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 automatically 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.
Highlights
The celebrated Chirikov resonance-overlap criterion [1, 2] constitutes a simple analytic estimate for the onset of chaos in an integrable, deterministic Hamiltonian system weakly perturbed from integrability
What we found was that not all the resonances identified in the classical system are eligible to being included in the resonance overlap consideration
The quantum analogues of the classical resonances appear as contiguous patches of low purity unperturbed eigenstates
Summary
The celebrated Chirikov resonance-overlap criterion [1, 2] constitutes a simple analytic estimate for the onset of chaos in an integrable, deterministic Hamiltonian system weakly perturbed from integrability. This criterion can be considered as a heuristic and intuitive precursor to the rigorous Kolmogorov-Arnold-Moser (KAM) theorem [3,4,5] that serves the same purpose for classical systems. In [10,11,12,13], the authors study a quantum system with exactly two nonlinear resonances, while in [14, 15], the studied quantum system is truncated to two resonances Both systems consist of a single particle driven by an external field. In the quantum model the threshold for the emergence of chaos is restored even for a system with short-range interactions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
