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Zap. Nauchn. Sem. POMI, 2012, Volume 398, Pages 5–25 (Mi znsl5193)  

This article is cited in 3 scientific papers (total in 3 papers)

Scalar products of the state vectors in the totally asymmetric exactly solvable models on a ring

N. M. Bogoliubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The exactly solvable totally asymmetric models of the low dimensional non-equilibrium physics on a ring, namely the totally asymmetric simple exclusion process and the totally asymmetric simple zero range process, are considered. The Quantum Inverse Method allows to calculate the scalar products of the state vectors of the models and to represent the answers in the determinantal form. It is shown that the eigenvectors of the models form a complete orthogonal basis. The projections of the state vectors on a stationary states, time independent ones, are studied.

Key words and phrases: quantum integrability, correlation functions, stochastic particle dynamics, totally asymmetric process.

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English version:
Journal of Mathematical Sciences (New York), 2013, 192:1, 1–13

Bibliographic databases:

UDC: 517.9
Received: 02.02.2012

Citation: N. M. Bogoliubov, “Scalar products of the state vectors in the totally asymmetric exactly solvable models on a ring”, Questions of quantum field theory and statistical physics. Part 22, Zap. Nauchn. Sem. POMI, 398, POMI, St. Petersburg, 2012, 5–25; J. Math. Sci. (N. Y.), 192:1 (2013), 1–13

Citation in format AMSBIB
\Bibitem{Bog12}
\by N.~M.~Bogoliubov
\paper Scalar products of the state vectors in the totally asymmetric exactly solvable models on a~ring
\inbook Questions of quantum field theory and statistical physics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 398
\pages 5--25
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5193}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2944986}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 1
\pages 1--13
\crossref{https://doi.org/10.1007/s10958-013-1368-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878687938}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. M. Bogolyubov, “Calculation of correlation functions in totally asymmetric exactly solvable models on a ring”, Theoret. and Math. Phys., 175:3 (2013), 755–762  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. G. Pronko, “The five-vertex model and enumerations of plane partitions”, J. Math. Sci. (N. Y.), 213:5 (2016), 756–768  mathnet  crossref  mathscinet
    3. A. G. Pronko, G. P. Pronko, “Off-shell Bethe states and the six-vertex model”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 228–243  mathnet
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