arXiv subjects

Nikolai A. Stepanov

Publications and source records attributed to Nikolai A. Stepanov.

5 recordsLinked to original sources

arXiv2025

Statistics of the vortex pinning potential in superconducting films

We investigate the statistical properties of the vortex pinning potential in a thin superconducting film. Modeling intrinsic inhomogeneities by a random-temperature Ginzburg-Landau functional with short-range Gaussian disorder, we derive the pinning landscape $E(\mathbf{R})$ by determining how the vortex core adapts to randomness. Within the hard-core approximation, applicable for weak disorder, the energy landscape exhibits Gaussian statistics. In this regime, the mean areal density of its minima is given by $n_\text{min}\approx(6ξ)^{-2}$, indicating that the typical spacing between neighboring minima is significantly larger than the vortex core size $ξ$. Going beyond the hard-core approximation, we allow the vortex order parameter to relax in response to the inhomogeneities. As a result, the pinning potential statistics become non-Gaussian. We calculate the leading correction due to the core deformation, which reduces the density of minima with a relative magnitude scaling as $(T_c-T)^{-1/2}$.

cond-mat.supr-con↗

arXiv2023

Electron-phonon relaxation in a model of a granular film

We study the electron-phonon relaxation in the model of a granular metal film, where the grains are formed by regularly arranged potential barriers of arbitrary transparency. The relaxation rate of Debye acoustic phonons is calculated, taking into account two mechanisms of electron-phonon scattering: the standard Fröhlich interaction of the lattice deformation with the electron density and the interaction mediated by the displacement of grain boundaries dragged by the lattice vibration. At the lowest temperatures, the electron-phonon cooling power follows the power-law temperature dependence typical for clean systems but with the prefactor growing as the transparency of the grain boundaries decreases.

cond-mat.mes-hall↗

arXiv2022

Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the "square root" of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong driving (no gravitation), we obtain an exact analytical solution for the instantaneous joint probability distribution function of the pendulum's angle and its velocity.

cond-mat.stat-mech↗

arXiv2020

Lyapunov exponent for Whitney's problem with random drive

We consider the statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case when the external force is white noise, we recently found the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval using a transfer-matrix analysis of the supersymmetric field theory. Here, we generalize our approach to the case of finite time intervals and multipoint correlation functions. Using the developed formalism, we calculate the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory.

cond-mat.stat-mech↗

arXiv2018

Superconducting fluctuations at arbitrary disorder strength

We study the effect of superconducting fluctuations on the conductivity of metals at arbitrary temperatures $T$ and impurity scattering rates $τ^{-1}$. Using the standard diagrammatic technique but in the Keldysh representation, we derive the general expression for the fluctuation correction to the dc conductivity applicable for any space dimensionality and analyze it the case of the film geometry. We observe that the usual classification in terms of the Aslamazov-Larkin, Maki-Thompson and density-of-states diagrams is to some extent artificial since these contributions produce similar terms, which partially cancel each other. In the diffusive limit, our results fully coincide with recent calculations in the Keldysh technique. In the ballistic limit near the transition, we demonstrate the absence of a divergent term $(Tτ)^2$ attributed previously to the density-of-states contribution. In the ballistic limit far above the transition, the temperature-dependent part of the conductivity correction is shown to scale roughly as $Tτ$.

cond-mat.supr-con↗