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SIGMA, 2009, Volume 5, 052, 11 pages (Mi sigma398)  

This article is cited in 12 scientific papers (total in 12 papers)

Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model

Nikolay M. Bogolyubov

St. Petersburg Department of V. A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia

Abstract: The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the “crystalline limit” ($q\rightarrow\infty$) of the $SU_q(2)$ quantum algebra. Using the quantum inverse scattering method we obtain the exact expression for the time-dependent stationary correlation function of the totally asymmetric simple exclusion process on a one dimensional lattice with the periodic boundary conditions.

Keywords: quantum inverse method; algebraic Bethe ansatz; asymmetric exclusion process

DOI: https://doi.org/10.3842/SIGMA.2009.052

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Full text: http://emis.mi.ras.ru/.../052
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Bibliographic databases:

ArXiv: 0904.3680
MSC: 82C23; 81R50
Received: October 30, 2008; in final form April 14, 2009; Published online April 23, 2009
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Citation: Nikolay M. Bogolyubov, “Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model”, SIGMA, 5 (2009), 052, 11 pp.

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Eynard B., “A matrix model for plane partitions”, Journal of Statistical Mechanics-Theory and Experiment, 2009, P10011  crossref  mathscinet  isi  scopus
    2. Mallick K., “Some exact results for the exclusion process”, J Stat Mech Theory Exp, 2011, P01024  crossref  mathscinet  isi  scopus
    3. Chou T., Mallick K., Zia R.K.P., “Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport”, Rep Progr Phys, 74:11 (2011), 116601  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. N. M. Bogoliubov, “Scalar products of the state vectors in the totally asymmetric exactly solvable models on a ring”, J. Math. Sci. (N. Y.), 192:1 (2013), 1–13  mathnet  crossref  mathscinet
    5. Motegi K., Sakai K., Sato J., “Long Time Asymptotics of the Totally Asymmetric Simple Exclusion Process”, J. Phys. A-Math. Theor., 45:46 (2012), 465004  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Motegi K., Sakai K., Sato J., “Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process”, Phys. Rev. E, 85:4, Part 1 (2012), 042105  crossref  mathscinet  adsnasa  isi  elib  scopus
    7. 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
    8. Motegi K., Sakai K., “Vertex Models, Tasep and Grothendieck Polynomials”, J. Phys. A-Math. Theor., 46:35 (2013), 355201  crossref  mathscinet  zmath  isi  elib  scopus
    9. Prolhac S., “Asymptotics For the Norm of Bethe Eigenstates in the Periodic Totally Asymmetric Exclusion Process”, J. Stat. Phys., 160:4, SI (2015), 926–964  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Prolhac S., “Finite-Time Fluctuations For the Totally Asymmetric Exclusion Process”, Phys. Rev. Lett., 116:9 (2016), 090601  crossref  adsnasa  isi  elib  scopus
    11. Prolhac S., “Extrapolation methods and Bethe ansatz for the asymmetric exclusion process”, J. Phys. A-Math. Theor., 49:45 (2016), 454002  crossref  mathscinet  zmath  isi  elib  scopus
    12. Prolhac S., “Perturbative Solution For the Spectral Gap of the Weakly Asymmetric Exclusion Process”, J. Phys. A-Math. Theor., 50:31 (2017), 315001  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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