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arXiv · 0805.0869

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

Jean-Philippe Aguilar·Nils Berglund
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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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Jean-Philippe Aguilar, Nils Berglund. 2008-05-07. The effect of classical noise on a quantum two-level system. https://doi.org/10.1063/1.2988180

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