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Classical and quantum diffusion in the presence of velocity-dependent coupling
Zhan-Wu Bai1, Jing-Dong Bao, Yan-Li Song
1Department of Physics, Beijing Normal University, Beijing 100875, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
Velocity-dependent couplings in system-reservoir models lead to unique thermal noise spectra and can induce ballistic diffusion in particles. This contrasts with coordinate couplings, revealing distinct physical behaviors and quantum phenomena.
Area of Science:
- Statistical Mechanics
- Quantum Dynamics
- Condensed Matter Physics
Background:
- System-plus-reservoir models are crucial for understanding complex physical phenomena.
- The nature of coupling (coordinate vs. velocity-dependent) between a system and its environment significantly impacts system dynamics.
- Understanding thermal noise and its spectral properties is key to characterizing environmental interactions.
Purpose of the Study:
- To introduce a generalized system-plus-reservoir model with various coupling types.
- To investigate the non-equivalence of velocity-dependent and coordinate couplings due to differing thermal noise spectra.
- To explore the implications of velocity-dependent couplings, including ballistic diffusion and quantum phenomena.
Main Methods:
- Development of a generalized system-plus-reservoir model incorporating four types of couplings.
- Analysis of power spectra of thermal noise for different coupling mechanisms.
- Theoretical investigation of particle diffusion, including quantum ballistic diffusion, under velocity-dependent couplings.
Main Results:
- Velocity-dependent coupling yields different thermal noise power spectra compared to coordinate coupling.
- Harmonic velocity and acceleration noises are proposed for specific spectral distributions.
- Velocity-dependent coupling can induce ballistic diffusion, with mean square velocity dependent on initial conditions; quantum ballistic diffusion exhibits unstable velocity correlations.
Conclusions:
- Velocity-dependent couplings represent a distinct physical regime from coordinate couplings in system-reservoir interactions.
- The study highlights the potential for ballistic diffusion and unique quantum effects arising from velocity-dependent interactions.
- Examples like electron-atom interaction and particles in periodic potentials illustrate the relevance of these findings.
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