Spacing Distribution for Two-Particle Fermion System in Gaussian Unitary Ensemble: Exact Results

"In this seminar talk we deduce an analytical expression for spacing distance probability distribution for a two-charged particle system in the gaussian unitary ensemble, for which the particles behave like free fermions, i.e., without electric interaction. Starting with the Langevin equation for N interacting charged particles in a 2D Coulomb potential merged in a thermal bath, we found the associated Fokker-Planck equation and then we map it to a Schrödinger equation. In this representation and working in GUE formalism, we get a free fermion system. For N=2, we solve exactly the Schrödinger equation finding the spacing distribution contrasting with simulated data for this system.
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