arXiv subjects

A. Ya. Maltsev

Publications and source records attributed to A. Ya. Maltsev.

At least 19 recordsLinked to original sources

arXiv2026

Analytical approximations of dispersion laws and ultra-complex conductivity diagrams

We study the probability of the emergence of ultra-complex conductivity diagrams in conductors that satisfy the tight-binding approximation and have the simple or body-centered cubic lattice. The presence of ultra-complex conductivity diagrams allows us to observe a number of highly nontrivial effects in strong magnetic fields, however, the probability of their emergence in a given substance is quite low. In the case of the simple or body-centered cubic lattice, the leading tight-binding approximation does not allow us to estimate this probability due to the peculiarities of the spectra in this situation. To estimate this probability, we use higher-order corrections to the leading approximation, which yield more accurate analytical expressions for the electron spectra.

cond-mat.mtrl-sci↗

arXiv2026

Ultra-complex conductivity diagrams in the nearly free electron approximation

We investigate the possibility of the emergence of ultra-complex conductivity diagrams in the nearly free electron approximation for metals with cubic symmetry. Estimates show that the emergence of such diagrams requires the Fermi level to fall into very narrow energy intervals within the conduction band. In our view, this circumstance is mostly due to the high symmetry and the simplest analytical form of the dispersion relations $ε({\bf p})$ under consideration.

cond-mat.mtrl-sci↗

arXiv2025

On chaotic regimes of conductivity behavior in the tight-binding approximation

We investigate the probability of detecting the most nontrivial conductivity behavior regimes in metals whose electron spectrum is described by the tight-binding approximation. These regimes are associated with the emergence of highly complex electron trajectories on the Fermi surface and correspond to a nontrivial (scaling) behavior of the conductivity tensor in strong magnetic fields. The geometry of such trajectories, as well as the corresponding conductivity regimes, have been well studied theoretically; however, they have not yet been observed experimentally. The results of our study allow us, in particular, to estimate the probability of their occurrence and to indicate the conditions for their possible detection for a wide class of conductors.

cond-mat.mtrl-sci↗

arXiv2025

On the Novikov problem for dihedral symmetry potentials

We consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic potentials of this type can have open level lines only at a single energy level $\, ε= ε_{0} \, $, which brings them close to random potentials on a plane.

math-ph↗

arXiv2025

On the scaling properties of quasicrystalline potentials of eightfold rotational symmetry

We consider a special class of quasi-periodic potentials arising in the physics of photonic systems and possessing rotational symmetry of the 8th order. We are interested in the ``scaling'' properties of such potentials, namely, the growth rate of their closed level lines near the percolation threshold. Estimates of the corresponding scaling indices allow, in particular, to carry out some comparison of such potentials with various models of random potentials on the plane.

math-ph↗

arXiv2025

On the level lines of two-layer symmetric potentials

We consider the behavior of level lines of two-dimensional potentials, which play an important role in the physics of ``two-layer'' systems. Potentials of this type are quasiperiodic and, at the same time, can also be considered as a model of random potentials on a plane. The description of level lines of such potentials is a special case of the Novikov problem for potentials with four quasiperiods and uses many features that arise in the study of the general Novikov problem. At the same time, the potentials under consideration also have their own clearly expressed specificity, which makes them very interesting for research from a variety of points of view.

math-ph↗

arXiv2024

On the Novikov problem for superposition of periodic potentials

We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems. Potentials of this type are given by a superposition of periodic potentials and represent quasiperiodic functions on a plane with four quasiperiods. Here we study an important special case when the periodic potentials have the same rotational symmetry. In the generic case, their superpositions have ``chaotic'' open level lines, which brings them close to random potentials. At the same time, the Novikov problem has interesting features also for ``magic'' rotation angles, which lead to the emergence of periodic superpositions.

math-ph↗

arXiv2024

Specificity of $τ$ -- approximation for chaotic electron trajectories on complex Fermi surfaces

The work examines a special behavior of the magnetic conductivity of metals that arises when chaotic electron trajectories appear on the Fermi surface. This behavior is due to the scattering of electrons at singular points of the dynamic system describing the dynamics of electrons in $\, {\bf p}$-space, and caused by small-angle scattering of electrons on phonons. In this situation, the electronic system is described by a "non-standard" relaxation time, which plays the main role in a certain range of temperature and magnetic field values.

cond-mat.stat-mech↗

arXiv2024

On the Novikov problem with a large number of quasiperiods and its generalizations

The paper considers the Novikov problem of describing the geometry of level lines of quasi-periodic functions on the plane. We consider here the most general case, when the number of quasi-periods of a function is not limited. The main subject of investigation is the arising of open level lines or closed level lines of arbitrarily large sizes, which play an important role in many dynamical systems related to the general Novikov problem. As can be shown also, the results obtained for quasiperiodic functions on the plane can be generalized to the multidimensional case. In this case, we are dealing with a generalized Novikov problem, namely, the problem of describing level surfaces of quasiperiodic functions in a space of arbitrary dimension. Like the Novikov problem on the plane, the generalized Novikov problem plays an important role in many systems containing quasiperiodic modulations.

math-ph↗

arXiv2023

Lifshitz transitions and angular conductivity diagrams in metals with complex Fermi surfaces

We consider the Lifshitz topological transitions and the corresponding changes in the galvanomagnetic properties of a metal from the point of view of the general classification of open electron trajectories arising on Fermi surfaces of arbitrary complexity in the presence of magnetic field. The construction of such a classification is the content of the Novikov problem and is based on the division of non-closed electron trajectories into topologically regular and chaotic trajectories. The description of stable topologically regular trajectories gives a basis for a complete classification of non-closed trajectories on arbitrary Fermi surfaces and is connected with special topological structures on these surfaces. Using this description, we describe here the distinctive features of possible changes in the picture of electron trajectories during the Lifshitz transitions, as well as changes in the conductivity behavior in the presence of a strong magnetic field. As it turns out, the use of such an approach makes it possible to describe not only the changes associated with stable electron trajectories, but also the most general changes of the conductivity diagram in strong magnetic fields.

cond-mat.mtrl-sci↗

arXiv2023

Geometry of quasiperiodic functions on the plane

The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the results obtained for functions with three quasi-periods, which play a very important role in the theory of transport phenomena in metals. In this part, along with previously known results, a number of new results are presented that significantly refine the general description of the picture that arises in this case. New statements are also presented for the case of functions with more than three quasi-periods, which open up approaches to the further study of Novikov's problem in the most general formulation. The role of Novikov's problem in various fields of mathematical and theoretical physics is also discussed.

math-ph↗

arXiv2023

Resonant contributions to oscillatory phenomena under conditions of magnetic breakdown during reconstructions of electron dynamics on the Fermi surface

We consider here special closed electron trajectories that arise during reconstructions of electron dynamics on the Fermi surface in the presence of strong magnetic fields, as well as the phenomenon of intraband magnetic breakdown that occurs on such trajectories. We consider cases where the electronic spectrum arising in such a situation corresponds to the resonant contribution to quantum oscillations. In the paper, all cases where this occurs are singled out, and the possible influence of the appearance of the Berry phase and other effects on the described phenomena is also considered.

cond-mat.mtrl-sci↗

arXiv2022

The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields

We consider angular diagrams describing the dependence of the magnetic conductivity of metals on the direction of the magnetic field in rather strong fields. As it can be shown, all angular conductivity diagrams can be divided into a finite number of classes with different complexity. The greatest interest among such diagrams is represented by diagrams with the maximal complexity, which can occur for metals with rather complicated Fermi surfaces. In describing the structure of complex diagrams, in addition to the description of the conductivity itself, the description of the Hall conductivity for different directions of the magnetic field plays very important role. For the evaluation of the complexity of angular diagrams of the conductivity of metals, it is convenient also to compare such diagrams with the full mathematical diagrams that are defined (formally) for the entire dispersion relation.

cond-mat.mtrl-sci↗

arXiv2022

Open level lines of a superposition of periodic potentials on a plane

We consider here open level lines of potentials resulting from the superposition of two different periodic potentials on the plane. This problem can be considered as a particular case of the Novikov problem on the behavior of open level lines of quasi-periodic potentials on the plane with four quasi-periods. At the same time, the formulation of this problem may have many additional features that arise in important physical systems related to it. Here we will try to give a general description of the emerging picture both in the most general case and in the presence of additional restrictions. The main approach to describing the possible behavior of the open level lines will be based on their division into topologically regular and chaotic level lines.

math-ph↗

arXiv2021

Distinctive features of oscillatory phenomena in reconstructions of the topological structure of electron trajectories on complex Fermi surfaces

We consider the behavior of classical and quantum oscillations in metals with complex Fermi surfaces near the directions of $\, {\bf B} \, $ corresponding to changes in the topological structure of the dynamical system describing the semiclassical motion of quasiparticles along the Fermi surface. The transitions through the boundaries of change in this structure are accompanied by sharp changes in the picture of oscillations, the form of which depends in the most essential way on the topological type of the corresponding reconstruction. We list here the main features of such changes for all topological types of elementary reconstructions and discuss the possibilities of experimental identification of such types based on these features.

cond-mat.mtrl-sci↗

arXiv2021

Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter

The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider here the history of the question, the current state of research in this field, and a number of applications of this problem to various physical problems. The main attention is paid to the applications of the results obtained in the field under consideration to the theory of transport phenomena in electron systems.

math-ph↗

arXiv2021

The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems

The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the trajectories of dynamical systems, arising at the Fermi surface in the presence of an external magnetic field, and the behavior of the conductivity tensor in a metal in the limit $\, ω_{B} τ\rightarrow \infty $. The paper contains a description of the history of the question and the investigation of special features of such behavior in the case of the appearance of trajectories of the most complex type on the Fermi surface of a metal.

math-ph↗

arXiv2020

Poisson brackets of hydrodynamic type and their generalizations

In this paper, we consider Hamiltonian structures of hydrodynamic type and some of their generalizations. In particular, we discuss the questions concerning the structure and special forms of the corresponding Poisson brackets and the connection of such structures with the theory of integration of systems of hydrodynamic type.

math-ph↗