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N-species stochastic models with boundaries and quadratic algebras

N-species stochastic models with boundaries and quadratic algebras
N-species stochastic models with boundaries and quadratic algebras
Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of representations considered depend on the boundary conditions. In the language of quantum chains we obtain the ground state of N-state quantum chains with free boundary conditions or with non-diagonal boundary terms at one or both ends. In contrast to problems involving the Bethe Ansatz, we do not have a general framework for arbitrary N which when specialized, gives the known results for N=2; in fact, the N=2 and N>2 cases appear to be very different.
0305-4470
845-878
Alcaraz, F. C.
2dcb0444-4454-4fa4-b510-025d19fc4680
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Rittenberg, Vladimir
c5663764-b49a-4692-b204-8a22515c82a1
Alcaraz, F. C.
2dcb0444-4454-4fa4-b510-025d19fc4680
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Rittenberg, Vladimir
c5663764-b49a-4692-b204-8a22515c82a1

Alcaraz, F. C., Dasmahapatra, Srinandan and Rittenberg, Vladimir (1998) N-species stochastic models with boundaries and quadratic algebras. Journal of Physics A: Mathematical and General, 31, 845-878.

Record type: Article

Abstract

Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of representations considered depend on the boundary conditions. In the language of quantum chains we obtain the ground state of N-state quantum chains with free boundary conditions or with non-diagonal boundary terms at one or both ends. In contrast to problems involving the Bethe Ansatz, we do not have a general framework for arbitrary N which when specialized, gives the known results for N=2; in fact, the N=2 and N>2 cases appear to be very different.

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Published date: 1998
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 264092
URI: https://eprints.soton.ac.uk/id/eprint/264092
ISSN: 0305-4470
PURE UUID: 1b67d9ee-45b4-46ed-bb54-0061e7ce6026

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Date deposited: 29 May 2007
Last modified: 11 Nov 2017 10:31

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