Exact many-body dynamics of a harmonically quenched Tonks-Giradeau gas at finite temperature
Yasar ATAS (University of Queensland, Brisbane, Australia)
Ultracold quantum gases offer a fascinating and remarkably insightful playground for exploring and understanding the fundamentals of out-of-equilibrium behaviour of quantum matter. Experimental systems whose non-equilibrium dynamics can be described by exactly solvable models of quantum many-body theory play a particularly important role. A paradigmatic example in this realm is the Tonks-Girardeau (TG) gas of strongly interacting bosons, previously treated only for zero-temperature dynamics.
In this talk, I will present an exact finite temperature dynamical theory of a harmonically trapped TG gas, and apply it to the problem of breathing-mode oscillations after a sudden confinement quench. The method is based on the Fredholm determinant expression of the density matrix at finite temperature and provides a straightforward and efficient technique to compute finite temperature properties of TG. I will identify physical regimes for observing a phenomenon of frequency doubling in the oscillations of the momentum distribution of the gas. Exact results will be compared to a finite-temperature hydrodynamic approach based on local density approximation with the frequency quasi-doubling phenomena surprisingly well captured. The exact dynamical theory developed opens the way to solving finite-temperature problems involving anharmonic traps, as well as arbitrary quench protocols of the trapping potential.