Quantum diffusion
Abstract
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ``quantum diffusion'' terms arise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source.
- Publication:
-
Presented at the Drexel Conference on Quantum Non Integrability
- Pub Date:
- 1994
- DOI:
- arXiv:
- arXiv:hep-th/9410181
- Bibcode:
- 1994qni..conf.....H
- Keywords:
-
- Boltzmann-Vlasov Equation;
- Diffusion;
- Fokker-Planck Equation;
- Liouville Equations;
- Noise Generators;
- Quantum Mechanics;
- Stochastic Processes;
- Applications Of Mathematics;
- Distribution Functions;
- Hamiltonian Functions;
- Thermodynamics and Statistical Physics;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems
- E-Print:
- 5 pages, LA-UR-94-3329, LaTeX (to appear in Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability)