Antiquantization as a specific way from the Statistical physics to the Regular physics

Research output: Contribution to journalReview articleResearchpeer-review

Abstract

An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.

LanguageEnglish
Pages512-518
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume521
DOIs
StatePublished - 1 May 2019

Keywords

  • Antiquantization
  • Apparent singularity
  • Confluent Heun equation
  • Fuchsian singularity
  • Heun equation
  • Isomonodromic property
  • Painlevé equation

Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Antiquantization as a specific way from the Statistical physics to the Regular physics",
abstract = "An extended analysis is given of links between linear Heun class equations and the nonlinear Painlev{\'e} equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlev{\'e} equations in an nonconventional manner is presented.",
keywords = "Antiquantization, Apparent singularity, Confluent Heun equation, Fuchsian singularity, Heun equation, Isomonodromic property, Painlev{\'e} equation",
author = "Sergey Slavyanov and Olga Stesik",
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language = "English",
volume = "521",
pages = "512--518",
journal = "Physica A: Statistical Mechanics and its Applications",
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Antiquantization as a specific way from the Statistical physics to the Regular physics. / Slavyanov, Sergey; Stesik, Olga.

In: Physica A: Statistical Mechanics and its Applications, Vol. 521, 01.05.2019, p. 512-518.

Research output: Contribution to journalReview articleResearchpeer-review

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AB - An extended analysis is given of links between linear Heun class equations and the nonlinear Painlevé equations. For linear equations, Heun class equations, deformed Heun class equations, parallel to various first-order systems, are chosen. The role of an accessory parameter in each case is explained. Links to isomonodromic property is traced. The complete list of Painlevé equations in an nonconventional manner is presented.

KW - Antiquantization

KW - Apparent singularity

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KW - Fuchsian singularity

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