Attractive non-relativistic optical potential balancing Fermi energy of a fermion gas

M. Grado-Caffaro, M. Grado-Caffaro

Luis Grave de Peralta

Background : The theory of a Fermi gas constitutes a useful physical model with multiple applications from solid state to stellar physics. The theory of a non-relativistic Fermi gas is relatively simple when compared with the one for a relativistic Fermi gas. Therefore, it would be useful if a rigorous theory of a relativistic Fermi gas could be constructed like the theory of a non-relativistic Fermi gas. Methods : Such a theory, for T > 0 K, is presented here. It is based on using a recently reported formula for the energies of a relativistic spin-0 particle in a three-dimensional infinite well. The Pauli exclusion principle is used for taking care of the fermion nature of the particles forming a Fermi gas. Results : A unified description of a Fermi gas at low temperatures is presented. This description is valid from the non-relativistic to the ultra-relativistic limits. Moreover, it is simple. The theory follows the relatively simple approach often used for constructing the theory of a non-relativistic Fermi gas. Conclusions : The ultra-relativistic results reported here are often obtained using a different approach than the one used in this work. These results are not new, but they corroborate the correctness of the presented approach. In addition, the relative simplicity of the approach presented in this work allows for teaching the theory of a relativistic Fermi gas in introductory quantum mechanics courses.

Oleksandr Fialko, A. Gammal, K. Ziegler

Olga Goulko, Matthew Wingate A

In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances $h=\ensuremath{\Delta}\ensuremath{\mu}/{\ensuremath{\varepsilon}}_{F}\ensuremath{\lesssim}0.2$. We obtain the continuum result ${T}_{c}=0.171(5){\ensuremath{\varepsilon}}_{F}$ in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit, ${T}_{c}(h)\ensuremath{-}{T}_{c}(0)>\ensuremath{-}0.5{\ensuremath{\varepsilon}}_{F}{h}^{2}$. Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.

J. Tempere

Sebastian Will