On the generators of quantum dynamical semigroups

@article{Lindblad1976OnTG,
  title={On the generators of quantum dynamical semigroups},
  author={G{\"o}ran Lindblad},
  journal={Communications in Mathematical Physics},
  year={1976},
  volume={48},
  pages={119-130}
}
  • G. Lindblad
  • Published 1976
  • Mathematics
  • Communications in Mathematical Physics
The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Lévy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained. 
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References

SHOWING 1-10 OF 49 REFERENCES
On quantum statistical mechanics of non-Hamiltonian systems
Abstract An axiomatic definition of time evolution (dynamical semi-group) of a physical system has been given. A dynamical semi-group is defined as a one-parametersemi-group of linear endomorphismsExpand
Markovian master equations
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 showExpand
General state changes in quantum theory
Abstract General state changes of quantum systems (operations) due to external interventions (measurements) are studied. The formalism developed in previous papers is simplified and generalized toExpand
Harmonic Analysis of Operators on Hilbert Space
Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.-Expand
On the connection of nonequilibrium information thermodynamics with non-hamiltonian quantum mechanics of open systems
Abstract A critical and improved version of the non-Hamiltonian quantum mechanics and nonequilibrium information thermodynamics is presented. It has been shown that the latter is connected with theExpand
Quantum stochastic processes
In order to describe rigorously certain measurement procedures, where observations of the arrival of quanta at a counter are made throughout an interval of time, it is necessary to introduce theExpand
Difficulty with a kinematic concept of unstable particles: the SZ.-Nagy extension and the Matthews-Salam-Zwanziger representation
We discuss the possibility of describing unstable systems, or dissipative systems in general, by vectors in a Hilbert space, evolving in time according to some non-unitary group or semigroup ofExpand
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
On the identity of three generalized master equations
Abstract Three apparently different quantum mechanical master equations, derived by Prigogine and Resibois, by Montroll, and independently by Nakajima and Zwanzig, are shown to be identical. TheExpand
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
...
1
2
3
4
5
...