Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are injected and extracted. By means of the method of Derrida e...
| Hlavní autoři: | , |
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| Médium: | Journal article |
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1996
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| _version_ | 1826305525132820480 |
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| author | Essler, F Rittenberg, V |
| author_facet | Essler, F Rittenberg, V |
| author_sort | Essler, F |
| collection | OXFORD |
| description | We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are injected and extracted. By means of the method of Derrida et al the stationary probability measure can be expressed as a matrix-product state involving two matrices forming a Fock-like representation of a general quadratic algebra. We obtain the representations of this algebra, which were unknown in the mathematical literature and use the two-dimensional one to derive exact expressions for the density profile and correlation functions. Using the correspondence between the stochastic model and a quantum spin chain, we obtain exact correlation functions for a spin-1/2 Heisenberg XXZ chain with non-diagonal boundary terms. Generalizations to other reaction-diffusion models are discussed. © 1996 IOP Publishing Ltd. |
| first_indexed | 2024-03-07T06:34:09Z |
| format | Journal article |
| id | oxford-uuid:f705561d-887c-43a8-b97c-a7f1a1bd983e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:34:09Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:f705561d-887c-43a8-b97c-a7f1a1bd983e2022-03-27T12:39:34ZRepresentations of the quadratic algebra and partially asymmetric diffusion with open boundariesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f705561d-887c-43a8-b97c-a7f1a1bd983eSymplectic Elements at Oxford1996Essler, FRittenberg, VWe consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are injected and extracted. By means of the method of Derrida et al the stationary probability measure can be expressed as a matrix-product state involving two matrices forming a Fock-like representation of a general quadratic algebra. We obtain the representations of this algebra, which were unknown in the mathematical literature and use the two-dimensional one to derive exact expressions for the density profile and correlation functions. Using the correspondence between the stochastic model and a quantum spin chain, we obtain exact correlation functions for a spin-1/2 Heisenberg XXZ chain with non-diagonal boundary terms. Generalizations to other reaction-diffusion models are discussed. © 1996 IOP Publishing Ltd. |
| spellingShingle | Essler, F Rittenberg, V Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title | Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title_full | Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title_fullStr | Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title_full_unstemmed | Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title_short | Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| title_sort | representations of the quadratic algebra and partially asymmetric diffusion with open boundaries |
| work_keys_str_mv | AT esslerf representationsofthequadraticalgebraandpartiallyasymmetricdiffusionwithopenboundaries AT rittenbergv representationsofthequadraticalgebraandpartiallyasymmetricdiffusionwithopenboundaries |