Diffusion for weakly coupled quantum oscillators

@article{Davies1972DiffusionFW,
  title={Diffusion for weakly coupled quantum oscillators},
  author={E. B. Davies},
  journal={Communications in Mathematical Physics},
  year={1972},
  volume={27},
  pages={309-325}
}
  • E. Davies
  • Published 1972
  • Physics, Mathematics
  • Communications in Mathematical Physics
We construct a simple model which exhibits some of the properties discussed by van Hove in his study of the Pauli master equation. The model consists of an infinite chain of quantum oscillators which are coupled so that the interaction Hamiltonian is quadratic. We suppose the chain is in equilibrium at an inverse temperature β and study the return to equilibrium when a chosen oscillator is given an arbitrary perturbation. We show that in the limit as the interaction becomes weaker and of longer… 
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39 Citations

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References

SHOWING 1-10 OF 13 REFERENCES
Quantum-mechanical perturbations giving rise to a statistical transport equation
Brownian Motion of a Quantum Oscillator
An action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical…
On the equilibrium states in quantum statistical mechanics
AbstractRepresentations of theC*-algebra $$\mathfrak{A}$$ of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finite…
Statistical Mechanics of Assemblies of Coupled Oscillators
It is shown that a system of coupled harmonic oscillators can be made a model of a heat bath. Thus a particle coupled harmonically to the bath and by an arbitrary force to a fixed center will (in an…
Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory
Cyclic representations of the canonical commutation relations and their connection with the Hamiltonian formalism are studied. The vacuum expectation functional E(f)=(Ψ0,ei[open phi](f)Ψ0) turns out…
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 exist…
Foundations of the Theory of Dynamical Systems of Infinitely Many Degrees of Freedom, II
  • I. Segal
  • Mathematics
    Canadian Journal of Mathematics
  • 1961
The notion of quantum field remains at this time still rather elusive from a rigorous standpoint. In conventional physical theory such a field is defined in essentially the same way as in the…
REPRESENTATIONS OF THE CANONICAL COMMUTATION RELATIONS DESCRIBING A NONRELATIVISTIC INFINITE FREE BOSE GAS
The existence of inequivalent representations of the canonical commutation relations which describe a nonrelativistic infinite free Bose gas of uniform density is investigated, with a view to…
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 the…
On the projection of norm one in $W^ *$-algebras
In the present paper, we will study on the projection of norm one from any W*-algebra onto its subalgebra. By a projection of norm one we mean a projection mapping from any Banach space onto its…
...
1
2
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