Emergence of correlations in the process of thermalization of interacting bosons

Abstract

We address the question of the relevance of thermalization to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons. Specifically, we study how, in the process of thermalization, the correlations between occupation numbers increase in time resulting in the emergence of the Bose-Einstein distribution. We show, both analytically and numerically, that before saturation the two-point correlation function increases quadratically in time. This time dependence is at variance with the exponential increase of the number of principal components of the wave function, recently discovered and explained in Ref.\cite{BIS18}. We also demonstrate that the out-of-time-order correlator (OTOC) increases algebraically in time but not exponentially as predicted in many publications. Our results, that can be confirmed experimentally in traps with interacting bosons, may be also relevant to the problem of black hole scrambling.

10 pages

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Cited by in corpus (14)

• Gauging classical and quantum integrability through out-of-time ordered correlators
• Scrambling and Complexity in Phase Space
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• OTOC, complexity and entropy in bi-partite systems
• Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
• Work statistics for sudden quenches in interacting quantum many-body systems
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Quantum Lyapunov exponent in dissipative systems
• Modelling equilibration of local many-body quantum systems by random graph ensembles
• Relevant OTOC operators: footprints of the classical dynamics
• Threshold coupling strength for equilibration between small systems
• Two species $k$-body embedded Gaussian unitary ensembles: $q$-normal form of the eigenvalue density
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos