×
Bollé, D.; Danneels, C.; Osborn, T. A.

Local and global spectral shift functions in \({\mathbb{R}}^ 2\). (English) Zbl 0664.46076

J. Math. Phys. 30, No. 2, 420-432 (1989).
The energy-dependent trace-class time-delay operator associated with the transit time of a scattering system through a finite space region \(\Sigma \subseteq {\mathbb{R}}^ 2\) is used to define a local (\(\Sigma\)-dependent) version of the Krein spectal shift function. If the region \(\Sigma\) is a disk of radius r, it is proved that as \(r\to \infty\) the local spectral shift function converges, for almost all energies, to the original spectral shift function of Krein. This result continues to be valid for systems exhibiting zero-energy resonance behavior.

Cited in 3 Documents

MSC:

46N99 Miscellaneous applications of functional analysis
47A40 Scattering theory of linear operators
81U05 \(2\)-body potential quantum scattering theory

Keywords:

quantum-mechanical scattering in two dimensions of a single spinless particle; energy-dependent trace-class time-delay operator; transit time of a scattering system; Krein spectal shift function; zero-energy resonance behavior
Cite Review PDF
Full Text: DOI

References:

[1] Krein M. G., Mat. Sb. 75 pp 597– (1953)
[2] Krein M. G., Sov. Math. Dokl. 3 pp 707– (1962)
[3] Birman M. S., Sov. Math. Dokl. 3 pp 740– (1962)
[4] DOI: 10.1103/PhysRev.118.349 · Zbl 0092.19001 · doi:10.1103/PhysRev.118.349
[5] Jauch J. M., Helv. Phys. Acta 40 pp 217– (1967)
[6] Jauch J. M., Helv. Phys. Acta 45 pp 398– (1972)
[7] DOI: 10.1016/0003-4916(80)90370-X · Zbl 0428.47008 · doi:10.1016/0003-4916(80)90370-X
[8] Martin Ph. A., Acta Phys. Austriaca Suppl. 23 pp 157– (1981)
[9] DOI: 10.1007/BF01609841 · doi:10.1007/BF01609841
[10] DOI: 10.1007/BF00419932 · Zbl 0517.47010 · doi:10.1007/BF00419932
[11] DOI: 10.1007/BF00419932 · Zbl 0517.47010 · doi:10.1007/BF00419932
[12] DOI: 10.1063/1.525891 · Zbl 0517.47007 · doi:10.1063/1.525891
[13] DOI: 10.1063/1.526216 · Zbl 0565.35098 · doi:10.1063/1.526216
[14] Agmon S., Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 pp 151– (1975)
[15] DOI: 10.1007/BF02803406 · Zbl 0512.35062 · doi:10.1007/BF02803406
[16] DOI: 10.1016/0003-4916(80)90338-3 · Zbl 0455.35112 · doi:10.1016/0003-4916(80)90338-3
[17] Bollé D., Helv. Phys. Acta 56 pp 1064– (1983)
[18] DOI: 10.1063/1.526314 · Zbl 0554.35094 · doi:10.1063/1.526314
[19] DOI: 10.1103/PhysRevLett.56.900 · doi:10.1103/PhysRevLett.56.900
[20] Bollé D., Ann. Inst. H. Poincaré 48 pp 175– (1988)
[21] DOI: 10.1070/RM1971v026n01ABEH003813 · Zbl 0226.47029 · doi:10.1070/RM1971v026n01ABEH003813
[22] DOI: 10.1070/RM1971v026n01ABEH003813 · Zbl 0226.47029 · doi:10.1070/RM1971v026n01ABEH003813
[23] DOI: 10.1063/1.526704 · Zbl 0582.47013 · doi:10.1063/1.526704
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.