N-species stochastic models with boundaries and quadratic algebras

被引:46
作者
Alcaraz, FC [1 ]
Dasmahapatra, S
Rittenberg, V
机构
[1] Univ Fed Sao Carlos, Dept Fis, BR-13565905 Sao Carlos, SP, Brazil
[2] City Univ London, Dept Math, London EC1V 0HB, England
[3] SISSA, I-34014 Trieste, Italy
[4] Univ Bonn, Inst Phys, D-53115 Bonn, Germany
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1998年 / 31卷 / 03期
关键词
D O I
10.1088/0305-4470/31/3/004
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页码:845 / 878
页数:34
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