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Precise coupling terms in adiabatic quantum evolution
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UNSPECIFIED (2005) Precise coupling terms in adiabatic quantum evolution. ANNALES HENRI POINCARE, 6 (2). pp. 217-246. doi:10.1007/s00023-005-0204-1 ISSN 1424-0637.
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Official URL: http://dx.doi.org/10.1007/s00023-005-0204-1
Abstract
It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | ANNALES HENRI POINCARE | ||||
Publisher: | BIRKHAUSER VERLAG AG | ||||
ISSN: | 1424-0637 | ||||
Official Date: | April 2005 | ||||
Dates: |
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Volume: | 6 | ||||
Number: | 2 | ||||
Number of Pages: | 30 | ||||
Page Range: | pp. 217-246 | ||||
DOI: | 10.1007/s00023-005-0204-1 | ||||
Publication Status: | Published |
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