dorsal/arxiv
View SchemaNonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions
| Authors | R. Schilling, Mark Vogelsberger, D. A. Garanin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607221 |
| URL | https://arxiv.org/abs/quant-ph/0607221 |
| DOI | 10.1088/0305-4470/39/44/008 |
Abstract
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of \alpha_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a nonuniversal one, involving the full time dependence of E_(+-)(t). This general result is applied to the Akulin-Schleich model where the initial upper level is damped with damping constant $\gamma$. For analytic power-law sweeps we find that Stueckelberg oscillations of P exist for gamma smaller than a critical value gamma_c and disappear for gamma > gamma_c. A physical interpretation of this behavior will be presented by use of a damped harmonic oscillator.
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"abstract": "We study the Landau-Zener Problem for a decaying two-level-system described\nby a non-hermitean Hamiltonian, depending analytically on time. Use of a\nsuper-adiabatic basis allows to calculate the non-adiabatic transition\nprobability P in the slow-sweep limit, without specifying the Hamiltonian\nexplicitly. It is found that P consists of a ``dynamical\u0027\u0027 and a\n``geometrical\u0027\u0027 factors. The former is determined by the complex adiabatic\neigenvalues E_(t), only, whereas the latter solely requires the knowledge of\n\\alpha_(+-)(t), the ratio of the components of each of the adiabatic\neigenstates. Both factors can be split into a universal one, depending only on\nthe complex level crossing points, and a nonuniversal one, involving the full\ntime dependence of E_(+-)(t). This general result is applied to the\nAkulin-Schleich model where the initial upper level is damped with damping\nconstant $\\gamma$. For analytic power-law sweeps we find that Stueckelberg\noscillations of P exist for gamma smaller than a critical value gamma_c and\ndisappear for gamma \u003e gamma_c. A physical interpretation of this behavior will\nbe presented by use of a damped harmonic oscillator.",
"arxiv_id": "quant-ph/0607221",
"authors": [
"R. Schilling",
"Mark Vogelsberger",
"D. A. Garanin"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/44/008",
"title": "Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions",
"url": "https://arxiv.org/abs/quant-ph/0607221"
},
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