Finite-temperature dynamics of a Tonks-Girardeau gas in a frequency-modulated harmonic trap
arXiv:1908.01291 · doi:10.1103/PhysRevA.100.043602
Abstract
We study the out-of-equilibrium dynamics of a finite-temperature harmonically trapped Tonks-Girardeau gas induced by periodic modulation of the trap frequency. We give explicit exact solutions for the real-space density and momentum distributions of this interacting many-body system and characterize the stability diagram of the dynamics by mapping the many-body solution to the solution and stability diagram of Mathieu's differential equation. The mapping allows one to deduce the exact structure of parametric resonances in the parameter space characterized by the driving amplitude and frequency of the modulation. Furthermore, we analyze the same problem within the finite-temperature hydrodynamic approach and show that the respective solutions to the hydrodynamic equations can be mapped to the same Mathieu equation. Accordingly, the stability diagram and the structure of resonances following from the hydrodynamic approach is exactly the same as those obtained from the exact many-body solution.
arXiv comment15 pages, 8 figures
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Cited by in corpus (5)
- Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate
- Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
- Dynamical fermionization in one-dimensional spinor gases at finite temperature
- Phase-space stochastic quantum hydrodynamics for interacting Bose gases
- Dynamics of Momentum Distribution and Structure Factor in a Weakly Interacting Bose Gas with a Periodical Modulation