Thermofield dynamics: Quantum Chaos versus Decoherence

Abstract

Quantum chaos imposes universal spectral signatures that govern the thermofield dynamics of a many-body system in isolation. The fidelity between the initial and time-evolving thermofield double states exhibits as a function of time a decay, dip, ramp and plateau. Sources of decoherence give rise to a nonunitary evolution and result in information loss. Energy dephasing gradually suppresses quantum noise fluctuations and the dip associated with spectral correlations. Decoherence further delays the appearance of the dip and shortens the span of the linear ramp associated with chaotic behavior. The interplay between signatures of quantum chaos and information loss is determined by the competition among the decoherence, dip and plateau characteristic times, as demoonstrated in the stochastic Sachdev-Ye-Kitaev model.

BROTOCs and Quantum Information Scrambling at Finite Temperature

“…1 we plot the Bessel function form along with the numerical estimate of the long-time average of the connected BROTOC for the GUE, obtained by averaging (numerically generated) GUE Hamiltonians for d = 100. 1 We have implicitly assumed here that the ensemble averaging and the large-d limits commute, see [20,93] for a discussion.…”