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dc.contributor.author
Ibrogimov, Orif O.
dc.date.accessioned
2020-09-02T11:08:29Z
dc.date.available
2020-08-01T03:29:21Z
dc.date.available
2020-09-02T11:08:29Z
dc.date.issued
2020-07
dc.identifier.issn
0129-055X
dc.identifier.issn
1793-6659
dc.identifier.other
10.1142/S0129055X20500154
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/429547
dc.description.abstract
We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling alpha >0 in the case when the dispersion relation is a bounded function. We derive an explicit description of the essential spectrum which consists of the so-called two- and three-particle branches that can be separated by a gap if the coupling is sufficiently large. It turns out, that depending on the location of the coupling constant and the energy level of the atom (w.r.t. certain constants depending on the maximal and the minimal values of the boson energy) as well as the validity or the violation of the infrared regularity type conditions, the essential spectrum is either a single finite interval or a disjoint union of at most six finite intervals. The corresponding critical values of the coupling constant are determined explicitly and the asymptotic lengths of the possible gaps are given when a approaches to the respective critical value. Under minimal smoothness and regularity conditions on the boson dispersion relation and the coupling function, we show that discrete eigenvalues can never accumulate at the edges of the two-particle branch. Moreover, we show the absence of the discrete eigenvalue accumulation at the edges of the three-particle branch in the infrared regular case.
en_US
dc.language.iso
en
en_US
dc.publisher
World Scientific
en_US
dc.subject
Spin-boson Hamiltonian
en_US
dc.subject
Fock space
en_US
dc.subject
discrete spectrum
en_US
dc.subject
essential spectrum
en_US
dc.title
Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation
en_US
dc.type
Journal Article
dc.date.published
2019-11-21
ethz.journal.title
Reviews in Mathematical Physics
ethz.journal.volume
32
en_US
ethz.journal.issue
6
en_US
ethz.journal.abbreviated
Rev. Math. Phys.
ethz.pages.start
2050015
en_US
ethz.size
28 p.
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Singapore
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2020-08-01T03:29:26Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-09-02T11:08:40Z
ethz.rosetta.lastUpdated
2021-02-15T16:50:11Z
ethz.rosetta.versionExported
true
ethz.COinS
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