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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1849395466926555136 |
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| author | Wiktor Radzki |
| author_facet | Wiktor Radzki |
| author_sort | Wiktor Radzki |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a9f14fb4e0684a139ea08f83cb1256ee |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a9f14fb4e0684a139ea08f83cb1256ee2025-08-20T03:39:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/890523890523Contractions of Product Density Operators of Systems of Identical Fermions and BosonsWiktor Radzki0Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, PolandRecurrence 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.http://dx.doi.org/10.1155/2010/890523 |
| spellingShingle | Wiktor Radzki Contractions of Product Density Operators of Systems of Identical Fermions and Bosons International Journal of Mathematics and Mathematical Sciences |
| title | Contractions of Product Density Operators of Systems of Identical Fermions and Bosons |
| title_full | Contractions of Product Density Operators of Systems of Identical Fermions and Bosons |
| title_fullStr | Contractions of Product Density Operators of Systems of Identical Fermions and Bosons |
| title_full_unstemmed | Contractions of Product Density Operators of Systems of Identical Fermions and Bosons |
| title_short | Contractions of Product Density Operators of Systems of Identical Fermions and Bosons |
| title_sort | contractions of product density operators of systems of identical fermions and bosons |
| url | http://dx.doi.org/10.1155/2010/890523 |
| work_keys_str_mv | AT wiktorradzki contractionsofproductdensityoperatorsofsystemsofidenticalfermionsandbosons |