Markovian master equations

@article{Davies1974MarkovianME,
  title={Markovian master equations},
  author={E. B. Davies},
  journal={Communications in Mathematical Physics},
  year={1974},
  volume={39},
  pages={91-110}
}
  • E. Davies
  • Published 1974
  • Mathematics
  • Communications in Mathematical Physics
We give a rigorous proof that under certain technical conditions the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit. This is sufficient to show that a number of open systems obey an exponential decay law in the weak coupling limit for a rescaled time variable. The theory is applied to a fairly general finite dimensional system weakly coupled to an infinite free heat bath. 
Properties of Quantum Markovian Master Equations
In this paper we give an essentially self-contained account of some general structural properties of the dynamics of quantum open Markovian systems. We review some recent results regarding theExpand
Markovian master equations. II
We prove some theorems on the behaviour of solutions of master equations in the weak coupling limit, obtaining an exponential decay law under more general conditions than in an earlier paper. As wellExpand
On the quantum dissipative generator: weak-coupling approximation and stochastic approach
For a quantum open system the so-called Schr?dinger-Langevin picture has been revisited. In a second-order perturbation it is shown that a non-Markovian evolution for the stochastic state vectorExpand
The Quantum weak coupling limit (II): Langevin equation and finite temperature case
We complete the program started in [4] by proving that, in the weak coupling limit, the matrix elements, in the collective coherent vectors, of the Heisenberg evolved of an observable of a systemExpand
Completely Positive Markovian Quantum Dynamics in the Weak-Coupling Limit
We obtain new types of exponential decay laws for solutions of density-matrix master equations in the weak-coupling limit: after comparing with results already present in the literature andExpand
Quantum markovian master equations: Resonance theory overcomes the weak coupling regime
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitousExpand
The Markovian master equations for unstable particles
Abstract The theory of Markovian master equations is applied to a certain model of unstable particles. The exponential decay law is obtained in the weak coupling limit. The connection to the methodExpand
The open XY model
Using the weak coupling limit as a quantum functional central limit (in the sense of Accardi, Frigerio and Lu), we give a quantum Markovian description of the open XY-model, followed by the large-NExpand
Periodically driven quantum open systems: Tutorial
We present a short derivation and discussion of the master equation for an open quantum system weakly coupled to a heat bath and then its generalization to the case of with periodic external drivingExpand
Markovian master equations: a critical study
TLDR
The results of these illustrative examples serve to clarify the general properties of other open quantum system scenarios subject to treatment within a Markovian approximation, and assess the robustness of the assumptions usually made in the process of deriving the reduced Markovians. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 21 REFERENCES
Quantum stochastic processes II
We investigate properties of a class of quantum stochastic processes subject to a condition of irreducibility. These processes must be recurrent or transient and an equilibrium state can only existExpand
The harmonic oscillator in a heat bath
We study the time evolution of a quantum-mechanical harmonic oscillator in interaction with an infinite heat bath, which is supposed to be initially in the canonical equilibrium at some temperature.Expand
The Bloch equations
We consider a spinor interacting with a heat bath of harmonic oscillators in equilibrium and we prove that the phenomenological Bloch equations for time development are satisfied exactly if the spinExpand
A remark on ergodicity, dissipativity, return to equilibrium
Abstract Some notions of ergodicity, dissipativity and return to equilibrium for quantum systems are exhibited and compared in a simple situation of a pure state. As a by-product we develop aExpand
The statistical interpretation of nonequilibrium entropy
Boltzmann’s original scheme leading to the statistical interpretation of non-equilibrium entropy may be summarized as follows: Dynamics → Stochastic Process (kinetic equation) → Entropy. RecentExpand
States on Clifford algebras
We study states on Clifford algebras from the point of view of C*-algebras. A criterium is given under which the odd-point functions vanish. A particular set of states, called quasi-free states isExpand
Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors
We present a class of mean field model Hamiltonians consisting of a small, but macroscopic system S of N components interacting with a large reservoir R. The Dicke model of a laser is a particularExpand
Statistical treatment of open systems by generalized master equations
This paper deals with the dynamics of open systems (S) moving irreversibly under the influence of their surroundings (B). As a basis for the discussion of an open system S we use a completeExpand
Studies in the C*‐Algebraic Theory of Nonequilibrium Statistical Mechanics: Dynamics of Open and of Mechanically Driven Systems
We construct a C*‐algebraic formulation of the dynamics of a pair of mutually interacting quantum‐mechanical systems S and Ŝ, the former being finite and the latter infinite. Our basic assumptionsExpand
Dynamics of a multilevel Wigner‐Weisskopf atom
We study the dynamics of an atom with a finite number of discrete energy levels weakly coupled to a continuum of energy levels, showing that any bound state undergoes a decay into the continuumExpand
...
1
2
3
...