Exact dynamics of moments and correlation functions for fermionic Poisson-type GKSL equations

Dynamics of moments of arbitrary order for stochastic Poisson squeezings

The explicit dynamics of the moments for the GKSL equation is obtained. In our case the GKSL equation corresponds to Poisson stochastic processes which lead to unitary jumps. We consider squeeze operators as the unitary jumps.

Irreversible quantum evolution with quadratic generator: Review

We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.

具有双Lindblad结构的开放量子系统的Egorov型半经典极限

Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure

本文提出了一种将双Hamilton结构与GKSL形式化相结合的框架，用于研究开放量子系统的Egorov型半经典极限，并通过Euler-top型例子展示了其可积性和接触耗散特性。

Evolution of fermionic systems as an expectation over Poisson processes

We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.

An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.

A complete quasiclassical map for the dynamics of interacting fermions

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassic…