1997/05/17 by F. C. Alcaraz, F C Alcaraz, S. Dasmahapatra +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Matrix (chemical analysis) #Product (mathematics) #Quadratic equation #Quantum Information and Cryptography #Quantum many-body systems #State (computer science) #Stochastic process #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/31/3/004
50 pages, LaTeX with epic, eepic macros, submitted to J. Phys. A
arxiv created 1997/05/17 · openalex publication_date 1998/01/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.