The effect of classical noise on a quantum two-level system
arXiv:0805.0869 · doi:10.1063/1.2988180
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.
25 pages
References in corpus (6)
- Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
- Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
- Geometric singular perturbation theory for stochastic differential equations
- Asymptotic Behavior of Thermal Non-Equilibrium Steady States for a Driven Chain of Anharmonic Oscillators
- Pathwise description of dynamic pitchfork bifurcations with additive noise
- On the noise-induced passage through an unstable periodic orbit I: Two-level model