Perturbation Theory: Relatively Bounded Perturbations

1996 ◽  
pp. 149-159
Author(s):  
P. D. Hislop ◽  
I. M. Sigal
Keyword(s):  
Perturbation Theory ◽  
Bounded Perturbations

scholarly journals Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Liu ◽  
Meiru Xu
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Relations ◽  
Deficiency Indices ◽  
Bounded Perturbations

AbstractThis paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

scholarly journals Invariance of Deficiency Indices of Second-Order Symmetric Linear Difference Equations under Perturbations

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yan Liu
Keyword(s):  
Perturbation Theory ◽  
Difference Equations ◽  
Second Order ◽  
Linear Difference Equations ◽  
Linear Relations ◽  
Deficiency Indices ◽  
Bounded Perturbations

This paper focuses on the invariance of deficiency indices of second-order symmetric linear difference equations under perturbations. By applying the perturbation theory of Hermitian linear relations, the invariance of deficiency indices of the corresponding minimal subspaces under bounded and relatively bounded perturbations is built. As a consequence, the invariance of limit types of second-order symmetric linear difference equations under bounded and relatively bounded perturbations is obtained.

Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States

2003 ◽  
Vol 15 (05) ◽  
pp. 447-489 ◽  
Author(s):  
J. Dereziński ◽  
V. Jakšić ◽  
C.-A. Pillet
Keyword(s):  
Perturbation Theory ◽  
Large Class ◽  
Kms States ◽  
Kms State ◽  
Bounded Perturbations

Given a W*-algebra [Formula: see text] with a W*-dynamics τ, we prove the existence of the perturbed W*-dynamics for a large class of unbounded perturbations. We compute its Liouvillean. If τ has a β-KMS state, and the perturbation satisfies some mild assumptions related to the Golden–Thompson inequality, we prove the existence of a β-KMS state for the perturbed W*-dynamics. These results extend the well known constructions due to Araki valid for bounded perturbations.

On the stability of the limit-point property of “Kauffman expressions” under relatively bounded perturbations

1986 ◽  
Vol 103 (1-2) ◽  
pp. 73-89 ◽  
Author(s):  
Bernhard Mergler ◽  
Bernd Schultze
Keyword(s):  
Perturbation Theory ◽  
Limit Point ◽  
Point Property ◽  
Limit Point Case ◽  
Whole Class ◽  
The Stability ◽  
Bounded Perturbations ◽  
Positive Coefficients

SynopsisIn this paper we show that for the whole class of differential expressions in the limit-point case considered by Kauffman in [2], the perturbation theory yields a limit-point criterion for a much wider class of ordinary differential expressions. More general coefficients are admitted which may be eventually negative provided they are “dominated” by some other positive coefficients. This generalises results in [4], [5] and [6].

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

Sign in / Sign up

Export Citation Format

Share Document