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

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

2008-05-07

arxiv.org/abs/0805.0869v1

Journal of Mathematical Physics 49 (2008) 102102

Mathematics

Probability

25 pages

Scientific paper

10.1063/1.2988180

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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