Quantum chaos in many-body systems of indistinguishable particles

• URL: http://arxiv.org/abs/2604.12745v1
• Date: Tue, 14 Apr 2026 13:57:41 GMT
• Title: Quantum chaos in many-body systems of indistinguishable particles
• Abstract summary: In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures.<n>The many-body version of the van Vleck-Gutzwillers semiclassical propagator is explained in detail.<n>It provides a unified framework for understanding a variety of quantum chaotic phenomena.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding quantum properties. Well established techniques dealing with ergodic wave interference in the usual semiclassical limit $\hbar \to 0$, where the classical limit is given by Hamiltonian mechanics of particles, constitute a now standard part of the toolkit of theoretical physics. During the last years, these ideas have been extended into the field theoretical domain of systems composed of $N$ indistinguishable particles, aka quantum fields, displaying a different type of semiclassical limit $\hbar_{\rm eff}=1/N \to 0$ and accounting for genuine many-body quantum interference. The foundational concept behind this idea of many-body interference, the many-body version of the van Vleck-Gutzwillers semiclassical propagator, is explained in detail. Based on this the corresponding semiclassical many-body theory is reviewed. It provides a unified framework for understanding a variety of quantum chaotic phenomena addressed, including random-matrix spectral correlations in many-body systems, the universal morphology of many-body eigenstates, interference effects kin to mesoscopic weak localization, and the key to the scrambling of many-body correlations characterized by out-of-time-order correlators.

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