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The effect of classical noise on a quantum two-level system

Authors
  • Aguilar, Jean-Philippe
  • Berglund, Nils
Publication Date
Oct 03, 2008
Identifiers
DOI: 10.1063/1.2988180
OAI: oai:HAL:hal-00277789v1
Source
Hal-Diderot
Keywords
Language
English
License
Unknown
External links

Abstract

We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine the invariant measure of the system and prove its uniqueness. In the case of Ornstein-Uhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate one-dimensional diffusion equation for the transition probabilities. The proofs use both spectral-theoretic and probabilistic methods.

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