Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics:
  Interactions, Disorder, and Thermalization   The interplay of fluctuations, ergodicity, and disorder in many-body
interacting systems has been striking attention for half a century, pivoted on
two celebrated phenomena: Anderson localization predicted in disordered media,
and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence observed in a nonlinear system.
The destruction of Anderson localization by nonlinearity and the recovery of
ergodicity after long enough computational times lead to more questions. This
thesis is devoted to contributing to the insight of the nonlinear system
dynamics in and out of equilibrium. Focusing mainly on the GP lattice, we
investigated elementary fluctuations close to zero temperature, localization
properties, the chaotic subdiffusive regimes, and the non-equipartition of
energy in non-Gibbs regime.
  Initially, we probe equilibrium dynamics in the ordered GP lattice and report
a weakly non-ergodic dynamics, and an ergodic part in the non-Gibbs phase that
implies the Gibbs distribution should be modified. Next, we include disorder in
GP lattice, and build analytical expressions for the thermodynamic properties
of the ground state, and identify a Lifshits glass regime where disorder
dominates over the interactions. In the opposite strong interaction regime, we
investigate the elementary excitations above the ground state and found a
dramatic increase of the localization length of Bogoliubov modes (BM) with
increasing particle density. Finally, we study non-equilibrium dynamics with
disordered GP lattice by performing novel energy and norm density resolved wave
packet spreading. In particular, we observed strong chaos spreading over
several decades, and identified a Lifshits phase which shows a significant
slowing down of sub-diffusive spreading.

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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph