Smooth adiabatic evolutions with leaky power tails

J. E. Avron; A. Elgart

doi:10.1088/0305-4470/32/50/102

Smooth adiabatic evolutions with leaky power tails

J. E. Avron, A. Elgart

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

2 Scopus citations

Abstract

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. In general, adiabatic evolutions without a gap condition do not seem to have this feature. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.

Original language	English
Pages (from-to)	L537-L546
Journal	Journal of Physics A: Mathematical and General
Volume	32
Issue number	50
DOIs	https://doi.org/10.1088/0305-4470/32/50/102
State	Published - 17 Dec 1999
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy (all)

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10.1088/0305-4470/32/50/102

Cite this

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title = "Smooth adiabatic evolutions with leaky power tails",

abstract = "Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. In general, adiabatic evolutions without a gap condition do not seem to have this feature. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.",

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AU - Elgart, A.

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N2 - Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. In general, adiabatic evolutions without a gap condition do not seem to have this feature. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.

AB - Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. In general, adiabatic evolutions without a gap condition do not seem to have this feature. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.

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DO - 10.1088/0305-4470/32/50/102

M3 - Article

AN - SCOPUS:0033579254

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

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Smooth adiabatic evolutions with leaky power tails

Abstract

ASJC Scopus subject areas

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