Related papers: Basic properties of a mean field laser equation
We deal with the dynamical system properties of a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation with mean-field Hamiltonian that models a simple laser by applying a mean field approximation to a quantum system describing a…
Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it…
The theory of open quantum system is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) Master Equation plays a key role as it is the most…
Applying probabilistic techniques we study regularity properties of quantum master equations (QMEs) in the Lindblad form with unbounded coefficients; a density operator is regular if, roughly speaking, it describes a quantum state with…
We present a fully quantum mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit…
A system of $N$ spin-1/2 particles interacting with a thermal reservoir is used as a pedagogical example for advanced undergraduate and graduate students. We introduce and illustrate some methods, approximations, and phenomena related to…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
We provide a rigorous construction of Markovian master equations for a wide class of quantum systems that encompass quadratic models of finite size, linearly coupled to an environment modeled by a set of independent thermal baths. Our…
A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with…
We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose the unified master equation that combines the…
A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems. In contrast to linear alternatives, its equilibrium solution is exactly the canonical Gibbs density matrix. The corresponding nonlinear…
The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are described using a quantum stochastic unitary model, where the continuous-mode…
A quantum system that interacts with an environment generally undergoes nonunitary evolution described by a non-Markovian or Markovian master equation. In this paper, we construct the non-Markovian Redfield master equation for a quantum…
By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the Parametric Representation with Environmental Coherent States) we derive an equation of motion for the reduced density operator of an…
A theory of Steady-State laser action is presented which loosely parallels the treatment by H. Frohlich on energy storage in biological systems. The principal lasing elements, taken as N bio level molecules and a single mode quantized…
We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch…
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 present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\"adler, for a Minkowski's background, were able to show that it is possible to derive a…
A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such many-body equation,…