Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization

TL;DR

This paper explores the complex dynamics of the Gross-Pitaevskii lattice, examining equilibrium and non-equilibrium behaviors, localization, chaos, and disorder effects, revealing new regimes and modifying existing theoretical frameworks.

Contribution

It provides new analytical expressions for thermodynamic properties, investigates localization and chaos in disordered GP lattices, and identifies novel phases like Lifshits glass and Lifshits phase.

Findings

Weakly non-ergodic equilibrium dynamics in ordered lattice

Disorder leads to Lifshits glass regime with dominant disorder effects

Strong chaos and slowed sub-diffusive spreading in disordered non-equilibrium dynamics

Abstract

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.