000			03842nam a22004813i 4500
001			EBC4901857
003			MiAaPQ
005			20240729131324.0
006			m o d |
007			cr cnu||||||||
008			240724s2016 xx o ||||0 eng d
020			_a9781470428280 _q(electronic bk.)
020			_z9781470417055
035			_a(MiAaPQ)EBC4901857
035			_a(Au-PeEL)EBL4901857
035			_a(OCoLC)938459033
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQC174.17.H3 B33 2015
082	0		_a515/.39
100	1		_aBach, Volker.
245	1	0	_aDiagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2016.
264		4	_c©2015.
300			_a1 online resource (134 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.240
505	0		_aCover -- Title page -- Chapter I. Introduction -- Chapter II. Diagonalization of Quadratic Boson Hamiltonians -- II.1. Quadratic Boson Operators -- II.2. Main Results -- II.3. Historical Overview -- Chapter III. Brocket-Wegner Flow for Quadratic Boson Operators -- III.1. Setup of the Brocket-Wegner Flow -- III.2. Mathematical Foundations of our Method -- III.3. Asymptotic Properties of the Brocket-Wegner Flow -- Chapter IV. Illustration of the Method -- IV.1. The Brocket-Wegner Flow on Bogoliubov's Example -- IV.2. Blow-up of the Brocket-Wegner Flow -- Chapter V. Technical Proofs on the One-Particle Hilbert Space -- V.1. Well-Posedness of the Flow -- V.2. Constants of Motion -- V.3. Asymptotics Properties of the Flow -- Chapter VI. Technical Proofs on the Boson Fock Space -- VI.1. Existence and Uniqueness of the Unitary Propagator -- VI.2. Brocket-Wegner Flow on Quadratic Boson Operators -- VI.3. Quasi -Diagonalization of Quadratic Boson Operators -- VI.4. -Diagonalization of Quadratic Boson Operators -- Chapter VII. Appendix -- VII.1. Non-Autonomous Evolution Equations on Banach Spaces -- VII.2. Autonomous Generators of Bogoliubov Transformations -- VII.3. Trace and Representation of Hilbert-Schmidt Operators -- References -- Back Cover.
520			_aThe authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aHamiltonian operator.
650		0	_aMatrices.
650		0	_aHilbert space.
655		4	_aElectronic books.
700	1		_aBru, Jean-Bernard.
776	0	8	_iPrint version: _aBach, Volker _tDiagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations _dProvidence : American Mathematical Society,c2016 _z9781470417055
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901857 _zClick to View
999			_c127893 _d127893