• Corpus ID: 233481847

Quantum spectral problems and isomonodromic deformations

@inproceedings{Bershtein2021QuantumSP,
  title={Quantum spectral problems and isomonodromic deformations},
  author={M. Bershtein and Pavlo Gavrylenko and A. M. Grassi},
  year={2021}
}
We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of 2 × 2 linear systems (Riemann-Hilbert correspondence). Our technique applies to a variety of problems, though in this paper we only analyse in detail two examples. First we review the case of the (modified) Mathieu operator, which corresponds to a certain linear system on the sphere and makes contact with the Painlevé III3 equation. Then… 

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References

SHOWING 1-10 OF 157 REFERENCES
Liouville Correlation Functions from Four-Dimensional Gauge Theories
We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class
N = 2∗ Gauge Theory
  • Free Fermions on the Torus and Painlevé VI, Commun. Math. Phys. 377
  • 2020
Conformal field theory of Painlevé VI
A bstractGeneric Painlevé VI tau function τ (t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c = 1. Using AGT combinatorial representation of
Irregular conformal blocks
  • Painlevé III and the blow-up equations, JHEP 12
  • 2020
Classical conformal blocks and Painlevé VI
A bstractWe study the classical c → ∞ limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial null-vector decoupling equation on a sphere leads to the
Darboux coordinates
  • Yang-Yang functional, and gauge theory, Theor. Math. Phys. 181
  • 2014
How instanton combinatorics solves Painlevé VI
  • V and IIIs, J. Phys. A46
  • 2013
Critical values of the Yang-Yang functional in the quantum sine-Gordon model
Abstract The critical values of the Yang–Yang functional corresponding to the vacuum states of the sine-Gordon QFT in the finite-volume are studied. Two major applications are discussed: (i)
Nekrasov prepotential with fundamental matter from the quantum spin chain
Abstract Nekrasov functions were conjectured in Mironov and Morozov (2009) [1] to be related to exact Bohr–Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for
Poles of tritronquée solution to the Painlevé I equation and cubic anharmonic oscillator
AbstractThe distribution of poles of zero-parameter solution to Painlevé I, specified by P. Boutroux as intégrale tritronquée, is studied in the complex plane. This solution has regular asymptotics
...
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2
3
4
5
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