The Weak Coupling Limit for a Fermi Gas in a Random Potential

Thomas Chen, Itaru Sasaki

V. Janiš, Jindřich Kolorenč

Shreemant Raman, L. K. Mishra

In this paper, we have studied the one-dimensional Fermi gas with attractive δ interaction potential in the quasi-particle random phase approximation at zero temperature. Using the theoretical formalism of Alm and Schuck, we have studied the behavior of collective modes over the whole coupling regime from weak coupling (high density) to strong coupling (low density). We observe that in the weak- coupling limit particle-hole RPA is approached to low momenta and the collective mode in the strong coupling limit reproduces the Bogoliubov mode for the weakly interacting bosons.

Tin-Lun Ho, Lawrence J. Landau, A. J. WILKINS

General conditions are derived for the essential self-adjointness of –∆ + V, where V is a translation-invariant random potential, and for the existence of the perturbation expansion. A sequence of graphs is exhibited violating Dell'Antonio's bound for skeleton graphs. For a translation-invariant and clustering Gaussian random potential V, and a translation-invariant and clustering initial state S of the Fermi gas, uncorrelated with the random potential, the weak coupling limit (Van Hove limit) yields increase of entropy, propagation of chaos, convergence of the state for sufficiently small values of the parameter τ to a gauge-invariant and quasi-free asymptotic state, and the semigroup describing the evolution of the two-point function. The asymptotic system is Bernoulli. Results are obtained not only for the average over the random potential but also with probability one. If the random potential V′ is absolutely continuous with respect to V, and if the state S′ is given by a density matrix in the GNS representation for S, then the weak coupling limit is the same as for V and S.

Niels Benedikter, Phan Thành Nam, Marcello Porta +2 more

Taira Kawamura, Daichi Kagamihara, Ryo Hanai +1 more