Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

Phan Thanh  Nam; Marcin Napiorkowski; Jan Philip Solovej

doi:10.1016/j.jfa.2015.12.007

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

Phan Thanh Nam, Marcin Napiorkowski, Jan Philip Solovej

Department of Mathematical Sciences

24 Citations (Scopus)

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.

Original language	English
Journal	Journal of Functional Analysis
Volume	270
Issue number	11
Pages (from-to)	4340–4368
ISSN	0022-1236
DOIs	https://doi.org/10.1016/j.jfa.2015.12.007
Publication status	Published - 1 Jun 2016

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10.1016/j.jfa.2015.12.007

https://arxiv.org/pdf/1508.07321v2.pdf

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title = "Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations",

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. ",

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AU - Nam, Phan Thanh

AU - Napiorkowski, Marcin

AU - Solovej, Jan Philip

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Y1 - 2016/6/1

N2 - 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.

AB - 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.

UR - https://arxiv.org/pdf/1508.07321v2.pdf

U2 - 10.1016/j.jfa.2015.12.007

DO - 10.1016/j.jfa.2015.12.007

M3 - Journal article

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VL - 270

SP - 4340

EP - 4368

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

ER -

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

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