arXiv subjects

Boris L. Altshuler

Publications and source records attributed to Boris L. Altshuler.

65 records · Page 4Linked to original sources

arXiv2001

Anderson Orthogonality Catastrophe in Disordered Systems

We study the Anderson orthogonality catastrophe (AOC) in finite conductors with diffusive disorder. The disorder averaged logarithm of $χ$, the overlap between the ground states before and after adding a static impurity, is found to depend nonmonotonically on the disorder. In two dimensions $<\lnχ^{-1}> \propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence on the number of electrons $N$ than in the canonical AOC. A very broad tail of the distribution of $χ$, found numerically, is a signature of the importance of a few-level statistics at the Fermi energy.

cond-mat.mes-hall↗

arXiv2000

Conductance peak motion due to a magnetic field in weakly coupled chaotic quantum dots

We study the influence of moderate exchange interactions of electrons on the behavior of the peaks in the conductance of single electron transistors. We numerically reproduce recently observed features of both the peak positions and the peak heights magnetic field dependence. These features unambiguously identify the total spin $S$ of each ground state. We evaluate the probability of each $S$ (combination of spontaneous and induced magnetization) as a function of the exchange strength, $J$, and external magnetic field, $B$. The expressions involve only $J$ and $g$-factor as adjustable parameters. Moreover, in a surprisingly broad parameter range these probabilities are determined by certain linear combinations of $J$ and $B$.

cond-mat.mes-hall↗

arXiv2000

"Scars" in parametrically excited surface waves

We consider the Faraday surface waves of a fluid in a container with a non-integrable boundary shape. We show that, at sufficiently low frequencies, the wave patterns are ``scars'' selected by the instability of the corresponding periodic orbits, the dissipation at the container side walls, and interaction effects which reflect the nonlinear nature of the Faraday waves. The results explain the observation of a limited number of scars with anomalous strengths in recent experiments by Kudrolli, Abraham and Gollub.

cond-mat↗

arXiv1998

On the Theory of Metal-Insulator Transitions in Gated Semiconductors

It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the oxide layer. The gate voltage changes the number of charged traps which results in a sharp change in the resistivity. The observed exponential temperature dependence of the resistivity in the metallic phase of the transition follows from the temperature dependence of the trap occupation number. The model naturally describes the experimentally observed scaling properties of the transition and effects of magnetic and electric fields.

cond-mat.dis-nn↗

arXiv1998

Spectral statistics in disordered metals: a trajectories approach

We show that the perturbative expansion of the two-level correlation function, $R(ω)$, in disordered conductors can be understood semiclassically in terms of self-intersecting particle trajectories. This requires the extension of the standard diagonal approximation to include pairs of paths which are non-identical but have almost identical action. The number of diagrams thus produced is much smaller than in a standard field-theoretical approach. We show that such a simplification occurs because $R(ω)$ has a natural representation as the second derivative of free energy $F(ω)$. We calculate $R(ω)$ to 3-loop order, and verify a one-parameter scaling hypothesis for it in 2d. We discuss the possibility of applying our ``weak diagonal approximation'' to generic chaotic systems.

cond-mat.mes-hall↗

arXiv1997

Deviations from the Gaussian distribution of mesoscopic conductance fluctuations

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive.

cond-mat.mes-hall↗

arXiv1996

Chaos, interactions, and nonequilibrium effects in the tunneling resonance spectra of small metallic particles

We explain the observation of clusters in the tunneling resonance spectra of small metallic particles of few nanometer size. Each cluster of resonances is identified with one excited single--electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single--electron states. Assuming the underlying classical dynamics of the electrons to be chaotic, we determine the typical shift to be $Δ/g$ where $g$ is the dimensionless conductance of the grain.

cond-mat↗

arXiv1996

Spin-Orbit Assisted Variable-Range Hopping in Strong Magnetic Fields

It is shown that in the presence of strong magnetic fields, spin-orbit scattering causes a sharp increase in the effective density of states in the variable-range hopping regime when temperature decreases. This effect leads to an exponential enhancement of the conductance above its value without spin-orbit scattering. Thus an experimental study of the hopping conductivity in a fixed, large magnetic field, is a sensitive tool to explore the spin-orbit scattering parameters in the strongly localized regime.

cond-mat↗

arXiv1996

Statistics of Rare Events in Disordered Conductors

Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of seldom occurring events than the approaches based on nonlinear $σ$-models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schrödinger equation. For two- and three-dimensional conductors new asymptotics of the distribution functions are obtained which in some cases differ significantly from previously established results.

cond-mat↗

arXiv1995

Spectral Statistics: From Disordered to Chaotic Systems

The relation between disordered and chaotic systems is investigated. It is obtained by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case. This association enables us to extend results obtained in the diffusive regime to general chaotic systems. In particular, the two--point level density correlator and the structure factor for general chaotic systems are calculated and characterized. The behavior of the structure factor around the Heisenberg time is quantitatively described in terms of short periodic orbits.

cond-mat↗

arXiv1995

Statistics of Oscillator Strengths in Chaotic Systems

The statistical description of oscillator strengths for systems like hydrogen in a magnetic field is developed by using the supermatrix nonlinear $σ$-model. The correlator of oscillator strengths is found to have a universal parametric and frequency dependence, and its analytical expression is given. This universal expression applies to quantum chaotic systems with the same generality as Wigner-Dyson statistics.

cond-mat↗