Vladimir N. Prigodin

SPATIAL CORRELATION IN QUANTUM CHAOTIC SYSTEMS WITH TIME-REVERSAL SYMMETRY: THEORY AND EXPERIMENT

The correlation between the values of wave functions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the wave function density for a given eigenstate, although the background wave function density fluctuates strongly. We show that for large fluctuations, once the value of the wave function at one point is known, its spatial dependence becomes highly predictable for increasingly large space around this point. These results are compared with the experimental wave functions obtained from billiard-shaped microwave cavities, and very good agreement is demonstrated.

Distribution of the absorption by chaotic states in quantum dots

The mesoscopic fluctuations of the absorption by optical transitions from a low-energy regular state to high- energy chaotic states are studied in an aggregate of semiconductor quantum dots. We derive a universal form of the distribution for the absorption coefficient which depends on the total number of dots and the level broadening. The fluctuation of absorption spectra remains appreciable even at large broadening, and it should demonstrate a strong sensitivity to weak magnetic field in the regions where large and small absorption occurs. The results also apply to the absorption of Rydberg atoms in a strong magnetic field at the prethreshold ionization. \textcopyright{} 1996 The American Physical Society.

STATISTICAL PROPERTIES OF LEVEL WIDTHS AND CONDUCTANCE PEAKS IN A QUANTUM DOT

We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wavefunction averaged over the contact area. The distribution function of level widths for a two-point contact is evaluated exactly. The distribution resembles closely the result obtained when the wavefunction fluctuates independently at each point, but differs from the one-point case. Analytical calculations and numerical simulations show that the distribution for many-point contacts has a power-law behavior at small level widths. The exponent is given by the number of points in the lead and diverges in the continuous limit. The distribution of level widths is used to determine the distribution of conductance peaks in the resonance regime. At intermediate temperatures, we find that the distribution tends to normal and fluctuations in the height of the peaks are suppressed as the lead size is increased.

One-dimensional localization effects in three-dimensional structures of highly-conducting polymers

Abstract Starting with a model of weakly overlapping metallic chains we developed a transport theory for degenerate electrons in an irregular structure of fibril-form polymers. The anisotropy of intrafibril kinetic characteristics is enhanced by highly anisotropic scattering by dopants. Therefore, in spite of the weak backward impurity scattering, the 1d localization effects can be profound on an intrinsic level. The kinetic state of the 3d polymer structure is determined by the interfibril electron transfer-rate and the density of cross-links. The role of phonons consists mainly in breaking of localization at higher temperatures. In the dielectric phase at low temperatures the transport is provided by phonon-assisted hopping. The interplay between weak interfibril hopping and fast intrafibril incoherent diffusion leads to the specific temperature dependence for the conductivity and the dielectric properties. These results describe very well the experimental dependencies for dc -conductivity and mw -dielectric constant in heavily doped polyacetylene and polyaniline.

The Anderson metal-insulator transition in quasi-1D systems: implication to polyacetylene

Abstract The recent experimental data on the low temperature dependence of conductivity and magnetoresistance of ‘new’ (i.e. highly oriented highly conducting) polyacetylene are discussed within the model of a quasi-1D metal. It is suggested that the high anisotropy of the internal kinetic parameters, which is required for the explanation of these data, could be additionally produced by the anisotropy of the electron scattering by dopants. The dopants provide a strong forward scattering of electrons, while a backward scattering remains unaffected by them. The phonon scattering leads only to the suppression of the weak localization effects.

NMR IN A SYSTEM OF SMALL METALLIC PARTICLES: A NOVEL MESOSCOPIC PHENOMENON

We consider the NMR line shape for a system of small metal particles. The problem is reduced to calculation of the local density of states distribution function. We present the first exact calculation of this quantity for the mesoscopic system. Using the super-symmetry method, we calculated exactly the whole distribution function which gives the resonance-line shape. It turns out that at low temperatures, the line becomes very broad and asymmetric. The Knight shift defined as the maximum of the line decreases when decreasing the temperature. We found a good agreement of our results with a few experiments done long ago.

Short-range interaction effects on the density of states of disordered two-dimensional crystals with a half filled band

The density of electronic states (DOS) of a two-dimensional square lattice with substitutional impurities is calculated in the presence of short-range electron-electron interactions. In the middle of the energy band, the Bragg reflections off the Brillouin zone boundary are shown to lead to additional quantum corrections to the DOS, the sign of which is opposite to the sign of the Altshuler-Aronov logarithmic correction. The resulting quantum correction to the DOS at half-filling is positive; i.e., the DOS increases logarithmically as the Fermi energy is approached. However, far from the commensurate points where the Bragg reflections are suppressed, the negative logarithmic corrections to the DOS survive.

Sensitivity of quantum chaotic wave-function intensities to changes in external perturbations.

We examine the sensitivity of wavefunction intensities in chaotic quantum systems to small changes in an arbitrary external perturbation. A universal scaling is proposed for all three Dyson ensembles and a novel theoretical approach is used to determine exact expressions for systems which violate T-invariance. Analytical results are compared with numerical simulations of tight-binding Anderson Hamiltonians.

Metal-insulator transition in an irregular structure of coupled metallic chains

Abstract A model of the random network of coupled metallic wires is suggested to describe transport properties of highly conducting fibril-form polymers. The suppression of closed paths in the model enables us to study exactly the transition from the dielectric to the conductive state. The critical concentration of the interwire crosslinks determining the transition depends on the localization length of a single wire and on the interwire coupling. The temperature dependence of the network conductivity near the transition is discussed.

SPATIAL CORRELATIONS OF CHAOTIC WAVE FUNCTIONS

The statistics of the spatial correlations of eigenfunctions is investigated in chaotic systems with or without time-reversal symmetry. It is rigorously shown that wave functions corresponding to different energy levels are uncorrelated in space. At a given eigenstate, we find that though the background of wave function density fluctuates strongly, there exist the long-standing Friedel oscillations in wave function intensity. The joint distribution of the intensity at two separate space points is presented by the universal law with one parameter — the average amplitude correlation. This distribution encompasses two different regions: One with an independent joint distribution for small values of density fluctuations, and the other showing an increasing spatial correlation for the large fluctuations.