arXiv subjects
Publications and source records attributed to A. R. Its.
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlevé equation $y_{xx}=2y^3+xy-α$. The precise description of the exponentially small jump in the dominant solution approaching $α/x$ as $|x|\to\infty$ is given. For the asymptotic power expansion of the dominant solution, the coefficient asymptotics is found.
We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann--Hilbert problem is used for analysing the leading term of the large time and long distance asymptotics of the correlation function.
We consider non-relativistic electrons in one dimension with infinitely strong repulsive delta function interaction. We calculate the long-time, large-distance asymptotics of field-field correlators in the gas phase. The gas phase at low temperatures is characterized by the ideal gas law. We calculate the exponential decay, the power law corrections and the constant factor of the asymptotics. Our results are valid at any temperature. They simplify at low temperatures, where they are easily recognized as products of free fermionic correlation functions with corrections arising due to the interaction.
We consider the Ferromagnetic-String-Formation-Probability correlation function (FSFP) for the spin-$1\over 2$ Heisenberg XXZ chain. We construct a completely integrable system of integro-difference equations (IDE), which has the FSFP as a $τ$-function. We derive the associated Riemann-Hilbert problem and obtain the large distance asymptotics of the FSFP correlator in some limiting cases.
Isotropic XY is considered. It describes interaction of quantum spins on 1-dimesional lattice. Alternatevly one can call the model XXO Hiesenberg antiferromagnet. We solved long standing problem of evaluation of temperature corelations. We proved that correlation function of the model is $τ$ function of Ablowitz-Ladik PDE. We explicitly evaluated asymptotics.