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S. A. Bulgadaev

Publications and source records attributed to S. A. Bulgadaev.

At least 19 recordsLinked to original sources
arXiv2006

Topological quantization of current in quantum tunnel contacts

It is shown that an account of the Berry phase (a topological $θ$-term) together with a dissipative term in the effective action $S[ϕ]$ of the tunnel contacts induces a strong quantization of the tunnel current at low temperatures. This phenomenon like the Coulomb blockade reflects a discrete charge structure of the quantum shot noise and can ensure a quantization of the tunnel current without a capacitive charging energy $E_C$, when the latter is strongly suppressed by quantum fluctuations. Since a value of the $θ$-parameter is determined by the gate voltage, this effect allows to control a current through the contact. A possible physical application of this effect is proposed.

cond-mat.mes-hall↗
arXiv2005

Classical Hall transition and magnetoresistance in strongly inhomogeneous planar systems

The magneto-transport properties of planar and layered strongly inhomogeneous two-phase systems are investigated, using the explicit expressions for the effective conductivities and resistivities obtained by the exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the effective resistivity of various inhomogeneous media at arbitrary concentrations $x$ and magnetic fields $H$. The corresponding plots of the $x$-dependence of the Hall constant $R_H(x,H)$ and the magnetoresistance $R(x,H)$ are constructed for various values of magnetic field at some values of inhomogeneity parameters. These plots for strongly inhomogeneous systems at high magnetic fields show a sharp transition between partial Hall resistivities (or Hall conductivities) with different dependencies of $R_H$ on the phase concentrations. It is shown that there is a strong correlation between large linear magnetoresistance effect and this sharp Hall transition. Both these effects are a consequence of the exact duality symmetry. A possible physical explanation of these effects and their correlation is proposed.

cond-mat.dis-nn↗
arXiv2005

Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

Explicit expressions for magnetoresistance $R$ of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations $x$ and magnetic fields $H$. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the $x$- and $H$-dependencies of $R(x,H)$ are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides $Ag_{2+δ}Se.$ A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures.

cond-mat.dis-nn↗
arXiv2005

Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and allow to describe sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.

cond-mat.dis-nn↗
arXiv2005

Duality and exact results for conductivity of 2D isotropic heterophase systems in magnetic field

Using a fact that the effective conductivity sigma_{e} of 2D random heterophase systems in the orthogonal magnetic field is transformed under some subgroup of the linear fractional group, connected with a group of linear transformations of two conserved currents, the exact values for sigma_{e} of isotropic heterophase systems are found. As known, for binary (N=2) systems a determination of exact values of both conductivities (diagonal sigma_{ed} and transverse Hall sigma_{et}) is possible only at equal phase concentrations and arbitrary values of partial conductivities. For heterophase (N > 2) systems this method gives exact values of effective conductivities, when their partial conductivities belong to some hypersurfaces in the space of these partial conductivities and the phase concentrations are pairwise equal. In all these cases sigma_e does not depend on phase concentrations. The complete, 3-parametric, explicit transformation, connecting sigma_e in binary systems with a magnetic field and without it, is constructed

cond-mat.dis-nn↗
arXiv2005

Effective conductivity of 2D isotropic two-phase systems in magnetic field

Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They allow to describe sigma_{e} of various inhomogeneous media at arbitrary phase concentrations x and magnetic fields. the x-dependence plots of sigma_e at some values of inhomogeneity and magnetic field are constructed. Their behaviour is qualitatively compatible with the existing experimental data. The obtained results are applicable for different two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and admit a direct experimental checking.

cond-mat.dis-nn↗
arXiv2004

Effective conductivity of self-dual random heterophase systems

The duality and other symmetry properties of the effective conductivity sigma_e of the classical two-dimensional isotropic randomly inhomogeneous heterophase systems at arbitrary number of phases N are discussed. A new approach for a obtaining sigma_e based on a duality relation is proposed. The exact values of sigma_e at some special sets of the partial parameters are found.The explicit basic solutions of the duality relation, connected with the higher moments and satisfying all necessary requirements, are found at arbitrary values of partial parameters. It is shown that one of them can describe sigma_e for systems with a finite maximal characteristic scale of the inhomogeneities in a wide range of parameters. The other solution, connected with a mean conductivity describes sigma_e of the random parquet model of N-phase randomly inhomogeneous medium in some mean field like approximation. The comparison with the known effective medium approximation and crossover to the continuous smoothly inhomogeneous case are also discussed.

cond-mat.dis-nn↗
arXiv2004

On universality of conductivity of planar random self-dual systems

General properties of the effective conductivity sigma_e of planar isotropic randomly inhomogeneous two-phase self-dual systems are investigated. A new approach for finding out sigma_e of random systems based on a duality, a series expansion in the inhomogeneous parameter z and additional assumptions, is proposed. Two new approximate expressions for sigma_e at arbitrary values of phase concentrations are found. They satisfy all necessary inequalities, symmetries, including a dual one, and reproduce known results in various limiting cases. Two corresponding models with different inhomogeneity structures, whose sigma_e coincide with these expressions, are constructed. First model describes systems with a finite maximal characteristic scale of the inhomogeneities. In this model sigma_e is a solution of the approximate functional equation, generalizing the duality relation. The second model is constructed from squares with random layered structure. The difference of sigma_e for these models means a nonuniversality of the effective conductivity even for binary random self-dual systems. The first explicit expression for sigma_e can be used also for approximate description of various inhomogeneous systems with compact inclusions of the second phase. The percolation problem of these models is briefly discussed.

cond-mat.dis-nn↗
arXiv2004

Duality and Effective Conductivity of Random Two-Phase Flat Systems

The possible functional forms of the effective conductivity sigma_e of the randomly inhomogeneous two-phase systems at arbitrary values of concentrations are discussed. Two explicit approximate expressions for effective conductivity are found using a duality relation, a series expansion of sigma_e in the inhomogeneity parameter z and some additional conjectures about functional form of sigma_e. They differ from the effective medium approximation, satisfy all necessary requirements and reproduce the known formulas for sigma_e in weakly inhomogeneous case. This can signify also that sigma_e of the two-phase randomly inhomogeneous systems may be a nonuniversal function, depending on some details of the structure of the random inhomogeneities.

cond-mat.dis-nn↗
arXiv2004

On the effective conductivity of flat random two-phase models

An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly inhomogeneous model is constructed by a hierarchical method and its effective conductivity at arbitrary phase concentrations is found in the mean-field-like approximation. These expressions satisfy all the necessary symmetries, reproduce the known formulas for sigma_eff in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that sigma_eff even of two-phase randomly inhomogeneous system may be a nonuniversal function and can depend on some details of the structure of the inhomogeneous regions. The percolation limit is briefly discussed.

cond-mat.dis-nn↗
arXiv2003

Exact Results for Conductivity of 2D Isotropic Heterophase Systems

The duality relation for the effective conductivity sigma_{e} of 2D isotropic heterophase systems is used for obtaining the exact results for sigma_{e} at arbitrary number of phases N. The exact values of sigma_{e} correspond to the fixed points of the duality transformations. The new exact results for sigma_{e}, generalizing the well-known exact values of sigma_{e} for N = 2,3 at equal phase concentrations, are found. It is shown that for N > 3 there exist the whole hyperplanes in the space of phase concentrations, on which sigma_{e} takes constant values. These results are checked in the framework of various approximations for different random heterophase systems.

cond-mat.dis-nn↗
arXiv2002

Duality and Effective Conductivity of Two-dimensional Two-phase Systems

The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is deduced for systems with a finite maximal characteristical scale of the inhomogeneties and its solution is found. A hierarchical method of the construction of the model random inhomogeneous medium is proposed and one such simple model is constructed. Its effective conductivity at arbitrary phase concentrations is found in mean field like approximation. The derived formulas for the effective conductivity are different and also (1) satisfy all necessary inequalities and symmetries, including a dual symmetry; (2) reproduce the known formulas for sigma_{eff} in weakly inhomogeneous case. It means that in general sigma_{eff} of the two-phase randomly inhomogeneous systems may be a nonuniversal function and can depend on some details of the structure of the randomly inhomogeneous regions. The percolation limit is briefly discussed.

cond-mat↗
arXiv2000

D-Dimensional Conformal $σ$-models and Topological Excitations

The D-dimensional conformal nonlinear sigma-models (NSM) sre constructed. It is shown that the NSM on spaces with $π_{D-1} = \mathbb {Z}$ have the topological solutions of a "hedgehog" and "anti-hedgehog" types with logarithmic energies. For spaces with $π_D \ne 0$ they have also the topological excitations of instanton types with finite energies.

hep-th↗
arXiv2000

3D van der Waals $σ$-model and its Topological Excitations

It is shown that 3D vector van der Waals (conformal) nonlinear $σ$-model (NSM) on a sphere $S^2$ has two types of topological excitations reminiscent vortices and instantons of 2D NSM. The first, the hedgehogs, are described by homotopic group $π_2(S^2) = \mathbb {Z}$ and have the logarithmic energies. They are an analog of 2D vortices. The energy and interaction of these excitations are found. The second, corresponding to 2D instantons, are described by hpmotopic group $π_3(S^2) = \mathbb {Z}$ or the Hopf invariant $H \in \mathbb {Z}$. A possibility of the topological phase transition in this model and its applications are briefly discussed.

hep-th↗
arXiv1999

3D van der Waals sigma-model and topological excitations with logarithmic energy

The 3D vector van der Waals (or conformal) nonlinear sigma-model is proposed. It is shown that it has the "hedgehog"-like topological excitations with logarithmic energy. Their "neutral" configurations have nontrivial topological structures described by Hopf invariant. A possible influence of these excitations on the properties of the model are discussed.

hep-th↗
arXiv1999

Topological phase transitions in two-dimensional systems with internal symmetries

Possible generalizations of the topological (or Berezinskii-Kosterlitz-Thouless) phase transition on multicomponent 2D systems with nontrivial vector homotopic group pi_1 are considered. Relations between Ginzburg-Landau like theories, non-linear sigma-models on maximal Cartan subgroups of simple compact Lie groups and generalized sine-Gordon type theories are discussed. D-dimensional non-linear sigma-model admitting topological excitations with logarithmic energies are constructed.

hep-th↗