dorsal/arxiv
View SchemaAn open--quantum--system formulation of particle decay
| Authors | Reinhold A. Bertlmann, Walter Grimus, Beatrix C. Hiesmayr |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602116 |
| URL | https://arxiv.org/abs/quant-ph/0602116 |
| DOI | 10.1103/PhysRevA.73.054101 |
| Journal | Phys.Rev.A73:054101,2006 |
Abstract
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional term of the Lindblad form, the socalled dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-hermitian part of H_{eff} --the ``particle decay''-- can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the new formulation of the time evolution on the enlarged space has a hermitian Hamiltonian and is probability conserving. The equivalence of the new formulation with the original one demonstrates that the time evolution which is governed by a non-hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with hermitian Hamiltonians.
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"abstract": "We consider an open quantum system which contains unstable states. The time\nevolution of the system can be described by an effective non-hermitian\nHamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an\nadditional term of the Lindblad form, the socalled dissipator. We show that,\nafter enlarging the original Hilbert space by states which represent the decay\nproducts of the unstable states, the non-hermitian part of H_{eff} --the\n``particle decay\u0027\u0027-- can be incorporated into the dissipator of the enlarged\nspace via a specific Lindblad operator. Thus the new formulation of the time\nevolution on the enlarged space has a hermitian Hamiltonian and is probability\nconserving. The equivalence of the new formulation with the original one\ndemonstrates that the time evolution which is governed by a non-hermitian\nHamiltonian and a dissipator of the Lindblad form is nevertheless completely\npositive, just as systems with hermitian Hamiltonians.",
"arxiv_id": "quant-ph/0602116",
"authors": [
"Reinhold A. Bertlmann",
"Walter Grimus",
"Beatrix C. Hiesmayr"
],
"categories": [
"quant-ph",
"hep-ph"
],
"doi": "10.1103/PhysRevA.73.054101",
"journal_ref": "Phys.Rev.A73:054101,2006",
"title": "An open--quantum--system formulation of particle decay",
"url": "https://arxiv.org/abs/quant-ph/0602116"
},
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