Statistic physics in bound state in 3D fermi gas system

Abstract

The bound state is treated as a long-lived quasiparticle with slow momenta and current relaxation in fermi liquid phase. In this paper, we discuss the realization of ensemble behavior in a 3D fermi gas system in non-fermi liquid phase. We reveal the relation between UV cutoff of relative momentum $\Lambda_{q}$ and its ensemble behavior. The behavior of a bound state system has rarely been investigated before, and the relation between the scattering momentum and the physics has not yet been explored before (to best of our knowledge). We found that the cutoff $\Lambda_{q}$ directly related to the distribution and statistical variance of coupling term, which becomes Gaussian variable (or Chi-square variable) in limit (i.e., with a large step number of a fractional distance $\Lambda_{q}^{-1}\rightarrow\infty$). Also, we show that the different $\Lambda_{q}^{-1}$ lending support to different phases, including non-fermi liquid phase and (disordered) fermi liquid phase, which correspond to ill-defined and well-defined bound states, respectively. The pair condensation induced by local coupling, which happen at critical temperature, would suppresses the non-fermi liquid for constant on-site coupling (it is not the case when the coupling be variant). % We deduce the free energy density and the divergent behaviors of anomalous propagator in this case. % Finally, we also present a discussion of ensembles of level statistic that depending on which symmetry class the system belongs to, and that can be controlled by the type of disorder. Further, when the range of condensation is larger, the homogeneous character will emerge and the thermalization can be observed where eigenstates with higher energy has lower overlap with the low-entangled states.