Second Josephson excitations beyond mean field as a toy model for thermal pressure: exact quantum dynamics and the quantum phase model
arXiv:1205.3511 · doi:10.1088/0031-8949/2012/T151/014046
Abstract
A simple four-mode Bose-Hubbard model with intrinsic time scale separation can be considered as a paradigm for mesoscopic quantum systems in thermal contact. In our previous work we showed that in addition to coherent particle exchange, a novel slow collective excitation can be identified by a series of Holstein-Primakoff transformations. This resonant energy exchange mode is not predicted by linear Bogoliubov theory, and its frequency is sensitive to interactions among Bogoliubov quasi-particles; it may be referred to as a second Josephson oscillation, in analogy to the second sound mode of liquid Helium II. In this paper we will explore this system beyond the Gross-Pitaevskii mean field regime. We directly compare the classical mean field dynamics to the exact full quantum many-particle dynamics and show good agreement over a large range of the system parameters. The second Josephson frequency becomes imaginary for stronger interactions, however, indicating dynamical instability of the symmetric state. By means of a generalized quantum phase model for the full four-mode system, we then show that, in this regime, high-energy Bogoliubov quasiparticles tend to accumulate in one pair of sites, while the actual particles preferentially occupy the opposite pair. We interpret this as a simple model for thermal pressure.
References in corpus (18)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
- Breakdown of thermalization in finite one-dimensional systems
- The Fermi-Pasta-Ulam problem: 50 years of progress
- Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate
- A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
- Condensates beyond mean field theory: quantum backreaction as decoherence
- Josephson effects in dilute Bose-Einstein condensates
- Macroscopic Quantum Fluctuations in the Josephson Dynamics of Two Weakly Linked Bose-Einstein Condensates
- A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
- Irregular Dynamics in a One-Dimensional Bose System
- Thermal equilibration between two quantum systems
- Nonequilibrium Josephson oscillations in Bose-Einstein condensates without dissipation
- N-conserving Bogoliubov vacuum of a two component Bose-Einstein condensate: Density fluctuations close to a phase separation condition
- Second Josephson oscillations
- An extension of Bogoliubov theory for a many-body system with a time scale hierarchy: the quantum mechanics of second Josephson oscillations