Exact BCS stochastic schemes for a time dependent many-body fermionic system

TL;DR

This paper introduces exact stochastic BCS schemes for simulating the quantum dynamics of a time-dependent fermionic system, capturing effects beyond mean-field approximations through optimized stochastic equations.

Contribution

It derives the most general Ito stochastic equations for exact fermionic state evolution and analyzes their relation to mean-field equations, applying the method to a two-site model.

Findings

Simulations reveal effects not captured by mean-field approximation.

Optimized stochastic equations reduce trajectory spreading.

Method provides exact quantum state evolution for fermionic gases.

Abstract

The exact quantum state evolution of a fermionic gas with binary interactions is obtained as the stochastic average of BCS-state trajectories. We find the most general Ito stochastic equations which reproduce exactly the dynamics of the system and we obtain some conditions to minimize the stochastic spreading of the trajectories in the Hilbert space. The relation between the optimized equations and mean-field equations is analyzed. The method is applied to a simple two-site model. The simulations display effects that cannot be obtained in the mean-field approximation.