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B. A. Muzykantskii

Publications and source records attributed to B. A. Muzykantskii.

9 recordsLinked to original sources
arXiv2005

A minimal approach for the local statistical properties of a one-dimensional disordered wire

We consider a one-dimensional wire in gaussian random potential. By treating the spatial direction as imaginary time, we construct a `minimal' zero-dimensional quantum system such that the local statistical properties of the wire are given as products of statistically independent matrix elements of the evolution operator of the system. The space of states of this quantum system is found to be a particular non-unitary, infinite dimensional representation of the pseudo-unitary group, U(1,1). We show that our construction is minimal in a well defined sense, and compare it to the supersymmetry and Berezinskii techniques.

cond-mat.mes-hall↗
arXiv2003

Scattering Approach to Counting Statistics in Quantum Pumps

We consider the Fermi gas in a non-equilibrium state obtained by applying an arbitrary time-dependent potential to the Fermi gas in the ground state. We present a general method that gives the quantum statistics of any single-particle quantity, such as the charge, total energy or momentum, in this non-equilibrium state. We show that the quantum statistics may be found from the solution of a matrix Riemann-Hilbert problem. We use the method to study how the finite measuring time modifies the distribution of the charge transferred through a biased quantum point contact.

cond-mat↗
arXiv2000

Level and Eigenfunction Statistics in Billiards with Surface Scattering

Statistical properties of billiards with diffusive boundary scattering are investigated by means of the supersymmetric sigma-model in a formulation appropriate for chaotic ballistic systems. We study level statistics, parametric level statistics, and properties of electron wavefunctions. In the universal regime, our results reproduce conclusions of the random matrix theory, while beyond this regime we obtain a variety of system-specific results determined by the classical dynamics in the billiard. Most notably, we find that level correlations do not vanish at arbitrary separation between energy levels, or if measured at arbitrarily large difference of magnetic fields. Saturation of the level number variance indicates strong rigidity of the spectrum. To study spatial correlations of wavefunction amplitudes, we reanalyze and refine derivation of the ballistic version of the sigma-model. This allows us to obtain a proper matching of universal short-scale correlations with system-specific ones.

cond-mat↗
arXiv1998

Quantum Billiards with Surface Scattering: Ballistic Sigma-Model Approach

Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated.

cond-mat.mes-hall↗
arXiv1997

Fluctuations of Conductance Peak Spacings in the Coulomb Blockade Regime: Role of Electron-Electron Interaction

We study influence of electron-electron interaction on statistics of Coulomb blockade peak spacings in disordered quantum dots. It is shown that the interaction combined with fluctuations of eigenfunctions of the Fermi sea, enhances the peak spacing fluctuations, in accordance with recent experiments. In addition, account of the spin degrees of freedom leads to a pronounced odd-even structure for weak interaction ($e^2/ε\ll v_F$); in the opposite case ($e^2/ε\gtrsim v_F$) this structure is washed out.

cond-mat.mes-hall↗
arXiv1996

Finite-temperature Fermi-edge singularity in tunneling studied using random telegraph signals

We show that random telegraph signals in metal-oxide-silicon transistors at millikelvin temperatures provide a powerful means of investigating tunneling between a two-dimensional electron gas and a single defect state. The tunneling rate shows a peak when the defect level lines up with the Fermi energy, in excellent agreement with theory of the Fermi-edge singularity at finite temperature. This theory also indicates that defect levels are the origin of the dissipative two-state systems observed previously in similar devices.

cond-mat↗
arXiv1996

Nearly Localised States in Weakly Disordered Conductors. II. Beyond Diffusion Approximation

We use optimal fluctuation method for a new ballistic $σ$-model to study the long time dispersion of conductance $G(t)$ of a mesoscopic sample. In the long time limit the conductance of a $d$-dimensional sample decays as $\exp (-A \ln^d t ) $. At shorter times the new results match those in our previous paper. It is found that at very long times the diffraction effects are important and the ballistic treatment is not valid. We also suggest a physical picture of trapping.

cond-mat↗
arXiv1994

Nearly Localized States in Weakly Disordered Conductor

The time dispersion of the averaged conductance $G(t)$ of a mesoscopic sample is calculated in the long time limit when $t$ is much larger than the diffusion travelling time $ t_D$. In this case the functional integral in the effective supersymmetric field theory is determined by the saddle point contribution. If $t$ is shorter than the inverse level spacing $Δ$ ($Δt / \hbar \ll 1$), then $G(t)$ decays as $\exp[-t/t_D]$. In the ultra-long time limit ($Δt / \hbar \gg 1$) the conductance $G(t)$ is determined by the electron states that are poorly connected with the outside leads. The probability to find such a state decreases more slowly than any exponential funcion as $t$ tends to infinity. It is worth mentioning, that the saddle point equation looks very similar to the well known Eilenberger equation in the theory of dirty superconductors.

cond-mat↗