Loschmidt echo and Poincaré recurrences of entanglement

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

doi:10.1088/1751-8121/ac6af9

Cited by 3 publications

(1 citation statement)

References 59 publications

(128 reference statements)

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“…Properties of entanglement of two (non)interacting particles in the quantum chaotic Chirikov standard map were very recently numerically considered in Ref. [248].…”

Section: Perspectivesmentioning

confidence: 99%

Semiclassical roots of universality in many-body quantum chaos

Richter¹,

Urbina²,

Tomsovic³

2022

Preprint

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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 → 0 have begun to be transformed into the field theoretical domain of N -particle systems in the analogous semiclassical limit 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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“…Properties of entanglement of two (non)interacting particles in the quantum chaotic Chirikov standard map were very recently numerically considered in Ref. [248].…”

Section: Perspectivesmentioning

confidence: 99%

Semiclassical roots of universality in many-body quantum chaos

Richter¹,

Urbina²,

Tomsovic³

2022

Preprint

View full text Add to dashboard Cite

show abstract

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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Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

Marković,

Čubrović

2024

Preprint

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We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).

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Loschmidt echo and Poincaré recurrences of entanglement

Cited by 3 publications

References 59 publications

Semiclassical roots of universality in many-body quantum chaos

Semiclassical roots of universality in many-body quantum chaos

Semiclassical roots of universality in many-body quantum chaos

Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

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