Periodic Mean-Field Solutions and the Spectra of Discrete Bosonic Fields: Trace Formula for Bose-Hubbard Models

Abstract

We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, non-perturbative solutions of the, typically non-linear, wave equation of the classical (mean-field) limit. To this end we construct the semiclassical approximation for both the smooth and oscillatory part of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects like vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommesurable frequencies, our formulas are generically valid also in the free-field case of non-interacting bosons.

submitted to Phys. Rev. E

References in corpus (5)

• Realization of a single Josephson junction for Bose-Einstein condensates
• Semiclassical quantization of an N-particle Bose-Hubbard model
• Wavepacket dynamics in energy space of a chaotic trimeric Bose-Hubbard system
• Semiclassical analysis of Bose-Hubbard dynamics
• Describing many-body bosonic waveguide scattering with the truncated Wigner method

Cited by in corpus (26)

• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Many-body quantum chaos: Analytic connection to random matrix theory
• Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
• Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
• Semiclassical roots of universality in many-body quantum chaos
• Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System
• Bose-Hubbard Hamiltonian: Quantum Chaos approach
• Post-Ehrenfest many-body quantum interferences in ultracold atoms far-out-of-equilibrium
• Quantum chaos in a system with high degree of symmetries
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• Optimal route to quantum chaos in the Bose-Hubbard model
• Universal Dephasing Mechanism of Many-Body Quantum Chaos
• Understanding quantum work in a quantum many-body system
• Spectral analysis of two-dimensional Bose-Hubbard models
• Complex saddle trajectories for multidimensional quantum wave packet/coherent state propagation: application to a many-body system
• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Eigenstate thermalization scaling in approaching the classical limit
• The semiclassical propagator in Fock space: dynamical echo and many-body interference
• Semiclassical Prediction of Large Spectral Fluctuations in Interacting Kicked Spin Chains
• Classical, semiclassical and quantum signatures of quantum phase transitions in a (pseudo) relativistic many-body system
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• A corrected Maslov index for complex saddle trajectories
• Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins
• Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos