An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances

Details An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances

2010-06-03

arxiv.org/abs/1006.0606v2

Physics

Mathematical Physics

latex; 26 pages

Scientific paper

This paper is concerned with a linearized version of the transport problem where the Schr\"{o}dinger-Poisson operator is replaced by a non-autonomous Hamiltonian, slowly varying in time. We consider an explicitly solvable model where a semiclassical island is described by a flat potential barrier, while a time dependent 'delta' interaction is used as a model for a single quantum well. Introducing, in addition to the complex deformation, a further modification formed by artificial interface conditions, we give a reduced equation for the adiabatic evolution of the sheet density of charges accumulating around the interaction point.

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