Non-exponential decay for Polaron model

Accardi, Luigi; Козырев, С. В.; Волович, И. В.

doi:10.1016/s0375-9601(99)00510-1

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…is the corresponding energy difference. The difference of energies (14) coincides with the difference of energies in the Bogoliubov-Landau condition (9) that justify the fact that Hamiltonian (10) describe the non-ideal Bose gas considered above.…”

Section: Condensate-normal Phase Interaction In the Stochastic Limitsupporting

confidence: 64%

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Superfluidity in the stochastic limit

Accardi

Козырев

2004

Discrete Dynamics in Nature and Society

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Section: Condensate-normal Phase Interaction In the Stochastic Limitsupporting

confidence: 64%

“…One particle version of this quantum stochastic differential equation was obtained and investigated in [14].…”

Section: Condensation Of a Non-ideal Bose Gasmentioning

confidence: 99%

Superfluidity in the stochastic limit

Accardi

Козырев

2004

Discrete Dynamics in Nature and Society

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“…in the weak coupling limit. It was applied to study the spin-boson model [2], polaron model and nonrelativistic quantum electrodynamics [3,4], quantum Hall effect [5], relations between Hepp-Lieb and Alli-Sewell laser models [6], bifurcation phenomenon in a spin relaxation [7], etc.…”

Section: Introductionmentioning

confidence: 99%

Quantum stochastic equation for a test particle interacting with a dilute Bose gas

Pechen

2003

Journal of Mathematical Physics

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Abstract. We use the stochastic limit method to study long time quantum dynamics of a test particle interacting with a dilute Bose gas. The case of arbitrary form-factors and an arbitrary, not necessarily equilibrium, quasifree low density state of the Bose gas is considered. Starting from microscopic dynamics we derive in the low density limit a quantum white noise equation for the evolution operator. This equation is equivalent to a quantum stochastic equation driven by a quantum Poisson process with intensity S − 1, where S is the one-particle S matrix. The novelty of our approach is that the equations are derived directly in terms of correlators, without use of a FockantiFock (or Gel'fand-Naimark-Segal) representation. Advantages of our approach are the simplicity of derivation of the limiting equation and that the algebra of the master fields and the Ito table do not depend on the initial state of the Bose gas. The notion of a causal state is introduced. We construct master fields (white noise and number operators) describing the dynamics in the low density limit and prove the convergence of chronological (causal) correlators of the field operators to correlators of the master fields in the causal state. † permanent address:

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“…The path integral variational method has been successfully applied to the analysis of this idealized problem, see for example the work of Bogoliubov, 3 Feynman 6 or Höhler. 8 More recently the polaron model has also been treated from different points of view by Accardi et al, 1 Donsker and Varadhan, 5 Löwen, 10 . .…”

Section: Introductionmentioning

confidence: 99%