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Sergey Medvedev

Publications and source records attributed to Sergey Medvedev.

At least 19 recordsLinked to original sources
arXiv2026

Fast eight-order Pade schemes based on Chebyshev polynomials for direct Zakharov-Shabat problem

In this work, we construct fast eighth-order Pade schemes for the direct Zakharov-Shabat scattering problem. The schemes are based on an eighth-order exponential integrator obtained from the Magnus expansion. A direct extension of the conventional fast Pade representation to the eighth-order case leads to insufficiently accurate fast variants in the considered tests. To overcome this difficulty, we reformulate the spectral dependence on a finite real interval using the Joukowski mapping and represent the local numerators and denominators in the Chebyshev polynomial basis. This makes it possible to construct the global transition matrix by a fast product tree while retaining a compact polynomial representation. Numerical experiments for chirped hyperbolic secant potentials with both signs of dispersion show that the proposed Chebyshev-based fast schemes substantially improve the accuracy of the corresponding direct fast variants and can be used for efficient computation of the continuous nonlinear spectrum.

math.NA↗
arXiv2025

Oxygen-isotope effect on density wave transitions in La$_3$Ni$_2$O$_{7}$

TThe isotope effect is a powerful probe of electron-phonon interactions in solid-state systems, offering key insights into how atomic mass influences emergent quantum states. Here, the impact of oxygen isotope substitution ($^{16}{\rm O}\rightarrow \; ^{18}{\rm O}$) on charge- and spin-density wave (CDW and SDW) transitions in the double-layer Ruddlesden-Popper nickelate La$_3$Ni$_2$O$_7$ is investigated. A clear isotope effect is observed in the CDW transition: the transition temperature ($T_{\rm CDW}$) increases upon $^{18}$O substitution. In contrast, the SDW transition temperature remains unaffected within experimental uncertainty. These findings point to a strong involvement of lattice vibrations in the formation of charge order, while spin order appears to be predominantly of electronic origin. The results suggest that electron-phonon coupling, manifested through the CDW response to isotope substitution, may be relevant to the superconducting pairing mechanism in Ruddlesden-Popper nickelates.

cond-mat.supr-con↗
arXiv2024

Superconductivity in ternary pyrite-type compound IrBi$_{1-x}$Te$_{1+x}$ ($x \approx 0.2$) at ambient and high pressure

We report superconductivity in the ternary compound IrBi$_{0.8}$Te$_{1.2}$ with critical temperature 1.7 K. The replacement of Bi by Te leads to the metallic conductivity in contrast to the semiconducting parent compound IrBiTe. The superconductivity can be further enhanced by application of external pressure. $T_c$ demonstrates dome-shaped dependence on pressure with a maximum value of 2.6 K at 26.5 GPa. Pressure effects on electronic properties and lattice dynamic of IrBi$_{0.8}$Te$_{1.2}$ were studied by pressure dependent electrical resistivity, Hall effect and Raman spectroscopy measurements.

cond-mat.supr-con↗
arXiv2024

High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation

We propose a high precision algorithm for solving the Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson's type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations.

math.NA↗
arXiv2022

Preservation of complete Baireness

The main result is the following. Let $f \colon X \rightarrow Y$ be a continuous mapping of a completely Baire space $X$ onto a hereditary weakly Preiss-Simon regular space $Y$ such that the image of every open subset of $X$ is a resolvable set in $Y$. Then $Y$ is completely Baire. The classical Hurewicz theorem about closed embedding of the space of rational numbers into metrizable spaces is generalized to weakly Preiss-Simon regular spaces.

math.GN↗
arXiv2021

Processing of optical signals by "surgical" methods for the Gelfand-Levitan-Marchenko equation

We propose a new method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an arbitrary point to start the calculation. This makes it possible to find solutions of the GLME at an arbitrary point with a cutoff of the matrix coefficient, which allows to avoid the occurrence of numerical instability and to perform calculations for soliton solutions spaced apart in the time domain. Using an example of two solitons, we demonstrate our method and its range of applicability. An example of eight solitons shows how the method can be applied to a more complex signal configuration.

math.NA↗
arXiv2021

Inverse cascade anomalies in fourth-order Leith models

We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrodinger model and for the gravitational waves in the Einstein's vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

physics.flu-dyn↗
arXiv2020

Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications

Based on the generalized Cayley transform, a family of conservative one-step schemes of the sixth order of accuracy for the Zakharov-Shabat system is constructed. The exponential integrator is a special case. Schemes based on rational approximation allow the use of fast algorithms to solve the initial problem for a large number of values of the spectral parameter.

math.NA↗
arXiv2020

Suppression of axionic charge density wave and onset of superconductivity in the chiral Weyl semimetal Ta$_2$Se$_8$I

A Weyl semimetal with strong electron-phonon interaction can show axionic coupling in its insulator state at low temperatures, owing to the formation of a charge density wave (CDW). Such a CDW emerges in the linear chain compound Weyl semimetal Ta$_2$Se$_8$I below 263 K, resulting in the appearance of the dynamical condensed-matter axion quasiparticle. In this study, we demonstrate that the interchain coupling in Ta$_2$Se$_8$I can be varied to suppress the CDW formation with pressure, while retaining the Weyl semimetal phase at high temperatures. Above 17 GPa, the Weyl semimetal phase does not survive and we induce superconductivity, due to the amorphization of the iodine sub-lattice. Structurally, the one-dimensional Ta-Se-chains remain intact and provide a superconducting channel in one dimension. We highlight that our results show a near-complete suppression of the gap induced by the axionic charge-density wave at pressures inaccessible to previous studies. Including this CDW phase, our experiments and theoretical predictions and analysis reveal the complete topological phase diagram of Ta$_2$Se$_8$I and its relationship to the nearby superconducting state. The results demonstrate Ta$_2$Se$_8$I to be a distinctively versatile platform for exploring correlated topological states.

cond-mat.supr-con↗
arXiv2020

Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem

We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function $a(ζ)$, the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.

math.NA↗
arXiv2019

Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme

A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is based on a fourth-order three-exponential scheme, which contains only one exponent with a spectral parameter. This exponent is factorized to the fourth-order with the Suzuki formula of 11 exponents. The obtained scheme allows the use of a fast algorithm in calculating the initial problem for a large number of spectral parameters and conserves the quadratic invariant exactly for real spectral parameters.

math.NA↗
arXiv2019

Large Resistivity Reduction in Mixed-Valent CsAuBr$_3$ Under Pressure

We report on high-pressure $p \leq 45$ GPa resistivity measurements on the perovskite-related mixed-valent compound CsAuBr$_3$. The compounds high-pressure resistivity can be classified into three regions: For low pressures ($p < 10$ GPa) an insulator to metal transition is observed; between $p= 10$ GPa and 14 GPa the room temperature resistivity goes through a minimum and increases again; above $p = 14$ GPa a semiconducting state is observed. From this pressure up to the highest pressure of $p = 45$ GPa reached in this experiment, the room-temperature resistivity remains nearly constant. We find an extremely large resistivity reduction between ambient pressure and 10 GPa by more than 6 orders of magnitude. This decrease is among the largest reported changes in the resistivity for this narrow pressure regime. We show - by an analysis of the electronic band structure evolution of this material - that the large change in resistivity under pressure in not caused by a crossing of the bands at the Fermi level. We find that it instead stems from two bands that are pinned at the Fermi level and that are moving towards one another as a consequence of the mixed-valent to single-valent transition. This mechanism appears to be especially effective for the rapid buildup of the density of states at the Fermi level.

cond-mat.mtrl-sci↗
arXiv2019

Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem

We propose two finite-difference algorithms of fourth order of accuracy for solving the initial problem of the Zakharov-Shabat system. Both schemes have the exponential form and conserve quadratic invariant of Zakharov-Shabat system. The second scheme contains the spectral parameter in exponent only and allows to apply the fast computational algorithm.

math.NA↗
arXiv2017

On the Jayne-Rogers theorem

In 1982, J.E. Jayne and C.A. Rogers proved that a mapping $f \colon X \rightarrow Y$ of an absolute Souslin-F set X to a metric space Y is $Δ^0_2$-measurable if and only if it is piecewise continuous. We now give a similar result for a perfectly paracompact first-countable space X and a regular space Y.

math.GN↗
arXiv2016

On piecewise continuous mappings of metrizable spaces

Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is resolvable-measurable if and only if it is piecewise continuous.

math.GN↗
arXiv2015

Anomalous spectral laws in differential models of turbulence

Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the $k$-space were analysed. Both types of models predict formation an anomalous transient power-law spectra. The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation. Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system.

physics.flu-dyn↗