24 results on '"A. Ya. Maltsev"'
Search Results
2. Reconstructions of the Electron Dynamics in Magnetic Field and the Geometry of Complex Fermi Surfaces
- Author
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A. Ya. Maltsev
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Solid-state physics ,Oscillation ,FOS: Physical sciences ,General Physics and Astronomy ,Semiclassical physics ,Fermi surface ,01 natural sciences ,Magnetic field ,Condensed Matter - Other Condensed Matter ,Dispersion relation ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,010306 general physics ,Geometry and topology ,Other Condensed Matter (cond-mat.other) ,Fermi Gamma-ray Space Telescope - Abstract
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., 34 pages, 56 figures, revtex
- Published
- 2020
3. Theory of Dynamical Systems and Transport Phenomena in Normal Metals
- Author
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R. De Leo, S. P. Novikov, A. Ya. Maltsev, and Ivan Dynnikov
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Physics ,Solid-state physics ,Dynamical systems theory ,General Physics and Astronomy ,Motion (geometry) ,Electron ,01 natural sciences ,Magnetic field ,Theoretical physics ,0103 physical sciences ,010306 general physics ,Transport phenomena ,Topology (chemistry) ,Fermi Gamma-ray Space Telescope - Abstract
The results of recent studies in the theory of dynamical systems related to the motion of electrons on complex Fermi surfaces in normal metals are presented. The problem considered is closely related to the description of electron transport phenomena in strong magnetic fields and is therefore of great interest from the viewpoint of topology and dynamical systems theory. We will try to give a brief overview of the state of the art in this research area, as well as point out a number of interesting issues that are being actively studied at present.
- Published
- 2019
4. The Second Boundaries of Stability Zones and the Angular Diagrams of Conductivity for Metals Having Complicated Fermi Surfaces
- Author
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A. Ya. Maltsev
- Subjects
Physics ,Condensed Matter - Materials Science ,Solid-state physics ,Condensed matter physics ,010102 general mathematics ,Diagram ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,General Physics and Astronomy ,Boundary (topology) ,Fermi surface ,Mathematical Physics (math-ph) ,Electron ,Space (mathematics) ,01 natural sciences ,Magnetic field ,0103 physical sciences ,0101 mathematics ,010306 general physics ,Mathematical Physics ,Fermi Gamma-ray Space Telescope - Abstract
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., Comment: 27 pages, 42 figures, RevTex
- Published
- 2018
5. The Theory of Closed 1-Forms, Levels of Quasiperiodic Functions and Transport Phenomena in Electron Systems
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S. P. Novikov and A. Ya. Maltsev
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Mathematics (miscellaneous) ,Classical mechanics ,Dynamical systems theory ,Quasiperiodic function ,Condensed Matter::Strongly Correlated Electrons ,Fermi surface ,Electron ,Limit (mathematics) ,Transport phenomena ,Connection (mathematics) ,Magnetic field - Abstract
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 ωBτ →∞. We describe the history of the question and investigate 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.
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- 2018
6. The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields
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A. Ya. Maltsev
- Subjects
Physics ,Condensed Matter - Materials Science ,Mathematical diagram ,Condensed matter physics ,Solid-state physics ,General Physics and Astronomy ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Conductivity ,01 natural sciences ,Magnetic field ,Dispersion relation ,0103 physical sciences ,Complexity class ,010306 general physics ,Finite set ,Fermi Gamma-ray Space Telescope - Abstract
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., Comment: 24 pages, 32 figures, revtex
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- 2019
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7. Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter
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S. P. Novikov and A. Ya. Maltsev
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Physics ,Current (mathematics) ,Field (physics) ,Dynamical systems theory ,Plane (geometry) ,General Mathematics ,010102 general mathematics ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,01 natural sciences ,Quantum chaos ,Theoretical physics ,Quasiperiodic function ,0103 physical sciences ,Novikov self-consistency principle ,010307 mathematical physics ,0101 mathematics ,Transport phenomena ,Mathematical Physics - Abstract
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., Comment: 39 pages, 17 figures, Latex
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- 2018
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8. Deformations of the Whitham systems in the almost linear case
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A. Ya. Maltsev
- Published
- 2008
9. The Lorentz-invariant deformation of the Whitham system for the nonlinear Klein-Gordon equation
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A. Ya. Maltsev
- Subjects
Applied Mathematics ,Lorentz covariance ,symbols.namesake ,Nonlinear system ,Formalism (philosophy of mathematics) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Classical mechanics ,symbols ,Nonlinear Sciences::Pattern Formation and Solitons ,Klein–Gordon equation ,Analysis ,Lagrangian ,Mathematical physics ,Mathematics - Abstract
We consider a deformation of the Whitham system for the nonlinear Klein-Gordon equation. This deformation has a Lorentz-invariant form. Using the Lagrangian formalism of the original system, we obtain the first nontrivial correction to the Whitham system in the Lorentz-invariant approach.
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- 2008
10. On the canonical forms of the multi-dimensional averaged Poisson brackets
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A. Ya. Maltsev
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Pure mathematics ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,010102 general mathematics ,Bracket ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Field (mathematics) ,Mathematical Physics (math-ph) ,Type (model theory) ,01 natural sciences ,Poisson bracket ,Transformation (function) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Mathematics::Quantum Algebra ,0103 physical sciences ,Multi dimensional ,Initial value problem ,Canonical form ,010307 mathematical physics ,0101 mathematics ,Exactly Solvable and Integrable Systems (nlin.SI) ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematics - Abstract
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., Comment: 33 pages, Latex
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- 2015
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11. Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type
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A. Ya. Maltsev
- Subjects
Physics ,Conservation law ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Integrable system ,Structure (category theory) ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Type (model theory) ,Action (physics) ,Connection (mathematics) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Exactly Solvable and Integrable Systems (nlin.SI) ,Korteweg–de Vries equation ,Mathematics::Symplectic Geometry ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematical Physics ,Symplectic geometry ,Mathematical physics - Abstract
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., Comment: 64 pages, Latex
- Published
- 2004
12. Dynamical Systems, Topology, and Conductivity in Normal Metals
- Author
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A. Ya. Maltsev and S. P. Novikov
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Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Dynamical systems theory ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Observable ,Electron ,Conductivity ,Topology ,Resonance (particle physics) ,Magnetic field ,Topological group ,Condensed Matter - Statistical Mechanics ,Mathematical Physics ,Topology (chemistry) - Abstract
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., Comment: Latex, 51 pages, 14 eps figures
- Published
- 2004
13. Quasiperiodic functions and dynamical systems in quantum solid state physics
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A. Ya. Maltsev and S. P. Novikov
- Subjects
Physics ,Theoretical physics ,Dynamical systems theory ,General Mathematics ,Quantum mechanics ,Quasiperiodic function ,Fermi surface ,Limit (mathematics) ,State (functional analysis) ,Topology (chemistry) ,Fermi Gamma-ray Space Telescope ,Magnetic field - Abstract
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.
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- 2003
14. The Balian–Low theorem for the symplectic form on R2d
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John J. Benedetto, Wojciech Czaja, and Andrei Ya. Maltsev
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Pure mathematics ,Symplectic basis ,Uncertainty principle ,Balian–Low theorem ,Statistical and Nonlinear Physics ,Differential operator ,Mathematical Physics ,Symplectic geometry ,Mathematics - Abstract
In this paper we extend the Balian--Low theorem, which is a version of the uncertainty principle for Gabor (Weyl--Heisenberg) systems, to functions of several variables. In particular, we first prove the Balian--Low theorem for arbitrary quadratic forms. Then we generalize further and prove the Balian--Low theorem for differential operators associated with a symplectic basis for the symplectic form on ${\mathbb R}^{2d}$.
- Published
- 2003
15. Universal dynamical phase diagram of lattice spin models and strongly correlated ultracold atoms in optical lattices
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A. Ya. Maltsev, Eugene Demler, and A O Prokofiev
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Physics ,Quantum Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed matter physics ,FOS: Physical sciences ,Condensed Matter Physics ,01 natural sciences ,Atomic and Molecular Physics, and Optics ,010305 fluids & plasmas ,Condensed Matter - Strongly Correlated Electrons ,Quantum Gases (cond-mat.quant-gas) ,Ultracold atom ,Lattice (order) ,0103 physical sciences ,Condensed Matter - Quantum Gases ,Quantum Physics (quant-ph) ,010306 general physics ,Phase diagram - Abstract
We study semiclassical dynamics of anisotropic Heisenberg models in two and three dimensions. Such models describe lattice spin systems and hard core bosons in optical lattices. We solve numerically Landau-Lifshitz type equations on a lattice and show that in the phase diagram of magnetization and interaction anisotropy, one can identify several distinct regimes of dynamics. These regions can be distinguished based on the character of one dimensional solitonic excitations, and stability of such solitons to transverse modulation. Small amplitude and long wavelength perturbations can be analyzed analytically using mapping of non-linear hydrodynamic equations to KdV type equations. Numerically we find that properties of solitons and dynamics in general remain similar to our analytical results even for large amplitude and short distance inhomogeneities, which allows us to obtain a universal dynamical phase diagram. As a concrete example we study dynamical evolution of the system starting from a state with magnetization step and show that formation of oscillatory regions and their stability to transverse modulation can be understood from the properties of solitons. In regimes unstable to transverse modulation we observe formation of lump type solutions with modulation in all directions. We discuss implications of our results for experiments with ultracold atoms.
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- 2017
16. On the local systems Hamiltonian in the weakly non-local Poisson brackets
- Author
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A. Ya. Maltsev and S. P. Novikov
- Subjects
Physics ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,010102 general mathematics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Condensed Matter Physics ,First order ,01 natural sciences ,symbols.namesake ,Poisson bracket ,0103 physical sciences ,symbols ,Canonical form ,Boundary value problem ,Exactly Solvable and Integrable Systems (nlin.SI) ,0101 mathematics ,010306 general physics ,Hamiltonian (quantum mechanics) ,Mathematical Physics ,Mathematical physics - Abstract
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., Comment: 45 pages, latex
- Published
- 2001
17. Anomalous behavior of the electrical conductivity tensor in strong magnetic fields
- Author
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A. Ya. Maltsev
- Subjects
Physics ,Blocking (linguistics) ,Solid-state physics ,Condensed matter physics ,Electrical resistivity and conductivity ,Quantum electrodynamics ,General Physics and Astronomy ,Fermi surface ,Tensor ,Electron ,Conductivity ,Magnetic field - Abstract
The behavior of the electrical conductivity tensor in strong magnetic fields in the presence of unclosed quasiclassical electron trajectories of complex form near the Fermi surface is considered. It is shown that the asymptotic behavior of the conductivity tensor in the limit B→∞ differs in this case from the picture previously described for trajectories of simpler form. The possibility of blocking the longitudinal conductivity in strong magnetic fields at low temperatures in the case of a Fermi surface of special form is also treated theoretically.
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- 1997
18. Topological characteristics of electronic spectra of single crystals
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A. Ya. Maltsev and Ivan Dynnikov
- Subjects
Physics ,Solid-state physics ,Condensed matter physics ,Dispersion (optics) ,General Physics and Astronomy ,Topological order ,Electron ,Electronic band structure ,Topology ,Energy (signal processing) ,Spectral line ,Magnetic field - Abstract
The paper considers the topological characteristics of dispersion functions ɛs(p) in energy bands in single crystals related to classical electron trajectories in uniform magnetic fields. Specifically, the topological properties of open trajectories in p-space on various energy levels within one energy band and related physical effects are described.
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- 1997
19. Topological quantum characteristics observed in the investigation of the conductivity in normal metals
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A. Ya. Maltsev and S. P. Novikov
- Subjects
Physics ,Physics and Astronomy (miscellaneous) ,Solid-state physics ,Condensed matter physics ,Plane (geometry) ,Fermi surface ,Electron ,Conductivity ,Topology ,Quantum ,Topology (chemistry) ,Magnetic field - Abstract
It is shown that the investigation of the conductivity in a single crystal of a normal metal with a complicated Fermi surface in strong magnetic fields B can reveal integral topological characteristics which are determined by the topology of open-ended quasiclassical electron trajectories. Specifically, in the case of open-ended trajectories of the general position there always exists a direction η orthogonal to B in which the conductivity approaches zero for large B, and this direction lies in some integral (i.e., generated by two reciprocal-lattice vectors) plane that remains stationary for small variations of the direction of B.
- Published
- 1996
20. The conservation of the Hamiltonian structures in the deformations of the Whitham systems
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A. Ya. Maltsev
- Subjects
Statistics and Probability ,Physics ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,General Physics and Astronomy ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Poisson distribution ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Modeling and Simulation ,symbols ,Exactly Solvable and Integrable Systems (nlin.SI) ,Hamiltonian (quantum mechanics) ,Korteweg–de Vries equation ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematical physics - Abstract
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., Comment: 54 pages, 2 figures
- Published
- 2009
- Full Text
- View/download PDF
21. On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations
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A. Ya. Maltsev
- Subjects
Conservation law ,Partial differential equation ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Mathematical analysis ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,symbols.namesake ,Poisson bracket ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Hamiltonian structure ,symbols ,Exactly Solvable and Integrable Systems (nlin.SI) ,Korteweg–de Vries equation ,Hamiltonian (quantum mechanics) ,Mathematics::Symplectic Geometry ,Mathematical Physics ,Mathematics - Abstract
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., Comment: 69 pages, 1 figure, latex
- Published
- 2015
22. Topology, Quasiperiodic Functions, and the Transport Phenomena
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S. P. Novikov and A. Ya. Maltsev
- Subjects
Physics ,Theoretical physics ,Simple (abstract algebra) ,Quasiperiodic function ,Conductivity tensor ,Statistical physics ,Fermi gas ,Topology ,Transport phenomena ,Electrical phenomena ,Topology (chemistry) ,Electron trajectory - Abstract
In this chapter we give the basic concept of the “topological numbers” in the theory of quasiperiodic functions. Attention is especially paid to appearance of such quantities in transport phenomena, including galvanomagnetic phenomena in normal metals (Sect. 2.1) and the modulations of 2D electron gas (Sect. 2.3). We give a detailed introduction to both these areas and explain in a simple way the appearance of the “integral characteristics” in both these problems. Though this chapter cannot be considered a detailed survey in the area, it explains the main basic features of the corresponding phenomena.
- Published
- 2006
23. The averaging of local field-theoretic Poisson brackets
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A. Ya. Maltsev
- Subjects
Poisson bracket ,General Mathematics ,Mathematical analysis ,Local field ,Mathematics - Published
- 1997
24. Averaging of weakly non-local symplectic structures
- Author
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A. Ya. Maltsev
- Subjects
Symplectic vector space ,Symplectic group ,General Mathematics ,Mathematical analysis ,Symplectic representation ,Symplectomorphism ,Moment map ,Symplectic matrix ,Symplectic manifold ,Symplectic geometry ,Mathematics ,Mathematical physics - Published
- 2004
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