arXiv subjects
Publications and source records attributed to H. A. Weidenmueller.
The analogue of the Kolmogorov's four-fifths law is derived for two-dimensional, homogeneous, isotropic EMHD turbulence in the energy cascade inertial range. Direct numerical simulations for the freely decaying case show that this relation holds true for different values of the adimensional electron inertial length scale, $d_e$. The energy spectrum is found to be close to the expected Kolmogorov spectrum.
We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal wavefunction. This fact may cause strong correlations of neighboring conductance peaks. We demonstrate the relevance of our results for the interpretation of recent experiments on semiconductor quantum dots.
The passage of light or of electrons through a disordered medium is modified in the presence of resonances. We describe a simple model for this problem, and present first results.
Motivated by a recent experiment by Yacoby et al.\ [preprint, 1994], we calculate magnitude and phase $α$ of the transmission amplitude through a quantum dot. We work in the Coulomb blockade regime, assume the electrons not to interact, and consider tunneling through isolated resonances. Assuming a non--resonant background, we find that $α$ increases by $2 π$ over each resonance, with a sharp rise by $π$ over an energy interval much smaller than the thermal width. This is consistent with the experimental data. Our assumptions can be tested by further experiments.
We study random-matrix ensembles with a non-Gaussian probability distribution $P(H) \sim \exp (-N {\rm tr }\, V(H))$ where $N$ is the dimension of the matrix $H$ and $V(H)$ is independent of $N$. Using Efetov's supersymmetry formalism, we show that in the limit $N \rightarrow \infty$ both energy level correlation functions and correlation functions of $S$-matrix elements are independent of $P(H)$ and hence universal on the scale of the local mean level spacing. This statement applies to each of the three generic ensembles (unitary, orthogonal, and symplectic). Universality is also found for correlation functions depending on some external parameter. Our results generalize previous work by Brezin and Zee [Nucl.\ Phys.\ B {\bf 402}, 613 (1993)].
We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of recent experiments, which show suppression of weak localization due to magnetic field, in the framework of random-matrix theory. By analysing a random-matrix Hamiltonian for the billiard-lead system with the aid of Landauer's formula and Efetov's supersymmetry technique, we derive a universal expression for the weak-localization contribution to the mean conductance that depends only on the number of channels and the magnetic flux. We consequently gain a theoretical understanding of the continuous crossover from orthogonal symmetry to unitary symmetry arising from the violation of time-reversal invariance for generic chaotic systems.