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Perturbation theory for the logarithm of a positive operator.
- Source :
-
Journal of High Energy Physics . Nov2023, Vol. 2023 Issue 11, p1-24. 24p. - Publication Year :
- 2023
-
Abstract
- In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆0, whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some "contact terms". [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11266708
- Volume :
- 2023
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- 174312545
- Full Text :
- https://doi.org/10.1007/JHEP11(2023)097