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A. Chervyakov

Publications and source records attributed to A. Chervyakov.

15 recordsLinked to original sources
arXiv2017

Numerical modelling of MgB2 conductors for high power AC transmission

Cables made of MgB2 superconductors are currently explored as a viable solution for transporting high electrical power in the AC regime. In order to be competitive against the DC solution, the cables need to have an acceptable level of AC losses. In this contribution, we discuss the main aspects relevant for designing a cable with a sufficiently low AC loss level. To this end, we perform finite-element-method (FEM) simulations to determine the current and field distributions and calculate the AC losses of such cable configuration. For current capacities of 2-5 kA (peak), power cables are assembled from a relatively small number of MgB2 strands. The performance of such cables strongly depends on the current and field distributions, which are in turn influenced by the number and the arrangement of the superconducting components and also by the magnetic properties of supporting materials. Numerical simulations can help to test different cable configurations and provide important insights for optimizing the cable's design. The numerical model includes the field dependence of the superconductor's critical current density Jc(B) as well as the non-linear properties of magnetic materials.

cond-mat.supr-con↗
arXiv2011

On Electron-Positron Pair Production by a Spatially Nonuniform Electric Field

A detailed analysis of electron-positron pair creation induced by a spatially nonuniform and static electric field from vacuum is presented. A typical example is provided by the Sauter potential. For this potential, we derive the analytic expressions for vacuum decay and pair production rate accounted for the entire range of spatial variations. In the limit of a sharp step, we recover the divergent result due to the singular electric field at the origin. The limit of a constant field reproduces the classical result of Euler, Heisenberg and Schwinger, if the latter is properly averaged over the width of a spatial variation. The pair production by the Sauter potential is described for different physical regimes from weak to strong fields. In all these regimes, the locally constant-field rate is shown to be the upper limit.

hep-th↗
arXiv2009

Exact Pair Production Rate for a Smooth Potential Step

We derive the exact rate of pair production of oppositely charged scalar particles by a smooth potential proportional to tanh kz in three dimensions. As a check we recover from this the known results for an infinitely sharp step as well as for a uniform electric field.

hep-th↗
arXiv2005

Perturbation Theory for Path Integrals of Stiff Polymers

The wormlike chain model of stiff polymers is a nonlinear $σ$-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physically interesting quantities in powers of $L/ξ$, where $L$ is the length and $ξ$ the persistence length of the polymer. This requires special procedures for regularizing highly divergent Feynman integrals which we have developed in previous work. We show that by adding to the unperturbed action a correction term ${\cal A}^{\rm corr}$, we can calculate all Feynman diagrams with Green functions satisfying Neumann boundary conditions. Our expansions yield, order by order, properly normalized end-to-end distribution function in arbitrary dimensions $d$, its even and odd moments, and the two-point correlation function.

cond-mat.soft↗
arXiv2003

Perturbatively Defined Effective Classical Potential in Curved Space

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -βV^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average ${\bf x_0\equiv β^{-1}\int_0^ βdτ{\bf x}(τ)$. We show how to generalize this concept to paths $q^μ(τ)$ in curved space with metric $g_{μν(q)$, and calculate perturbatively the high-temperature expansion of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate transformations $q^μ(τ)\to q'^μ(τ)$ introduces subtleties in the definition and treatment of the path average $q_0^μ$, and covariance is achieved only with the help of a suitable Faddeev-Popov procedure.

quant-ph↗
arXiv2002

Integrals over Products of Distributions from Manifest Coordinate Invariance of Perturbation Expansions of Path Integrals in Curved Space

We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating products of distributions. The rules are derived using equations of motion and partial integration, while keeping track of certain minimal features stemming from the unique definition of all singular integrals in 1 - epsilon dimensions. Our rules guarantee complete agreement with much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. In contrast to our previous papers where we solved the same problem for an infinite time interval or zero temperature, we consider here the more involved case of finite-time (or non-zero temperature) amplitudes.

quant-ph↗
arXiv2002

Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals

In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac delta-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in $1 - ε$ dimensions. Our rules yield the same results as the much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval.

quant-ph↗
arXiv2000

Coordinate Independence of of Quantum-Mechanical Path Integrals

We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the form dot q^2 q^n, which give rise to highly singular Feynman integrals. The new rules ensure the invariance of perturbatively defined path integrals under coordinate transformations.

quant-ph↗
arXiv2000

Reparametrization Invariance of Perturbatively Defined Path Integrals. II. Integrating Products of Distributions

We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under coordinate transformations. The integrals are uniquely defined by expressing the propagators in 1- epsilon dimensions in terms of modified Bessel functions.

quant-ph↗
arXiv1999

Reparametrization Invariance of Path Integrals

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.

hep-th↗
arXiv1999

Perturbation Theory for Particle in a Box

Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum mechanics of a point particle in a one-dimensional box. Introducing an auxiliary harmonic mass term $m$, the ground-state energy $E^{(0)$ can be expanded perturbatively in powers of $1/md$, where $d$ is the box size. The removal of the infrared cutoff $m$ requires the resummation of the series at infinitely strong coupling. We show that strong-coupling theory yields a fast-convergent sequence of approximations to the well-known quantum-mechanical energy $E^{(0)= π^2/2d^2$.

cond-mat↗
arXiv1998

Simple Explicit Formulas for Gaussian Path Integrals with Time-Dependent Frequencies

Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary conditions on a line segment. This permits us to take advantage of Wronski's construction method for Green functions without knowledge of eigenvalues. Our final formula expresses the ratios of functional determinants in terms of an ordinary $2\times2$ -determinant of a constant matrix constructed from two linearly independent solutions of a the homogeneous differential equations associated with the second-order differential operators. For ratios of determinants encountered in semiclassical fluctuations around a classical solution, the result can further be expressed in terms of this classical solution. In the presence of a zero mode, our method allows for a simple universal regularization of the functional determinants. For Dirichlet's boundary condition, our result is equivalent to Gelfand-Yaglom's. Explicit formulas are given for a harmonic oscillator with an arbitrary time-dependent frequency.

quant-ph↗
arXiv1997

Functional determinants via Wronski construction of Green functions

A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator with an arbitrary time-dependent frequency. Here our result is a generalization of Gel'fand-Yaglom's famous formula which was restricted to Dirichlet boundary conditions. Apart from the generalization, our derivation is more transparent than theirs, the determinants requiring only knowledge of the classical trajectories. Special properties of operators with a zero mode are exhibited. Our technique does not require the calculation of the spectrum and is as simple as Wronski's method for Green functions.

math-ph↗