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В пятницу 6 сентября состоится коллоквиум:<br>
<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
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