Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12202/6449
Title: Thouless and relaxation time scales in many-body quantum systems.
Authors: Santos, Lea F.
Schiulaz, Mauro
Torres-Herrera, E. Jonathan
0000-0001-9400-2709
Keywords: Nonequilibrium statistical mechanics
Quantum statistical mechanics
Nonequilibrium systems
Quantum spin chains
quantum chaos
Nonequilibrium lattice models
Condensed Matter & Materials Physics
Statistical Physics
General Physics
Statistical Physics
quantum information
Metal-insulator transition
Issue Date: 28-May-2019
Publisher: American Physical Society
Citation: Santos, Lea F., Mauro Schiulaz, E Jonathan Torres-Herrera. (2019). Thouless and relaxation time scales in many-body quantum systems. Physical Review B 99(17): 174313.
Series/Report no.: Physical Review B;99(17)
Abstract: Abstract A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time scales can be analytically found by analyzing dynamical manifestations of spectral correlations. Using this approach, we show that the Thouless time tTh and the relaxation time tR increase exponentially with system size. We define tTh as the time at which the spread of the initial state in the many-body Hilbert space is complete and verify that it agrees with the inverse of the Thouless energy. tTh marks the point beyond which the dynamics acquire universal features, while relaxation happens later when the evolution reaches a stationary state. In chaotic systems, tTh≪tR, while for systems approaching a many-body localized phase, tTh→tR. Our analytical results for tTh and tR are obtained for the survival probability, which is a global quantity. We show numerically that the same time scales appear also in the evolution of the spin autocorrelation function, which is an experimental local observable. Our studies are carried out for realistic many-body quantum models. The results are compared with those for random matrices.
Description: Research article, peer-reviewed. Open Access.
URI: https://doi.org/10.1103/PhysRevB.99.174313
https://hdl.handle.net/20.500.12202/6449
ISSN: Print: 1098-0121 Electronic: 1550-235X
Appears in Collections:Stern College for Women -- Faculty Publications

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