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

Journal Article · Wed Oct 15 00:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2988180· OSTI ID:21175668

Aguilar, Jean-Philippe ^[1]; Berglund, Nils ^[2]

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1. Centre de Physique Theorique (CPT), CNRS, UMR 6207, Campus de Luminy, Case 907, 13288 Marseille Cedex 9 (France)
2. Laboratoire MAPMO, CNRS, UMR 6628, Federation Denis Poisson, FR 2964, Universite d'Orleans, Batiment de Mathematiques, B.P. 6759, 45067 Orleans Cedex 2 (France)

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.

• OSTI ID: 21175668
• Journal Information: Journal of Mathematical Physics, Vol. 49, Issue 10; Other Information: DOI: 10.1063/1.2988180; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BROWNIAN MOVEMENT
CONVERGENCE
DIFFUSION
DIFFUSION EQUATIONS
HAMILTONIANS
MAGNETIC FIELDS
MATRIX ELEMENTS
NOISE
ONE-DIMENSIONAL CALCULATIONS
PROBABILISTIC ESTIMATION
PROBABILITY
QUANTUM MECHANICS
SCHROEDINGER EQUATION