Langevin equations for interacting fermions and Cooper-like pairing in trapped one-dimensional fermions - art. no. 063409

Momentum correlations in a one-dimensional equilibrium ensemble of trapped fermions, with a point interaction between particles of opposite spin have been studied. In the degenerate regime correlations were observed between f ermions with opposite spins and momenta, similar to Cooper pairing. These c orrelations appear as soon as the temperature is below the Fermi energy, wh ich is a much less stringent condition than that of the BCS transition prop er. Calculations are carried out in both perturbative and non-perturbative regimes. To achieve the latter. it is shown that interacting fermionic dyna mics may be solved as a stochastic linear transformation of Grassmann algeb ra generators, much in the way random c-number paths are introduced in the conventional quantum stochastics of bosons. Importantly, the method thus em erging is inherently free of the sign problem.