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A. Ya. Maltsev

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

At least 37 records · Page 2Linked to original sources
arXiv2020

Oscillation phenomena and experimental determination of exact mathematical Stability Zones for magneto-conductivity in metals having complicated Fermi surfaces

We consider the problem of exact experimental determination of the boundaries of Stability Zones for magneto-conductivity in normal metals in the space of directions of $\, {\bf B} \, $. As can be shown, this problem turns out to be nontrivial since the exact boundaries of Stability Zones are in fact unobservable in direct measurements of conductivity. However, this problem can be effectively solved with the aid of the study of oscillation phenomena (cyclotron resonance, quantum oscillations) in normal metals, which reveal a singular behavior on the mathematical boundary of a Stability Zone.

cond-mat.mtrl-sci↗
arXiv2020

The second boundaries of Stability Zones and the angular diagrams of conductivity for metals having complicated Fermi surfaces

We consider some general aspects of dependence of magneto-conductivity on a magnetic field in metals having complicated Fermi surfaces. As it is well known, a nontrivial behavior of conductivity in metals in strong magnetic fields is connected usually with appearance of non-closed quasiclassical electron trajectories on the Fermi surface in a magnetic field. The structure of the electron trajectories depends strongly on the direction of the magnetic field and usually the greatest interest is caused by open trajectories that are stable to small rotations of the direction of $\, {\bf B} $. The geometry of the corresponding Stability Zones on the angular diagram in the space of directions of $\, {\bf B} \, $ represents a very important characteristic of the electron spectrum in a metal linking the parameters of the spectrum to the experimental data. Here we will consider some very general features inherent in the angular diagrams of metals with Fermi surfaces of the most arbitrary form. In particular, we will show here that any Stability Zone actually has a second boundary, restricting a larger region with a certain behavior of conductivity. Besides that, we shall discuss here general questions of complexity of the angular diagrams for the conductivity and propose a theoretical scheme for dividing the angular diagrams into "simple" and "complex" diagrams. The proposed scheme will in fact also be closely related to behavior of the Hall conductivity in a metal in strong magnetic fields. In conclusion, we will also discuss the relationship of the questions under consideration to the general features of an (abstract) angular diagram describing the behavior of quasiclassical electron trajectories at all energy levels in the conduction band.

cond-mat.mtrl-sci↗
arXiv2020

Reconstructions of the electron dynamics in magnetic field and the geometry of complex Fermi surfaces

The paper considers the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of closed extremal trajectories of a special form, closely related to geometry and topology of the Fermi surface. The study of oscillation phenomena on such trajectories allows, in particular, to propose a relatively simple method for refining the parameters of the dispersion relation in metals with complex Fermi surfaces.

cond-mat.mes-hall↗
arXiv2020

On the canonical forms of the multi-dimensional averaged Poisson brackets

We consider here special Poisson brackets given by the "averaging" of local multi-dimensional Poisson brackets in the Whitham method. For the brackets of this kind it is natural to ask about their canonical forms, which can be obtained after transformations preserving the "physical meaning" of the field variables. We show here that the averaged bracket can always be written in the canonical form after a transformation of "Hydrodynamic Type" in the case of absence of annihilators of initial bracket. However, in general case the situation is more complicated. As we show here, in more general case the averaged bracket can be transformed to a "pseudo-canonical" form under some special ("physical") requirements on the initial bracket.

math-ph↗
arXiv2018

On the analytical properties of the magneto-conductivity in the case of presence of stable open electron trajectories on a complex Fermi surface

We consider the electric conductivity in normal metals in presence of a strong magnetic field. It is assumed here that the Fermi surface of a metal has rather complicated form such that different types of quasiclassical electron trajectories can appear on the Fermi level for different directions of B. The effects we consider are connected with the existence of regular (stable) open electron trajectories which arise in general on complicated Fermi surfaces. The trajectories of this type have a nice geometric description and represent quasiperiodic lines with a fixed mean direction in the p-space. Being stable geometric objects, the trajectories of this kind exist for some open regions in the space of directions of B, which can be represented by "Stability Zones" on the unit sphere. The main goal of the paper is to give a description of the analytical behavior of conductivity in the Stability Zones, which demonstrates in general rather nontrivial properties.

cond-mat.other↗
arXiv2015

On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations

We consider the questions connected with the Hamiltonian properties of the Whitham equations in case of several spatial dimensions. An essential point of our approach here is a connection of the Hamiltonian structure of the Whitham system with the finite-dimensional Poisson bracket defined on the space of periodic or quasi-periodic solutions. From our point of view, this approach gives a possibility to construct the Hamiltonian structure of the Whitham equations under minimal requirements on the properties of the initial system. The Poisson bracket for the Whitham system can be considered here as a deformation of the finite-dimensional bracket with the aid of the Dubrovin - Novikov procedure of bracket averaging. At the end, we consider the examples where the constructions of the paper play an essential role for the construction of the Poisson bracket for the Whitham system.

nlin.SI↗
arXiv2014

The averaging of multi-dimensional Poisson brackets for systems having pseudo-phases

We consider features of the Hamiltonian formulation of the Whitham method in the presence of pseudo-phases. As we show, an analog of the procedure of averaging of the Poisson bracket with the reduced number of the first integrals can be suggested in this case. The averaged bracket gives a Poisson structure for the corresponding Whitham system having the form similar to the structures arising in the presence of ordinary phases.

nlin.SI↗
arXiv2010

The deformation of the Whitham systems in the almost linear case

We consider the deformation of the Whitham systems in the case when the initial system is close to linear one. It appears that the deformation procedure should be modified in this special case to make all the constructions stable in the linear limit. We suggest here the special deformation scheme which gives the stable deformation of the Whitham system for the almost linear initial systems.

nlin.SI↗
arXiv2010

The conservation of the Hamiltonian structures in the deformations of the Whitham systems

We consider the construction of the deformed Whitham system for the KdV-equation in the one-phase case and investigate the conservation of the Hamiltonian properties in this situation. It is shown then, that both the Gardner - Zakharov - Faddeev and the Magri brackets give the deformed Dubrovin - Novikov brackets (the brackets of Dubrovin - Zhang type) for the deformed Whitham system constructed by our procedure. The general approach used in the paper gives a scheme for the averaging of the Poisson structures in the general situation.

nlin.SI↗
arXiv2006

Whitham systems and deformations

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius manifolds corresponding to the Whitham systems of integrable hierarchies. Under some non-degeneracy requirements we suggest a general scheme of the deformation of the hyperbolic Whitham systems using the initial non-linear system. The general form of the deformed Whitham system coincides with the form of the "low-dispersion" asymptotic expansions used by B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius manifolds.

nlin.SI↗
arXiv2004

Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type

We consider the special type of the field-theoretical Symplectic structures called weakly nonlocal. The structures of this type are in particular very common for the integrable systems like KdV or NLS. We introduce here the special class of the weakly nonlocal Symplectic structures which we call the weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of "averaging" of the weakly nonlocal Symplectic structures. The averaging procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type for the corresponding Whitham system. The procedure gives also the "action variables" corresponding to the wave numbers of $m$-phase solutions of initial system which give the additional conservation laws for the Whitham system.

nlin.SI↗
arXiv2004

The averaging of weakly nonlocal Symplectic Structures

We consider the averaging of the weakly nonlocal Symplectic Structures corresponding to local evolution PDE's in the Whitham method. The averaging procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type for the corresponding Whitham system. The procedure gives also the "action variables" corresponding to the wave numbers of $m$-phase solutions of initial system which give the additional conservation laws for the Whitham system.

nlin.SI↗
arXiv2003

Topology, Quasiperiodic functions and the Transport phenomena

In this article we give the basic concept of the "Topological Numbers" in theory of quasiperiodic functions. The main attention is paid to apperance of such values in transport phenomena including Galvanomagnetic phenomena in normal metals (Chapter 1) and the modulations of 2D electron gas (Chapter 2). We give just the main introduction to both of these areas and explain in a simple way the appearance of the "integral characteristics" in both of these problems. The paper can not be considered as the detailed survey article in the area but explains the main basic features of the corresponding phenomena.

cond-mat↗
arXiv2003

Quasiperiodic functions and Dynamical Systems in Quantum Solid State Physics

This is a survey article dedicated to the study of topological quantities in theory of normal metals discovered in the works of the authors during the last years. Our results are based on the theory of dynamical systems on Fermi surfaces. The physical foundations of this theory (the so-called "Geometric Strong Magnetic Field Limit") were found by the school of I.M.Lifshitz many years ago. Here the new aspects in the topology of quasiperiodic functions are developed.

math-ph↗
arXiv2003

Dynamical Systems, Topology and Conductivity in Normal Metals

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our investigation is based on the study of dynamical systems on Fermi surfaces for the motion of semi-classical electron in magnetic field. All possible asymptotic regimes are also found for $B \to \infty$ based on the topological classification of trajectories.

cond-mat.stat-mech↗
arXiv2001

On the local systems Hamiltonian in the weakly nonlocal Poisson brackets

We study in this work the important class of nonlocal Poisson Brackets (PB) which we call weakly nonlocal. They appeared recently in some investigations in the Soliton Theory. However there was no theory of such brackets except very special first order case. Even in this case the theory was not developed enough. In particular, we introduce the Physical forms and find Casimirs, Momentum and Canonical forms for the most important Hydrodynamic type PB of that kind and their dependence on the boundary conditions.

nlin.SI↗