Physics – Quantum Physics
Scientific paper
1995-03-31
Phys.Rev. E51 (1995) 4267-4281
Physics
Quantum Physics
29 pages + 1 figure as compressed ps-file (uufiles) to appear in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.51.4267
We study the real time dynamics of a quantum system with potential barrier coupled to a heat-bath environment. Employing the path integral approach an evolution equation for the time dependent density matrix is derived. The time evolution is evaluated explicitly near the barrier top in the temperature region where quantum effects become important. It is shown that there exists a quasi-stationary state with a constant flux across the potential barrier. This state generalizes the Kramers flux solution of the classical Fokker-Planck equation to the quantum regime. In the temperature range explored the quantum flux state depends only on the parabolic approximation of the anharmonic barrier potential near the top. The parameter range within which the solution is valid is investigated in detail. In particular, by matching the flux state onto the equilibrium state on one side of the barrier we gain a condition on the minimal damping strength. For very high temperatures this condition reduces to a known result from classical rate theory. Within the specified parameter range the decay rate out of a metastable state is calculated from the flux solution. The rate is shown to coincide with the result of purely thermodynamic methods. The real time approach presented can be extended to lower temperatures and smaller damping.
Ankerhold Joachim
Grabert Hermann
Ingold Gert-Ludwig
No associations
LandOfFree
Dissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97205