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TMF, 2015, Volume 183, Number 3, Pages 409–433 (Mi tmf8874)  

This article is cited in 5 scientific papers (total in 5 papers)

One-dimensional two-component Bose gas and the algebraic Bethe ansatz

N. A. Slavnov

Steklov Mathematical Institute of the~RAS, Moscow, Russia

Abstract: We apply the nested algebraic Bethe ansatz to a model of a one-dimensional two-component Bose gas with a $\delta$-function repulsive interaction. Using a lattice approximation of the $L$-operator, we find the Bethe vectors of the model in the continuum limit. We also obtain a series representation for the monodromy matrix of the model in terms of Bose fields. This representation allows studying an asymptotic expansion of the monodromy matrix over the spectral parameter.

Keywords: Bethe ansatz, monodromy matrix, Bethe vector

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf8874

Full text: PDF file (617 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 800–821

Bibliographic databases:

Document Type: Article
Received: 19.02.2015

Citation: N. A. Slavnov, “One-dimensional two-component Bose gas and the algebraic Bethe ansatz”, TMF, 183:3 (2015), 409–433; Theoret. and Math. Phys., 183:3 (2015), 800–821

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v183/i3/p409

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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. O. I. Pâţu, A. Klümper, “Thermodynamics, density profiles, and correlation functions of the inhomogeneous one-dimensional spinor Bose gas”, Phys. Rev. A, 92 (2015), 043631  crossref  isi  scopus
    2. S. Pakuliak, E. Ragoucy, N. A. Slavnov, “Form factors of local operators in a one-dimensional two-component Bose gas”, J. Phys. A, 48:43 (2015), 435001, 21 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. K. K. Kozlowski, E. Ragoucy, “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288  crossref  mathscinet  zmath  isi  scopus
    4. J. Fuksa, N. A. Slavnov, “Form factors of local operators in supersymmetric quantum integrable models”, J. Stat. Mech.-Theory Exp., 2017, 043106  crossref  mathscinet  isi  scopus
    5. A. Liashyk, N. A. Slavnov, “On Bethe vectors in $\mathfrak{gl}_3$ -invariant integrable models”, J. High Energy Phys., 2018, no. 6, 018, 31 pp.  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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