Related papers: Correspondence between open bosonic systems and st…
We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
We show that the effect of a Gaussian Bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary Bosonic modes initially at zero temperature and…
In this paper we present an exact Grassmann stochastic Schr\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic…
These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective models based on statistical independence…
The effects of decoherence for quantum system coupled with a bosonic field are investigated. An application of the stochastic golden rule shows that in the stochastic limit the dynamics of such a system is described by a quantum stochastic…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation.…
Quantum systems that interact non-locally with an environment are paradigms for exploring collective phenomena. They naturally emerge in various physical contexts involving long-range, many-body interactions. We consider a general class of…
These lecture notes treat the mean-field approximation for equilibrium states of N body systems in classical and quantum statistical mechanics. A general strategy to justify effective models based on assumptions of statistical independence…
We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of Time Dependent Hartree-Fock equations. The noise is found from a path-integral representation of the evolution operator and…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation…
We derive the Bosonic Dynamical Mean-Field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbors. Hence the…
We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a…
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a…