Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations
Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations
AMS | Mathematics | November 13, 2015 | ISBN-10: 1470417057 | 134 pages | pdf | 1.5 mb
AMS | Mathematics | November 13, 2015 | ISBN-10: 1470417057 | 134 pages | pdf | 1.5 mb
by Volker Bach, Jean-Bernard Bru
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space.
Abstract
We study a non–autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal infinity. We demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket–Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non–linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
Table of Contents
Introduction
Diagonalization of quadratic boson Hamiltonians
Brocket-Wegner flow for quadratic boson operators
Illustration of the method
Technical proofs on the one-particle Hilbert space
Technical proofs on the boson Fock space
Appendix
References
More info and Hardcover at AMS
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