arXiv subjects

A. Prokhorov

Publications and source records attributed to A. Prokhorov.

5 recordsLinked to original sources

arXiv2019

Hertz-to-terahertz dielectric response of nanoconfined water molecules

Broad-band dielectric spectroscopy, heat capacity measurements and molecular dynamic simulations are applied to study excitations of interacting electric dipoles spatially arranged in a network with an inter-dipole distance of 5-10 A. The dipoles with magnitude of 1.85 Debye are represented by single H2O molecules located in voids (0.5 nm size) formed by ions of the crystal lattice of cordierite. We discover emergence of nontrivial disordered paraelectric phase of dipolar system with signs of phase transition below 3 K.

cond-mat.mtrl-sci↗

arXiv2018

Monodromy dependence and connection formulae for isomonodromic tau functions

We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results of M. Bertola generalizing a previous construction by B. Malgrange. We show how this 1-form can be used to solve a long-standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors. We explain how this scheme works for Fuchsian systems and, in particular, calculate the connection constant for generic Painlevé VI tau function. The result proves the conjectural formula for this constant proposed in \cite{ILT13}. We also apply the method to non-Fuchsian systems and evaluate constant factors in the asymptotics of Painlevé II tau function.

math-ph↗

arXiv2018

On some Hamiltonian properties of the isomonodromic tau functions

We discuss some new aspects of the theory of the Jimbo-Miwa-Ueno tau function which have come to light within the recent developments in the global asymptotic analysis of the tau functions related to the Painlev\'e equations. Specifically, we show that up to the total differentials the logarithmic derivatives of the Painlev\'e tau functions coincide with the corresponding classical action differential. This fact simplifies considerably the evaluation of the constant factors in the asymptotics of tau-functions, which has been a long-standing problem of the asymptotic theory of Painlev\'e equations. Furthermore, we believe that this observation is yet another manifestation of L. D. Faddeev's emphasis of the key role which the Hamiltonian aspects play in the theory of integrable system. This article will appear in the WSPC memorial volume dedicated to Ludwig Faddeev.

math-ph↗

arXiv2018

The Maxwell operator with periodic coefficients in a cylinder

In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.

math-ph↗

arXiv2015

Regularity of electromagnetic fields in convex domains

In this paper the "strong" Maxwell operator defined on fields from the Sobolev space $W_2^1$, and the "weak" Maxwell operator defined on the natural domain are considered. It is shown that in a convex domain, and, more generally, in a domain, which is locally $(W_3^2 \cap W^1_\infty)$-diffeomorphic to convex one, the "strong" and the "weak" Maxwell operators coincide.

math-ph↗