Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a “dynamical fermionization” occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime.

• Received 8 April 2005

DOI:https://doi.org/10.1103/PhysRevLett.94.240404