A note on the switching adiabatic theorem
| Autor: | Elgart, Alexander, Hagedorn, George A. |
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| Rok vydání: | 2012 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4748968 |
| Popis: | We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\alpha$ as a function of time, and we show that the error in adiabatic approximation remains small for running times of order $g^{-2}\,|\ln\,g\,|^{6\alpha}$. Here $g$ denotes the minimal spectral gap between the eigenvalue(s) of interest and the rest of the spectrum of the instantaneous Hamiltonian. Comment: 20 pages, no figures, to appear in JMP |
| Databáze: | arXiv |
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