skip to main content

SciTech ConnectSciTech Connect

Title: Quantum evolution in the regime of quantum wells in a semiclassical island with artificial interface conditions

We introduce a modified Schrödinger operator where the semiclassical Laplacian is perturbed by artificial interface conditions occurring at the boundaries of the potential's support. The corresponding dynamics is analyzed in the regime of quantum wells in a semiclassical island. Under a suitable energy constraint for the initial states, we show that the time propagator is stable with respect to the non-self-adjont perturbation, provided that this is parametrized through infinitesimal functions of the semiclassical parameter “h.” It has been recently shown that h-dependent artificial interface conditions allow a new approach to the adiabatic evolution problem for the shape resonances in models of resonant heterostructures. Our aim is to provide with a rigorous justification of this method.
Authors:
 [1]
  1. Laboratoire de Mathématiques de Reims, EA-4535 and FR ARC CNRS-3399, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2 (France)
Publication Date:
OSTI Identifier:
22306033
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INTERFACES; LAPLACIAN; PERTURBATION THEORY; PROPAGATOR; QUANTUM WELLS; SEMICLASSICAL APPROXIMATION