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

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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Submitted on : Wednesday, May 7, 2008 - 10:53:11 AM
Last modification on : Wednesday, December 18, 2019 - 1:41:07 AM
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Jean-Philippe Aguilar, Nils Berglund. The effect of classical noise on a quantum two-level system. Journal of Mathematical Physics, American Institute of Physics (AIP), 2008, 49, pp.102102. ⟨10.1063/1.2988180⟩. ⟨hal-00277789⟩

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