相关论文: Generalized master equation with nonhermitian oper…

We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…

The stochastic quantization of the fermion field is performed starting from Dirac equations. The statistical properties of stochastic terms in Langevin equations are described by explicit formulae of a Markov process. The interaction of the…

Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum…

A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…

Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…

The non-Markovian master equation for open quantum systems is obtained by generalization of the ordinary Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath…

We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by…

We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…

The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…

The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of…

General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…

We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density matrices, that the many-body quantum state…

In this paper we describe a new family of algebras which in the case of n = 2 reduces to the Fermion algebra and in the limiting case of n tends to infinity reduces to the Boson algebra. These generalized algebras describe particles which…

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…

Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method…

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not…

We consider the evolution of quasi-free states describing $N$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $N$, we study the convergence towards the classical Vlasov equation. For a…

We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…

In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that slightly generalized classical Maxwell electrodynamics can describe the…