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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.


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

UDC: 517.9
Received: 04.12.2017
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}


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