Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

TY - JOUR

T1 - Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

AU - Nam, Phan Thanh

AU - Napiorkowski, Marcin

AU - Solovej, Jan Philip

PY - 2016/6/1

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

SN - 0022-1236

VL - 270

SP - 4340

EP - 4368

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

ER -