Generalized Bogoliubov transformations versus D-pseudo-bosons

Fabio Bagarello, Bagarello, Fring

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We demonstrate that not all generalized Bogoliubov transformations lead to Dpseudo- bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining the transformation. For certain values of the parameters, we find that the norms of the vectors in sets of eigenvectors of two related apparently non-selfadjoint number-like operators possess different types of asymptotic behavior. We use this result to deduce further that they constitute bases for a Hilbert space, albeit neither of them can form a Riesz base. When the constraints are relaxed, they cease to be Hilbert space bases but remain D-quasibases.
Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Mathematical Physics
Volume56
Publication statusPublished - 2015

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Hilbert space
Bosons
space bases
bosons
Riesz Basis
norms
Eigenvector
Deduce
eigenvectors
Correspondence
Asymptotic Behavior
Norm
operators
Operator
Demonstrate

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Generalized Bogoliubov transformations versus D-pseudo-bosons. / Bagarello, Fabio; Bagarello; Fring.

In: Journal of Mathematical Physics, Vol. 56, 2015, p. 1-10.

Research output: Contribution to journalArticle

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