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Zapiski Nauchnykh Seminarov 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
Full-text PDF (294 kB) Citations (3)
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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.
Received: 02.02.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 1, Pages 1–13
DOI: https://doi.org/10.1007/s10958-013-1368-8
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878687938}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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