Consistency between adiabatic and nonadiabatic geometric phases for nonselfadjoint hamiltonians
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Publication:6402028
DOI10.1088/1751-8113/45/33/335301arXiv2206.06748MaRDI QIDQ6402028
John P. Killingbeck, Arnaud Leclerc, David Viennot, Georges Jolicard
Publication date: 14 June 2022
Abstract: We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one is the adiabatic limit of the nonadiabatic geometric phase. This apparent inconsistency is resolved by observing that the difference between the two expressions is compensated by a small deviation in the dynamical phases.
Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)
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