arXiv subjects

A. G. Kutlin

Publications and source records attributed to A. G. Kutlin.

7 recordsLinked to original sources

arXiv2023

On a new exact relation for the connection matrices in case of a linear second-order ODE with non-analytic coefficients

We consider the phase-integral method applied to an arbitrary linear ordinary second-order differential equation with non-analytical coefficients. We propose a universal technique based on the Frobenius method which allows to obtain new exact relation between connection matrices associated with its general solution. The technique allows the reader to write an exact algebraic equation for the Stokes constants provided the differential equation has at most one regular singular point in a finite area of the complex plane. We also propose a way to write approximate relations between Stokes constants in case of multiple regular singular points located far away from each other. The well-known Budden problem is solved with help of this technique as an illustration of its usage. To access the HTML version of the paper & discuss it with the author, visit https://enabla.com/pub/607.

math-ph↗

arXiv2023

Generalized symmetry relations for connection matrices in the phase-integral method

We consider the phase-integral method applied to an arbitrary ordinary linear differential equation of the second-order and study how its symmetries affect the connection matrices associated with its general solution. We reduce the obtained exact general relation for the matrices to its limiting case introducing a concept of the effective Stokes constant. We also propose a concept of an effective Stokes diagram which can be a useful tool for analyzing difficult equations. We show that effective Stokes domains which can be overlapped by a symmetry transformation are associated with the same effective Stokes constant and can be described by the same analytical function. Basing on the derived symmetry relations, we propose a way to write functional equations for the effective Stokes constants. Finally, we provide a generalization of the derived symmetry relations for an arbitrary order linear system of the ordinary linear differential equations. This work also contains an example of usage of the presented ideas in a case of a real physical problem. To access the HTML version of the paper & discuss it with the author, visit https://enabla.com/pub/1108.

math-ph↗

arXiv2021

Emergent fractal phase in energy stratified random models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

cond-mat.dis-nn↗

arXiv2021

Geometry controlled superconducting diode and anomalous Josephson effect triggered by the topological phase transition in curved proximitized nanowires

We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference $φ_0$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase $φ_0$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the subgap and the continuum quasiparticle levels are responsible for the above behavior of the anomalous Josephson phase. It is demonstrated that the crossover region on $φ_0(h)$ dependencies reveals itself in the superconducting diode effect. The resulting tunable phase battery can be used as a probe of topological transitions in Majorana networks and can become a useful element of various quantum computation devices.

cond-mat.mes-hall↗

arXiv2020

Renormalization to localization without a small parameter

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.

cond-mat.dis-nn↗

arXiv2020

Geometry -- dependent effects in Majorana nanowires

Starting from the Bogolubov - de Gennes theory describing the induced p-wave superconductivity in the Majorana wire of an arbitrary shape, we predict a number of intriguing phenomena such as the geometry-dependent phase battery (or a phi-Josephson junction with the spontaneous superconducting phase difference) and generation of additional quasiparticle modes at the Fermi level with the spatial position tuned by the external magnetic field direction. This tuning can be used to extend the capabilities of the braiding protocols in Majorana networks.

cond-mat.mes-hall↗

arXiv2017

Bound State Energies using Phase Integral Analysis

The study of asymptotic properties of solutions to differential equations has a long and arduous history, with the most significant advances having been made in the development of quantum mechanics. A very powerful method of analysis is that of Phase Integrals, described by Heading. Key to this analysis are the Stokes constants and the rules for analytic continuation of an asymptotic solution through the complex plane. These constants are easily determined for isolated singular points, by analytically continuing around them and, in the case of analytic functions, requiring the asymptotic solution to be single valued. However, most interesting problems of mathematical physics involve several singular points. By examination of analytically tractable problems and more complex bound state problems involving multiple singular points, we show that the method of Phase Integrals can greatly improve the determination of bound state energies over the simple WKB values. We also find from these examples that in the limit of large separation the Stokes constant for a first order singular point approaches the isolated singular point value.

quant-ph↗