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Zap. Nauchn. Sem. POMI, 2005, Volume 325, Pages 13–27 (Mi znsl348)  

This article is cited in 21 scientific papers (total in 21 papers)

$XX0$ Heisenberg chain and random walks

N. M. Bogolyubov

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

Abstract: The time-dependent correlation functions of the $XX0$ Heisenberg chain over the ferromagnetic vacuum are considered as the generating functions of random walks on a one-dimensional lattice with different boundary conditions. The long-time asymptotic behaviour of these functions is studied. Bibliography: 18 titles.

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English version:
Journal of Mathematical Sciences (New York), 2006, 138:3, 5636–5643

Bibliographic databases:

UDC: 519.14
Received: 26.04.2005

Citation: N. M. Bogolyubov, “$XX0$ Heisenberg chain and random walks”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Zap. Nauchn. Sem. POMI, 325, POMI, St. Petersburg, 2005, 13–27; J. Math. Sci. (N. Y.), 138:3 (2006), 5636–5643

Citation in format AMSBIB
\by N.~M.~Bogolyubov
\paper $XX0$ Heisenberg chain and random walks
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XII
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 325
\pages 13--27
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 138
\issue 3
\pages 5636--5643

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    This publication is cited in the following articles:
    1. N. M. Bogolyubov, “Integrable models for the vicious and friendly walkers”, J. Math. Sci. (N. Y.), 143:1 (2007), 2729–2737  mathnet  crossref  mathscinet  zmath
    2. N. M. Bogolyubov, “Four-vertex model”, J. Math. Sci. (N. Y.), 151:2 (2008), 2816–2828  mathnet  crossref  mathscinet
    3. Katori M., Tanemura H., “Noncolliding Brownian motion and determinantal processes”, J. Stat. Phys., 129:5-6 (2007), 1233–1277  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. J. Math. Sci. (N. Y.), 158:6 (2009), 771–786  mathnet  crossref  zmath
    5. Bogoliubov N.M., Malyshev C., “A Path-Integration Approach to the Correlators of Xy Heisenberg Magnet and Random Walks”, Path Integrals: New Trends and Perspectives, Proceedings, eds. Janke W., Pelster A., World Scientific Publ Co Pte Ltd, 2008, 508–513  crossref  mathscinet  zmath  isi
    6. N. M. Bogolyubov, K. L. Malyshev, “Correlation functions of the XX Heisenberg magnet and random walks of vicious walkers”, Theoret. and Math. Phys., 159:2 (2009), 563–574  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    7. N. M. Bogoliubov, K. Malyshev, “The correlation functions of the $XXZ$ Heisenberg chain in the case of zero or infinite anisotropy, and random walks of vicious walkers”, St. Petersburg Math. J., 22:3 (2011), 359–377  mathnet  crossref  mathscinet  zmath  isi
    8. N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, Theoret. and Math. Phys., 169:2 (2011), 1517–1529  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    9. J. Math. Sci. (N. Y.), 200:6 (2014), 662–670  mathnet  crossref
    10. Perez-Garcia D., Tierz M., “Mapping Between the Heisenberg XX Spin Chain and Low-Energy QCD”, Phys. Rev. X, 4:2 (2014), 021050  crossref  mathscinet  isi  elib  scopus
    11. Bogoliubov N.M., Malyshev C., “Correlation Functions of Xxo Heisenberg Chain, Q-Binomial Determinants, and Random Walks”, Nucl. Phys. B, 879 (2014), 268–291  crossref  mathscinet  zmath  isi  elib  scopus
    12. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. J. Math. Sci. (N. Y.), 216:1 (2016), 8–22  mathnet  crossref  mathscinet
    14. Perez-Garcia D., Tierz M., “Chern–Simons Theory Encoded on a Spin Chain”, J. Stat. Mech.-Theory Exp., 2016, 013103  crossref  mathscinet  isi  scopus
    15. J. Math. Sci. (N. Y.), 224:2 (2017), 199–213  mathnet  crossref  mathscinet
    16. Nicolay M. Bogoliubov, Cyril Malyshev, “Zero Range Process and Multi-Dimensional Random Walks”, SIGMA, 13 (2017), 056, 14 pp.  mathnet  crossref
    17. J. Math. Sci. (N. Y.), 238:6 (2019), 769–778  mathnet  crossref
    18. J. Math. Sci. (N. Y.), 238:6 (2019), 779–792  mathnet  crossref
    19. J. Math. Sci. (N. Y.), 242:5 (2019), 628–635  mathnet  crossref
    20. N. M. Bogoliubov, “Enumerative combinatorics of $XX0$ Heisenberg chain”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 26, Zap. nauchn. sem. POMI, 487, POMI, SPb., 2019, 53–67  mathnet
    21. N. M. Bogoliubov, C. L. Malyshev, “Heisenberg $XX0$ chain and random walks on a ring”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 48–63  mathnet
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