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Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations (1508.07321v2)
Published 28 Aug 2015 in math-ph, math.FA, and math.MP
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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