Quantum Chirikov criterion: Two particles in a box as a toy model for a quantum gas
Dmitry Yampolsky, N. L. Harshman, Vanja Dunjko, Zaijong Hwang, Maxim Olshanii
SciPost Phys. 12, 035 (2022) · published 24 January 2022
- doi: 10.21468/SciPostPhys.12.1.035
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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Dmitry Yampolsky,
- 2 Nathan Harshman,
- 1 Vanja Dunjko,
- 1 Zaijong Hwang,
- 1 Maxim Olshanii
- National Science Foundation [NSF]
- United States - Israel Binational Science Foundation (through Organization: United States-Israel Binational Science Foundation [BSF])