Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas

Abstract

We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter represented by two equal mass particles. To that system, we apply a quantum generalization of Chirikov's criterion for the onset of chaos, i.e. the criterion of overlapping resonances. There, classical nonlinear resonances translate almost verbatim to the quantum language. Quantum mechanics intervenes at a later stage: the resonances occupying less than one Hamiltonian eigenstate are excluded from the chaos criterion. Resonances appear as contiguous patches of low purity unperturbed eigenstates, separated by the groups of undestroyed states -- the quantum analogues of the classical KAM tori.

arXiv commentVersion 3: includes more information about KAM, Chirikov condition, and thermalization; revised introduction, section 2 and conclusion; 16 pages, 6 figures; Version 4: typos corrected and acknowledgements updated

References in corpus (8)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Non-ergodicity and localization of invariant measure for two colliding masses
• One particle in a box: the simplest model for a Fermigas in the unitary limit
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures

Cited by in corpus (2)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Quantum chaos in interacting Bose-Bose mixtures