A strong operator topology adiabatic theorem

Alexander Elgart; Jeffrey H. Schenker

doi:10.1142/S0129055X02001247

A strong operator topology adiabatic theorem

Alexander Elgart, Jeffrey H. Schenker

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

Original language	English
Pages (from-to)	569-584
Number of pages	16
Journal	Reviews in Mathematical Physics
Volume	14
Issue number	6
DOIs	https://doi.org/10.1142/S0129055X02001247
State	Published - 1 Jun 2002
Externally published	Yes

Keywords

Adiabatic evolution
Quantum theory
Spectral theory

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1142/S0129055X02001247

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title = "A strong operator topology adiabatic theorem",

abstract = "We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.",

keywords = "Adiabatic evolution, Quantum theory, Spectral theory",

author = "Alexander Elgart and Schenker, {Jeffrey H.}",

note = "Funding Information: We are grateful to M. Aizenman for the example presented in Sec. 5 as well as the suggestion to consider the strong operator topology. We are also indebted to Y. Avron for the insight that the norm adiabatic theorem is linked with the presence of an intrinsic time scale. This work was partially supported by the NSF Grant PHY-9971149 (AE).",

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AU - Elgart, Alexander

AU - Schenker, Jeffrey H.

N1 - Funding Information: We are grateful to M. Aizenman for the example presented in Sec. 5 as well as the suggestion to consider the strong operator topology. We are also indebted to Y. Avron for the insight that the norm adiabatic theorem is linked with the presence of an intrinsic time scale. This work was partially supported by the NSF Grant PHY-9971149 (AE).

PY - 2002/6/1

Y1 - 2002/6/1

N2 - We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

AB - We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

KW - Adiabatic evolution

KW - Quantum theory

KW - Spectral theory

UR - http://www.scopus.com/inward/record.url?scp=0036599848&partnerID=8YFLogxK

U2 - 10.1142/S0129055X02001247

DO - 10.1142/S0129055X02001247

M3 - Article

AN - SCOPUS:0036599848

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VL - 14

SP - 569

EP - 584

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 6

ER -

A strong operator topology adiabatic theorem

Abstract

Keywords

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