The quantum-state diffusion model applied to open systems

@article{Gisin1992TheQD,
  title={The quantum-state diffusion model applied to open systems},
  author={Nicolas Gisin and Ian Colin Percival},
  journal={Journal of Physics A},
  year={1992},
  volume={25},
  pages={5677-5691}
}
A model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation, derived from a density operator equation such as the Bloch equation, and consistent with it. The advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described. The method is applied to the nonlinear absorber, cascades of quantum transitions… 
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References

SHOWING 1-10 OF 40 REFERENCES

Quantum Zeno effect without collapse of the wave packet.

  • FrerichsSchenzle
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1991
The only experiment in which the Zeno effect has yet been clearly demonstrated, though, allows no conclusion on the necessity or validity of the projection postulate, as shown by calculating the outcome of the experiment on the basis of the standard three-level Bloch equations.

A Monte Carlo wave function method in quantum optics

Very recently there have been a number of papers discussing the applicability of stochastic methods as an alternative to the usual treatment of master equations in quantum mechanics.1-5 In this paper…

Wave-function approach to dissipative processes in quantum optics.

An alternative approach using a wave-function treatment to describe the atomic system and it is shown that this treatment is equivalent to the standard density matrix approach leading to the OBE's.

Reduction of the state vector by a nonlinear Schrödinger equation

It is hypothesized that the state vector describes the physical state of a single system in nature. Then it is necessary that the state vector of a macroscopic apparatus not assume the form of a…

Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles.

Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle and the stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces.

Quantum diffusions, quantum dissipation and spin relaxation

The authors develop the tool of quantum diffusion (i.e. Hilbert-space-valued stochastic differential equations) for dissipative quantum systems. The aims are to find possible limitations to this…

A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory

The measurement problem in quantum mechanics is re-examined and it is shown that it cannot really be solved in a satisfactory way, within the framework of the usual interpretation of the theory. We…

Bifurcations and the positiveP-representation

The role of quantum fluctuations in dynamical systems can be described conveniently in terms of quasi-probabilities, since this concept bears a strong but formal analogy to classical statistical…

Unified dynamics for microscopic and macroscopic systems.

A modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics.

Quantum Zeno effect.

The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state by means of pulses of light in an rf transition between two ground-state hyperfine levels.