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Title: Wave operators, similarity and dynamics for a class of Schrödinger operators with generic non-mixed interface conditions in 1D

We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schrödinger operators having this form allow a new approach to the transverse quantum transport through resonant heterostructures. In this perspective, it is important to control the deformations effects introduced on the spectrum and on the time propagator by this class of non-selfadjoint perturbations. In order to obtain uniform-in-time estimates of the perturbed semigroup, our strategy consists in constructing stationary wave operators allowing to intertwine the modified non-selfadjoint Schrödinger operator with a “physical” Hamiltonian. For small values of a deformation parameter “θ,” this yields a dynamical comparison between the two models showing that the distance between the corresponding semigroups is dominated by ‖θ‖ uniformly in time in the L{sup 2}-operator norm.
Authors:
 [1]
  1. Laboratoire de Mathématiques, Université de Reims - FR3399 CNRS, Moulin de la Housse BP 1039, 51687 Reims (France)
Publication Date:
OSTI Identifier:
22218152
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 8; Other Information: (c) 2013 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; DEFORMATION; HAMILTONIANS; LAPLACIAN; MODIFICATIONS; PERTURBATION THEORY; PROPAGATOR; SCHROEDINGER EQUATION