dorsal/arxiv
View SchemaDissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier
| Authors | Joachim Ankerhold, Hermann Grabert, Gert-Ludwig Ingold |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9503027 |
| URL | https://arxiv.org/abs/quant-ph/9503027 |
| DOI | 10.1103/PhysRevE.51.4267 |
| Journal | Phys.Rev. E51 (1995) 4267-4281 |
Abstract
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.
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"abstract": "We study the real time dynamics of a quantum system with potential barrier\ncoupled to a heat-bath environment. Employing the path integral approach an\nevolution equation for the time dependent density matrix is derived. The time\nevolution is evaluated explicitly near the barrier top in the temperature\nregion where quantum effects become important. It is shown that there exists a\nquasi-stationary state with a constant flux across the potential barrier. This\nstate generalizes the Kramers flux solution of the classical Fokker-Planck\nequation to the quantum regime. In the temperature range explored the quantum\nflux state depends only on the parabolic approximation of the anharmonic\nbarrier potential near the top. The parameter range within which the solution\nis valid is investigated in detail. In particular, by matching the flux state\nonto the equilibrium state on one side of the barrier we gain a condition on\nthe minimal damping strength. For very high temperatures this condition reduces\nto a known result from classical rate theory. Within the specified parameter\nrange the decay rate out of a metastable state is calculated from the flux\nsolution. The rate is shown to coincide with the result of purely thermodynamic\nmethods. The real time approach presented can be extended to lower temperatures\nand smaller damping.",
"arxiv_id": "quant-ph/9503027",
"authors": [
"Joachim Ankerhold",
"Hermann Grabert",
"Gert-Ludwig Ingold"
],
"categories": [
"quant-ph",
"cond-mat",
"nucl-th"
],
"doi": "10.1103/PhysRevE.51.4267",
"journal_ref": "Phys.Rev. E51 (1995) 4267-4281",
"title": "Dissipative Quantum Systems with Potential Barrier. General Theory and Parabolic Barrier",
"url": "https://arxiv.org/abs/quant-ph/9503027"
},
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