Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations Journal Article


Author(s): Nam, Phan Thanh; Napiórkowski, Marcin; Solovej, Jan P
Article Title: Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
Affiliation IST Austria
Abstract: We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute.
Keywords: Bogoliubov transformation; Fock space; Quadratic Hamiltonian
Journal Title: Journal of Functional Analysis
Volume: 270
Issue 11
ISSN: 1096-0783
Publisher: Academic Press  
Date Published: 2016-06-01
Start Page: 4340
End Page: 4368
URL:
DOI: 10.1016/j.jfa.2015.12.007
Notes: We thank Jan Dereziński for several inspiring discussions and useful remarks. We thank the referee for helpful comments. J.P.S. thanks the Erwin Schrödinger Institute for the hospitality during the thematic programme “Quantum many-body systems, random matrices, and disorder”. We gratefully acknowledge the financial supports by the European Union's Seventh Framework Programme under the ERC Advanced Grant ERC-2012-AdG 321029 (J.P.S.) and the REA grant agreement No. 291734 (P.T.N.), as well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185 and the Austrian Science Fund (FWF) project No. P 27533-N27 (M.N.).
Open access: yes (repository)