science, Republic of Korea)<br>
<b>Dynamical Glass - en route from KAM and FPUT to MBL</b><br>
<br>
Classical many body interacting systems are typically chaotic
(nonzero Lyapunov exponents) and their microcanonical dynamics
ensures that time averages and phase space averages are identical
(ergodic hypothesis). In proximity to an integrable limit the
long- or short-range properties of the network of nonintegrable
action space perturbations define the finite time relaxation
properties of the system towards Gibbs equilibrium. I will touch
upon few analytical results including the KAM theorem, and review
a number of computational studies which originate from the
pioneering work of Enrico Fermi, John Pasta, Stanislaw Ulam and
Mary Tsingou. I will then focus on short range networks which lead
to a dynamical glass (DG), using a classical Josephson junction
chain in the limit of large energy densities or small Josephson
energies. Close to these limits the Josephson coupling between the
superconducting grains induces a short-range nonintegrable network
in the corresponding action space. I will introduce a set of
quantitative measures which lead to the Lyapunov time TΛ, the
ergodization time TE, and to a diffusion constant D. In the DG the
system fragments into large patches of nonresonant ’integrable’
grains of size l separated by triplets of resonant chaotic
patches, all surviving over large times. TE sets the time scale
for chaotic dynamics in the triplets. Contrary, TE ≈ l2/D is the
much larger time scale of slow diffusion of chaotic triplets. The
DG is a generic feature of weakly non-integrable systems with a
short range coupling network in action space, and expected to be
related to nonergodic quantum metallic states of quantum many-body
<br>
<br>
16:00 Семинар <br>
<span style="background-color: rgb(255, 255, 255);" class="">
<div class="">Sergej Flach<br>
<b><span style="background-color: rgb(255, 255, 255);"
class="">The wonderful world of flatbands</span></b></div>
<div class=""><span style="background-color: rgb(255, 255,
255);" class=""><br class="">
</span></div>
Certain lattice wave systems in translationally invariant
settings have one or more spectral bands that are strictly flat
or independent of momentum in the tight binding approximation,
arising from either internal symmetries or fine-tuned coupling.
These flat bands display remarkable strongly interacting phases
of matter. Originally considered as a theoretical convenience
useful for obtaining exact analytical solutions of
ferromagnetism, flat bands have now been observed in a variety
of settings, ranging from electronic systems to ultracold atomic
gases and photonic devices. I will review the design and
implementation of flat bands and chart future directions of this
exciting field. In particular I will focus on the field of
photonic lattices. Flatband photonic lattices consist of arrays
of coupled waveguides or resonators where the peculiar lattice
geometry results in at least one completely flat or
dispersionless band in its photonic band structure. Although
bearing a strong resemblance to structural slow light, this
independent research direction is instead inspired by analogies
with “frustrated” condensed matter systems. In this talk, I will
critically analyze the research carried out to date, discuss how
this exotic physics may lead to novel photonic device
applications, and chart promising future directions in theory
and experiment.</span><span style="background-color: rgb(255,
255, 255);" class=""><br class="">
</span><br>
<br>
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