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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 142, Number 3, Pages 500–509
DOI: https://doi.org/10.4213/tmf1794 (Mi tmf1794) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Quantization scheme for modular q-difference equations

S. M. Sergeevab

a Australian National University
b Research School of Physical Sciences and Engineering
Full-text PDF (220 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf1794
Abstract: We consider modular pairs of certain second-order q-difference equations. An example of such a pair is the t-Q Baxter equations for the quantum relativistic Toda lattice in the strong coupling regime. Another example from quantum mechanics is q-deformation of the Schrödinger equation with a hyperbolic potential. We show that the analyticity condition for the wave function or the Baxter function leads to a set of transcendental equations for the coefficients of the potential or the transfer matrix, the solution of which is their discrete spectrum.
Keywords: Baxter equations, modular dualization, strong coupling regime.
Received: 28.06.2004
English version:
Theoretical and Mathematical Physics, 2005, Volume 142, Issue 3, Pages 422–430
DOI: https://doi.org/10.1007/s11232-005-0033-x
Bibliographic databases:
Language: Russian
Citation: S. M. Sergeev, “Quantization scheme for modular q-difference equations”, TMF, 142:3 (2005), 500–509; Theoret. and Math. Phys., 142:3 (2005), 422–430
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf1794
  • https://doi.org/10.4213/tmf1794
  • https://www.mathnet.ru/eng/tmf/v142/i3/p500
    • This publication is cited in the following 8 articles:
    1. Sergey Sergeev, “Functional Bethe Ansatz for a sinh-Gordon Model with Real q”, Symmetry, 16:8 (2024), 947  crossref
    2. Kashaev R., Sergeev S., “On the Spectrum of the Local P-2 Mirror Curve”, Ann. Henri Poincare, 21:11 (2020), 3479–3497  crossref  mathscinet  isi
    3. Kashaev R.M., Sergeev S.M., “Spectral Equations For the Modular Oscillator”, Rev. Math. Phys., 30:7, SI (2018), 1840009  crossref  mathscinet  isi  scopus
    4. Babelon O., Kozlowski K.K., Pasquier V., “Solution of Baxter Equation For the Q-Toda and Toda(2) Chains By Nlie”, SciPost Phys., 5:4 (2018), 035  crossref  mathscinet  isi
    5. Grassi A., Hatsuda Ya., Mario M., “Topological Strings from Quantum Mechanics”, Ann. Henri Poincare, 17:11 (2016), 3177–3235  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kaellen J., Marino M., “Instanton Effects and Quantum Spectral Curves”, Ann. Henri Poincare, 17:5 (2016), 1037–1074  crossref  mathscinet  zmath  isi  scopus
    7. Kaellen J., “the Spectral Problem of the Abj Fermi Gas”, J. High Energy Phys., 2015, no. 10, 029  crossref  mathscinet  isi  scopus  scopus
    8. Adivar M., “Quadratic Pencil of Difference Equations: Jost Solutions, Spectrum, and Principal Vectors”, Quaestiones Mathematicae, 33:3 (2010), 305–323  crossref  mathscinet  zmath  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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