Multi-Dimensional Random Walks and Integrable Phase Models
- Authors: Bogoliubov N.1, Malyshev C.1
-
Affiliations:
- St.Petersburg Department of Steklov Institute of Mathematics, ITMO University
- Issue: Vol 224, No 2 (2017)
- Pages: 199-213
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239524
- DOI: https://doi.org/10.1007/s10958-017-3405-5
- ID: 239524
Cite item
Abstract
We consider random multi-dimensional lattice walks bounded by a hyperplane, calling them walks over multi-dimensional simplicial lattices. We demonstrate that generating functions of these walks are dynamical correlation functions of a certain type of exactly solvable quantum phase models describing strongly correlated bosons on a chain. Walks over oriented lattices are related to the phase model with a non-Hermitian Hamiltonian, while walks over disoriented ones are related to the model with a Hermitian Hamiltonian. The calculation of the generating functions is based on the algebraic Bethe Ansatz approach to the solution of integrable models. The answers are expressed through symmetric functions. Continuous-time quantum walks bounded by a onedimensional lattice of finite length are also studied. Bibliography: 40 titles.
About the authors
N. Bogoliubov
St.Petersburg Department of Steklov Institute of Mathematics, ITMO University
Author for correspondence.
Email: bogoliubov@pdmi.ras.ru
Russian Federation, St.Petersburg
C. Malyshev
St.Petersburg Department of Steklov Institute of Mathematics, ITMO University
Author for correspondence.
Email: malyshev@pdmi.ras.ru
Russian Federation, St.Petersburg