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

Ali Faraj (1) , Andrea Mantile (2, 1) , Francis Nier (1, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CPT - Centre de Physique Théorique - UMR 7332
3 MICMAC - Methods and engineering of multiscale computing from atom to continuum

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.

Mots clés: linear adiabatic theory; non-selfadjoint Hamiltonians

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Ali Faraj, Andrea Mantile, Francis Nier. An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances. Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), 28 p. ⟨10.1088/1751-8113/43/47/474025⟩. ⟨hal-00492984⟩