[Landau ITP Seminars] Friday 06.09.2019

[Serge Krashakov]

В пятницу 6 сентября состоится коллоквиум:

Sergej Flach (Institute for Basic Science, Republic of Korea)
*Dynamical Glass - en route from KAM and FPUT to MBL*

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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