Contractions of Product Density Operators of Systems of Identical Fermions and Bosons
Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons are proved to be asymptotically equivalent to, respectively...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/890523 |
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| Summary: | Recurrence and explicit formulae for contractions (partial traces)
of antisymmetric and symmetric products of identical trace class operators
are derived. Contractions of product density operators of systems of identical
fermions and bosons are proved to be asymptotically equivalent to, respectively,
antisymmetric and symmetric products of density operators of a single
particle, multiplied by a normalization integer. The asymptotic equivalence
relation is defined in terms of the thermodynamic limit of expectation values
of observables in the states represented by given density operators. For
some weaker relation of asymptotic equivalence, concerning the thermodynamic
limit of expectation values of product observables, normalized antisymmetric
and symmetric products of density operators of a single particle are
shown to be equivalent to tensor products of density operators of a single
particle. |
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| ISSN: | 0161-1712 1687-0425 |