An exact solution of the boundary value problem on thermal creep for a quantum Fermi gas

A. V. Latyshev, Aleksandr Alekseevich Yushkanov

A. V. Latyshev, Aleksandr Alekseevich Yushkanov

E. Ruiz Arriola, S. Szpigel, V. S. Timóteo

We analyze the universality of the Unitary Fermi Gas in its ground state from a Wilsonian renormalization point of view and compute the effective range dependence of the Bertsch parameter $ξ$ exactly. To this end we construct an effective block-diagonal two-body separable interaction with the Fermi momentum as a cut-off which reduces the calculation to the mean field level. The interaction is separable in momentum space and is determined by Tabakin's inverse scattering formula. For a vanishing effective range we get $ξ= \frac{176}{9 π}-\frac{17}{3} = 0.56$. By using phase-equivalent similarity transformations we can show that there is a class of exact solutions with any value in the range $ 0.56 \ge ξ\ge -1/3$.

Alan H. Luther, Victor J. Emery

An exact solution to the one-dimensional electron gas with a particular attractive-interaction strength for scattering across the Fermi "surface" is given. It is shown that conductivity enhancement occurs for physically interesting values of the coupling constants. Scaling arguments are advanced to demonstrate that this solution applies generally for attractive backward scattering. In addition, the spinless problem is solved exactly for arbitrary couplings.

Toshiki Kobayashi

К. А. Матвеев, Zoran Ristivojević

We study how a system of one-dimensional spin-$\frac{1}{2}$ fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find the exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.