 0889 JeanPhilippe Aguilar, Nils Berglund
 The effect of classical noise on a quantum twolevel system
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May 7, 08

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Abstract. We consider a quantum twolevel system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the offdiagonal 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 OrnsteinUhlenbeck noise, we determine the speed of convergence to the invariant measure. Finally, we determine an approximate onedimensional diffusion equation for the transition probabilities. The proofs use both spectraltheoretic and probabilistic methods.
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