Tridiagonal Symmetries of Models of Nonequilibrium Physics

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2008
• Автор: Aneva, B.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2008
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/149025
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Tridiagonal Symmetries of Models of Nonequilibrium Physics / B. Aneva // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 36 назв. — англ.

We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices defining a noncommutative space with a quantum group symmetry. Boundary processes lead to a reduction of the bulk symmetry. We argue that the boundary operators of an interacting system with simple exclusion generate a tridiagonal algebra whose irreducible representations are expressed in terms of the Askey-Wilson polynomials. We show that the boundary algebras of the symmetric and the totally asymmetric processes are the proper limits of the partially asymmetric ones. In all three type of processes the tridiagonal algebra arises as a symmetry of the boundary problem and allows for the exact solvability of the model.