We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two nonperturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion, and a path-integral representation of the virial coefficients. To complement our numerical calculations, we present leading-order results in a semiclassical lattice approximation, which we find to be surprisingly close to the expected answers.We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two nonperturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion, and a path-integral representation of the virial coefficients. To complement our numerical calculations, we present leading-order results in a semiclassical lattice approximation, which we find to be surprisingly close to the expected answers.

arXiv:1808.07836Physical Review ANov 13, 201815 citations

Second virial coefficient of the interacting anyon gas

Nikitas I. Gidopoulos, A. K. Theophilou

Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert} ${\mathbf{r}}_{1}$ - ${\mathbf{r}}_{2}$ \ensuremath{\Vert}), where ${\mathit{r}}^{2}$ U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert}${\mathbf{r}}_{1}$-${\mathbf{r}}_{2}$\ensuremath{\Vert}), where ${\mathit{r}}^{2}$U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.

Physical review. B, Condensed matterMar 1, 19941 citation

The Virial Theorem and Quantum Statistics

R. J. Duffin

Physical ReviewMar 1, 193511 citations

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

\ensuremath{\Vert}), where

{\mathit{r}}^{2}

U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.