Positive quantum Lyapunov exponents in classically regular systems.

Date

2019-09-09

Authors

Pilatowsky-Cameo, Saúl
Chávez-Carlos, Jorge
Bastarrachea-Magnani, Miguel A.
Stránský, Pavel
Lerma-Hernández, Sergio
Hirsch, Jorge G.
Santos, Lea F.

Journal Title

Journal ISSN

Volume Title

Publisher

arXiv.org

Abstract

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of the quantum evolution of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated for different chaotic systems. In this work, however, we show that OTOCs can grow exponentially also in regular models. This happens when the classical system exhibits isolated unstable points. In the quantum domain, these points become finite regions, where the quantum Lyapunov exponents are throughout positive. Our results are illustrated for the Lipkin-Meshkov-Glick (LMG) model, which is integrable, and for the Dicke Hamiltonian in the regular regime. These models are currently realized in various experimental setups, such as those with cold atoms and ion traps.

Description

Scholarly article (pre-print)

Keywords

Statistical Mechanics (cond-mat.stat-mech), Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Positive quantum Lyapunov exponents, chaos

Citation

Pilatowsky-Cameo, Saúl ; Chávez-Carlos, Jorge ; Bastarrachea-Magnani, Miguel A. ; Stránský, Pavel ; Lerma-Hernández, Sergio ; Santos, Lea F. ; Hirsch, Jorge G. (9 Sep 2019). Positive quantum Lyapunov exponents in classically regular systems. Statistical Mechanics (cond-mat.stat-mech). arXiv.org. arXiv:1909.02578v2.