Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

Abstract

We study the unitary dynamics of a one-dimensional gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency $\omega (t)$. Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

24 pages, 6 figures

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• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Finite-temperature dynamics of a Tonks-Girardeau gas in a frequency-modulated harmonic trap
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain