Semiclassical roots of universality in many-body quantum chaos

Abstract

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 $\hslash \to 0$ have begun to be transformed into the field theoretical domain of N-particle systems in the analogous semiclassical limit ${\hslash }_{eff}=1/N\to 0$, 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.

63 pages, 14 figures, 258 references, published in J. Phys. A: Math. Theor. special issue dedicated to Fritz Haake

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Cited by in corpus (25)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Spectral and Krylov Complexity in Billiard Systems
• Genuine many-body quantum scars along unstable modes in Bose-Hubbard systems
• Dynamical quantum ergodicity from energy level statistics
• The Timescales of Quantum Breaking
• Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Exactly solvable many-body dynamics from space-time duality
• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Controlling Many-Body Quantum Chaos: Bose-Hubbard systems
• Loop current states and their stability in small fractal lattices of Bose-Einstein condensates
• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
• Classical Drift in the Arnold Web Induces Quantum Delocalization Transition
• Quantum Enhancement of Thermalization
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• Using Lagrangian descriptors to calculate the Maslov index of periodic orbits
• Statistics of local level spacings in single- and many-body quantum chaos
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Quantum Instability
• Ensemble-averaged mean-field many-body level density: an indicator of integrable versus chaotic single-particle dynamics
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
• Periodic orbit theory of Bethe-integrable quantum systems: an $N$-particle Berry-Tabor trace formula