Implementing Bogoliubov Transformations Beyond the Shale–Stinespring Condition
Year: 2025
Type: article
Abstract: We define infinite tensor product spaces that extend Fock space, and allow for implementing Bogoliubov transformations which violate the Shale or Shale-Stinespring condition. So an implementation on the usual Fock space would not be possible. Both the bosonic and fermionic case are covered. Conditions for implementability in an extended sense are stated and proved. From these, we derive conditions for a quadratic Hamiltonian to be diagonalizable by a Bogoliubov transformation that is implementable in the extended sense. We apply our results to Bogoliubov transformations from quadratic bosonic interactions and BCS models, where the Shale or Shale-Stinespring condition is violated, but an extended implementation nevertheless works.
Source: Journal of Statistical Physics
Author: Sascha Lill
Institution: University of Milan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funders: Università degli Studi di Milano, Ministerio de Ciencia, Innovación y Universidades, European Commission, Deutscher Akademischer Austauschdienst, Eusko Jaurlaritza, Ministerio de Ciencia e Innovación, Basque Center for Applied Mathematics, Gruppo Nazionale per la Fisica Matematica, European Research Council
OpenAlex ID: W4408910234