Bloch and Josephson Oscillations in a Ring of an Ideal Bose Gas

Abstract

We show that an Ideal Bose gas that is contained within a very thin ring exhibits phenomena analogous to the Bloch and Josephson oscillations of a charged Ideal Fermi gas in a thin ring. If the walls of the ring are constrained to have an angular velocity $\omega$, the angular momentum has an anomalous component that is periodic in $\omega$, with a period equal to the quantum of angular velocity $\omega_{0}\equiv \hbar /mR^{2}$. If a constant applied torque is applied to the walls, there will be component of the angular momentum of the gas that is periodic in time, with a 'Josephson frequency' given by $f_{J} =\tau/N \hbar$. Finally, we show that the oscillations are an automatic feature of the quantum regime of any ring of an ensemble of identical particles, even with particle interactions.