dorsal/arxiv
View SchemaTunneling out of a time-dependent well
| Authors | Tobias Kramer, Marcos Moshinsky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505099 |
| URL | https://arxiv.org/abs/quant-ph/0505099 |
| DOI | 10.1088/0305-4470/38/26/011 |
| Journal | J. Phys. A: Math. Gen. vol. 38 pp. 5993-6003 (2005) |
Abstract
Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent Hamiltonians which are not higher than quadratic in the position operator, like i.e the driven harmonic oscillator with time-dependent frequency. The second class is related to the existence of additional invariants in the Hamiltonian, which can be used to map the solution of the time-dependent problem to that of a related time-independent one. In this article we discuss and develop analytic methods for solving time-dependent tunneling problems, which cannot be addressed by using quadratic Hamiltonians. Specifically, we give an analytic solution to the problem of tunneling from an attractive time-dependent potential which is embedded in a long-range repulsive potential. Recent progress in atomic physics makes it possible to observe experimentally time-dependent phenomena and record the probability distribution over a long range of time. Of special interest is the observation of macroscopical quantum-tunneling phenomena in Bose-Einstein condensates with time-dependent trapping potentials. We apply our model to such a case in the last section.
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"abstract": "Solutions to explicit time-dependent problems in quantum mechanics are rare.\nIn fact, all known solutions are coupled to specific properties of the\nHamiltonian and may be divided into two categories: One class consists of\ntime-dependent Hamiltonians which are not higher than quadratic in the position\noperator, like i.e the driven harmonic oscillator with time-dependent\nfrequency. The second class is related to the existence of additional\ninvariants in the Hamiltonian, which can be used to map the solution of the\ntime-dependent problem to that of a related time-independent one.\n In this article we discuss and develop analytic methods for solving\ntime-dependent tunneling problems, which cannot be addressed by using quadratic\nHamiltonians. Specifically, we give an analytic solution to the problem of\ntunneling from an attractive time-dependent potential which is embedded in a\nlong-range repulsive potential.\n Recent progress in atomic physics makes it possible to observe experimentally\ntime-dependent phenomena and record the probability distribution over a long\nrange of time. Of special interest is the observation of macroscopical\nquantum-tunneling phenomena in Bose-Einstein condensates with time-dependent\ntrapping potentials. We apply our model to such a case in the last section.",
"arxiv_id": "quant-ph/0505099",
"authors": [
"Tobias Kramer",
"Marcos Moshinsky"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/26/011",
"journal_ref": "J. Phys. A: Math. Gen. vol. 38 pp. 5993-6003 (2005)",
"title": "Tunneling out of a time-dependent well",
"url": "https://arxiv.org/abs/quant-ph/0505099"
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