Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12202/6447
Title: Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system.
Authors: Santos, Lea F.
Bastarrachea-Magnani, M. A.
Lerma-Hernández, S.
Torres-Herrera, E.J.
Hirsch, J.G.
Villaseñor, D.
0000-0001-9400-2709
Keywords: Quantum statistical mechanics
quantum chaos
quantum quench
Dicke model
random matrix theory
Issue Date: 31-Jul-2019
Publisher: American Physical Society
Citation: Santos, Lea F., S. Lerma-Hernández, D. Villaseñor, M. A. Bastarrachea-Magnani, E. J. Torres-Herrera, and J. G. Hirsch. (2019). Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system. Physical Review E 100(1): 012218,
Series/Report no.: Physical Review E;100(1)
Abstract: Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the time scales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size.
Description: Research article, peer-reviewed. Open access.
URI: https://doi.org/10.1103/PhysRevE.100.012218
https://hdl.handle.net/20.500.12202/6447
ISSN: Print: 1539-3755 Electronic: 1550-2376
Appears in Collections:Stern College for Women -- Faculty Publications

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