Resonance eigenfunctions in chaotic scattering systems

Martin Sieber

doi:10.1007/s12043-009-0106-8

Resonance eigenfunctions in chaotic scattering systems

Martin Sieber^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

Abstract

We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ℏh 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.

Original language	English
Pages (from-to)	543-551
Number of pages	9
Journal	Pramana - Journal of Physics
Volume	73
Issue number	3
DOIs	https://doi.org/10.1007/s12043-009-0106-8
Publication status	Published - Sept 2009

Bibliographical note

Funding Information:
This work was supported by the EPSRC grant EP/C515137/1. The author would like to thank Arul Lakshminarayan for helpful suggestions.

Keywords

Quantum chaos
Resonances
Semiclassics

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title = "Resonance eigenfunctions in chaotic scattering systems",

abstract = "We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ℏh 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.",

keywords = "Quantum chaos, Resonances, Semiclassics",

author = "Martin Sieber",

note = "Funding Information: This work was supported by the EPSRC grant EP/C515137/1. The author would like to thank Arul Lakshminarayan for helpful suggestions.",

year = "2009",

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T1 - Resonance eigenfunctions in chaotic scattering systems

AU - Sieber, Martin

N1 - Funding Information: This work was supported by the EPSRC grant EP/C515137/1. The author would like to thank Arul Lakshminarayan for helpful suggestions.

PY - 2009/9

Y1 - 2009/9

N2 - We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ℏh 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.

AB - We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ℏh 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.

KW - Quantum chaos

KW - Resonances

KW - Semiclassics

UR - http://www.scopus.com/inward/record.url?scp=70349554441&partnerID=8YFLogxK

U2 - 10.1007/s12043-009-0106-8

DO - 10.1007/s12043-009-0106-8

M3 - Article (Academic Journal)

AN - SCOPUS:70349554441

SN - 0304-4289

VL - 73

SP - 543

EP - 551

JO - Pramana - Journal of Physics

JF - Pramana - Journal of Physics

IS - 3

ER -

Resonance eigenfunctions in chaotic scattering systems

Abstract

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Keywords

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