Application of the Fermi gas model

Jenő Sólyom

Joachim Alexander Maruhn, P.‐G. Reinhard, E. Suraud

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.

Min Liang

The degeneration conditions for quantum gas system were analyzed based on statistical mechanics method.We point out the coincidence among these methods and the dependent properties of quantum gas system to its degeneration by comparing and analyzing these methods.The application of degeneration Fermi gas model in astrophysics proves that quantum statistical theory plays a vitally important role in study area of modern physics.

Jenő Sólyom

Masaaki Tokieda, Shimpei Endo

We analytically study quantum dissipative dynamics described by the Caldirola-Kanai model with inter-particle interactions. We have found that the dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped to a dissipationless quantum dynamics under a negative external harmonic potential, even when the particles are strongly interacting. In particular, we show that the mapping is valid for the unitary Fermi gas, which is relevant for cold atoms and nuclear matters.