Hyperoctahedral Chen calculus for effective Hamiltonians

We tackle the problem of unraveling the algebraic structure of computations of effective Hamiltonians. This is an important subject in view of applications to chemistry, solid state physics or quantum field theory. We show, among other things, that the correct framework for these computations is pro...

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Bibliographic Details
Published inJournal of algebra Vol. 322; no. 11; pp. 4105 - 4120
Main Authors Brouder, Christian, Patras, Frédéric
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2009
Elsevier
Subjects
Descent algebras
Hyperoctahedral groups
Mathematical Physics
Mathematics
Noncommutative symmetric functions
Physics
Descent algebras
Hyperoctahedral groups
Noncommutative symmetric functions
effective Hamiltonians
limite adiabatique
Magnus formula
Hamiltoniens effectifs
adiabatic limit
hyperoctahedral group
Groupe hyperoctaédral
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ISSN0021-8693
1090-266X
DOI10.1016/j.jalgebra.2009.07.017

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Summary:We tackle the problem of unraveling the algebraic structure of computations of effective Hamiltonians. This is an important subject in view of applications to chemistry, solid state physics or quantum field theory. We show, among other things, that the correct framework for these computations is provided by the hyperoctahedral group algebras. We define several structures on these algebras and give various applications. For example, we show that the adiabatic evolution operator (in the time-dependent interaction representation of an effective Hamiltonian) can be written naturally as a Picard-type series and has a natural exponential expansion.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2009.07.017