Thermodynamics of rotating quantum matter in the virial expansion

Abstract

We characterize the high-temperature thermodynamics of rotating bosons and fermions in two- (2D) and three-dimensional (3D) isotropic harmonic trapping potentials. We begin by calculating analytically the conventional virial coefficients $b_n$ for all $n$ in the noninteracting case, as functions of the trapping and rotational frequencies. We also report on the virial coefficients for the angular momentum and associated moment of inertia. Using the bn coefficients, we analyze the deconfined limit (in which the angular frequency matches the trapping frequency) and derive explicitly the limiting form of the partition function, showing from the thermodynamic standpoint how both the 2D and 3D cases become effectively homogeneous 2D systems. To tackle the virial coefficients in the presence of weak interactions, we implement a coarse temporal lattice approximation and obtain virial coefficients up to third order.

10 pages, 6 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Ultra-cold Polarized Fermi Gases
• Exact few-body results for strongly correlated quantum gases in two dimensions
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity