Loschmidt echo and Poincaré recurrences of entanglement

Ermann, Leonardo; Frahm, Klaus M.; Shepelyansky, Dima L

doi:10.48550/arxiv.2201.02600

Cited by 1 publication

(1 citation statement)

References 44 publications

(85 reference statements)

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“…Only the so-called purity (a linearized version of the entanglement entropy) has allowed for a semiclassical study in first-quantized systems as carried out in [249,250]. Properties of entanglement of two (non)interacting particles in the quantum chaotic Chirikov standard map were very recently numerically considered in [251]. (e) Dual-unitary dynamics-In [53,63] a correspondence between unitary propagation in time and a non-unitary evolution in particle number in terms of an operator dual to the time evolution operator was established.…”

Section: Perspectivesmentioning

confidence: 99%

Semiclassical roots of universality in many-body quantum chaos

Richter

Urbina

Tomsovic

2022

J. Phys. A: Math. Theor.

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Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classically chaotic dynamics and corresponding universal features at the quantum level. Recently, single-particle techniques dealing with ergodic wave interference in the usual semiclassical limit ħ → 0 have begun to be transformed into the field theoretical domain of N -particle systems in the analogous semiclassical limit ħ_eff = 1/N → 0, thereby accounting for genuine many-body quantum interference. This semiclassical many-body theory provides a unified framework for understanding random-matrix correlations of both single-particle and many-body quantum chaotic systems. Certain braided bundles of classical orbits, and of mean field modes, govern interference, respectively, and provide the key to the foundation of universality. Case studies presented include a many-body version of Gutzwiller’s trace formula for the spectral density and out-of-time-order correlators along with brief remarks on where further progress may be forthcoming.

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