Ideal quantum gases in two dimensions

The exact equations of state of two-dimensional Bose gas (Equation 14) and Fermi gas (Equation 24) are derived, to calculate the degeneracy pressure. They are consistent with the second law of thermodynamics in the entire phase space. Under relevant conditions, they converge to the conventional equations.

The van-der-Waals version of the second virial coefficient is not far from being exact if the model parameters are appropriately chosen. It is shown how the van-der-Waals resemblance originates from the interplay of thermal averaging and superposition of scattering phase shift contributions. The derivation of the two parameters from the quantum virial coefficient reveals a fermion-boson symmetry in non-ideal quantum gases. Numerical details are worked out for the Helium quant...

We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field t...

This paper is concerned with statistical properties of a gas of $qp$-bosons without interaction. Some thermodynamical functions for such a system in $D$ dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters $q$ and $p$. Finally, the second-order correlation function of a gas of photons is calculated.

The ideal uniform two-dimensional (2D) Fermi and Bose gases are considered both in the thermodynamic limit and the finite case. We derive May's Theorem, viz. the correspondence between the internal energies of the Fermi and Bose gases in the thermodynamic limit. This results in both gases having the same heat capacity. However, as we shall show, the thermodynamic limit is never truly reached in two dimensions and so it is essential to consider finite-size effects. We show in ...

We generalize techniques previously used to compute ground-state properties of one-dimensional noninteracting quantum gases to obtain exact results at finite temperature. We compute the order-n R\'enyi entanglement entropy to all orders in the fugacity in one, two, and three spatial dimensions. In all spatial dimensions, we provide closed-form expressions for its virial expansion up to next-to-leading order. In all of our results, we find explicit volume scaling in the high-t...

Photon Bose-Einstein condensates are characterised by a quite weak interaction, so they behave nearly as an ideal Bose gas. Moreover, since the current experiments are conducted in a microcavity, the longitudinal motion is frozen out and the photon gas represents effectively a two-dimensional trapped gas of massive bosons. In this paper we focus on a harmonically confined ideal Bose gas in two dimensions, where the anisotropy of the confinement allows for a dimensional crosso...

We have analytically explored thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials of the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible specially in the intermediate regime between the classical and quantum limits.

We investigate pair correlations in trapped fermion and boson gases as a means to probe the quantum states producing the density fluctuations. We point out that "opposite sign correlations" (meaning pair correlations that are positive for fermions and negative for bosons) unambiguously indicate that the quantum many-particle state cannot be "free." In particular, a system of fermions that exhibits positive pair correlations cannot be described by any Slater determinant wavefu...

We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter $\alpha$. The lower bounds extend to Lieb-Thirring inequalities for all anyons except bosons.