Zapiski Nauchnykh Seminarov POMI
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zap. Nauchn. Sem. POMI: Year: Volume: Issue: Page: Find

 Zap. Nauchn. Sem. POMI, 2017, Volume 465, Pages 13–26 (Mi znsl6528)

Continuous time multidimensional walks as an integrable model

N. Bogoliubovab

a St.-Petersburg Department of Steklov Institute of Mathematics, RAS, Fontanka 27, St.-Petersburg, Russia
b ITMO University, Kronverksky 49, St.-Petersburg, Russia

Abstract: Continuous time walks in multidimensional symplectical lattices are considered. It is shown that the generating functions of random walks and the transition amplitudes of continuous time quantum walks are expressed through the dynamical correlation functions of the exactly solvable model describing strongly correlated bosons on a chain, the so-called phase model. The number of random lattice paths of fixed number of steps connecting the starting and ending points of the multidimensional lattice is expressed through the solutions of Bethe equations of the phase model. Its asymptotic is obtained in the limit of the large number of steps.

Key words and phrases: continuous time walks, random walks, quantum walks, multidimensional lattice, integrable models, correlation functions, Schur functions.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00296 Partially supported by RFBR grant no. 16-01-00296.

Full text: PDF file (203 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2019, 238:6, 769–778

UDC: 517.9
Language:

Citation: N. Bogoliubov, “Continuous time multidimensional walks as an integrable model”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 13–26; J. Math. Sci. (N. Y.), 238:6 (2019), 769–778

Citation in format AMSBIB
\Bibitem{Bog17} \by N.~Bogoliubov \paper Continuous time multidimensional walks as an integrable model \inbook Questions of quantum field theory and statistical physics. Part~24 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 465 \pages 13--26 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6528} \transl \jour J. Math. Sci. (N. Y.) \yr 2019 \vol 238 \issue 6 \pages 769--778 \crossref{https://doi.org/10.1007/s10958-019-04274-1}