dorsal/arxiv
View SchemaReal time approach to tunneling in open quantum systems: decoherence and anomalous diffusion
| Authors | Esteban Calzetta, Enric Verdaguer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603047 |
| URL | https://arxiv.org/abs/quant-ph/0603047 |
| DOI | 10.1088/0305-4470/39/30/008 |
| Journal | J.Phys.A39:9503-9532,2006 |
Abstract
Macroscopic quantum tunneling is described using the master equation for the reduced Wigner function of an open quantum system at zero temperature. Our model consists of a particle trapped in a cubic potential interacting with an environment characterized by dissipative and normal and anomalous diffusion coefficients. A representation based on the energy eigenfunctions of the isolated system, i.e. the system uncoupled to the environment, is used to write the reduced Wigner function, and the master equation becomes simpler in that representation. The energy eigenfunctions computed in a WKB approximation incorporate the tunneling effect of the isolated system and the effect of the environment is described by an equation that it is in many ways similar to a Fokker-Planck equation. Decoherence is easily identified from the master equation and we find that when the decoherence time is much shorter than the tunneling time the master equation can be approximated by a Kramers like equation describing thermal activation due to the zero point fluctuations of the quantum environment. The effect of anomalous diffusion can be dealt with perturbatively and its overall effect is to inhibit tunneling.
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"abstract": "Macroscopic quantum tunneling is described using the master equation for the\nreduced Wigner function of an open quantum system at zero temperature. Our\nmodel consists of a particle trapped in a cubic potential interacting with an\nenvironment characterized by dissipative and normal and anomalous diffusion\ncoefficients. A representation based on the energy eigenfunctions of the\nisolated system, i.e. the system uncoupled to the environment, is used to write\nthe reduced Wigner function, and the master equation becomes simpler in that\nrepresentation. The energy eigenfunctions computed in a WKB approximation\nincorporate the tunneling effect of the isolated system and the effect of the\nenvironment is described by an equation that it is in many ways similar to a\nFokker-Planck equation. Decoherence is easily identified from the master\nequation and we find that when the decoherence time is much shorter than the\ntunneling time the master equation can be approximated by a Kramers like\nequation describing thermal activation due to the zero point fluctuations of\nthe quantum environment. The effect of anomalous diffusion can be dealt with\nperturbatively and its overall effect is to inhibit tunneling.",
"arxiv_id": "quant-ph/0603047",
"authors": [
"Esteban Calzetta",
"Enric Verdaguer"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1088/0305-4470/39/30/008",
"journal_ref": "J.Phys.A39:9503-9532,2006",
"title": "Real time approach to tunneling in open quantum systems: decoherence and anomalous diffusion",
"url": "https://arxiv.org/abs/quant-ph/0603047"
},
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