Effect of resonances on the transport properties of two-dimensional disordered systems

We study both analytically and numerically how the electronic structure and the transport properties of a two-dimensional disordered system are modified in the presence of resonances. The energy dependence of the density of states and the localization length at different resonance energies and strengths of coupling between resonances and random states are determined. The results show, that at energy equals to the resonance energy there is an enhancement in the density of states. In contrast, the localization length remains unaffected from the presence of the resonances and is similar to the one of the standard Anderson model. Finally, we calculate the diffusion constant as a function of energy and we reveal interesting analogies with experimental results on light scattering in the presence of Mie resonances.Comment: 4 pages, 4 figures, accepted in Phys. Rev. B (2000

Non-linear supersymmetric Sigma-Model for Diffusive Scattering of Classical Waves with Resonance Enhancement

We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger waves) and display similarities of and differences between both cases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett. 66 (1991) 3132), we then generalize the non-linear sigma-model further to include resonance scattering. We find that the form of the effective action is unchanged but that a parameter of the effective action, the mean level density, is modified in a manner which correctly accounts for the data.Comment: 4 pages, 1 Figure, to be published in Europhysics Letter

About the determination of critical exponents related to possible phase transitions in nuclear fragmentation

We introduce a method based on the finite size scaling assumption which allows to determine numerically the critical point and critical exponents related to observables in an infinite system starting from the knowledge of the observables in finite systems. We apply the method to bond percolation in 2 dimensions and compare the results obtained when the bond probability p or the fragment multiplicity m are chosen as the relevant parameter.Comment: 12 pages, TeX, 4 figure

The Effect of Resonances on Diffusive Scattering

The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states, and the effective Lagrangean of the generating functional for the two-point function. We show that the diffusion constant scales with the effective mean level spacing. The latter exhibits a resonance dip. These facts allow us to interpret experimental results on light scattering for different concentrations of resonant scatterers.Comment: 12 pages, 1 Figure, to be published in Physical Review

Chaotic Scattering with Resonance Enhancement

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.Comment: 13 pages, 2 figures, REVTEX. To appear in Nucl. Phys. A (1996

Photocount statistics of chaotic lasers

We derive the photocount statistics of the radiation emitted from a chaotic laser resonator in the regime of single-mode lasing. Random spatial variations of the resonator eigenfunctions lead to strong mode-to-mode fluctuations of the laser emission. The distribution of the mean photocount over an ensemble of modes changes qualitatively at the lasing transition, and displays up to three peaks above the lasing threshold

Phonon-mediated thermal conductance of mesoscopic wires with rough edges

We present an analysis of acoustic phonon propagation through long, free-standing, insulating wires with rough surfaces. Due to a crossover from ballistic propagation of the lowest-frequency phonon mode at $\omega <\omega _{1}=\pi c/W$ to a diffusive (or even localized) behavior upon the increase of phonon frequency, followed by re-entrance into the quasi-ballistic regime, the heat conductance of a wire acquires an intermediate tendency to saturate within the temperature range $T\sim \hbar \omega_{1}/k_{B}$.Comment: 4 pages, 3 figures included; minor changes and corrections, figures 1 and 2 replaced by better versions; to appear in PRB Brief Report

Incorporating Radial Flow in the Lattice Gas Model for Nuclear Disassembly

We consider extensions of the lattice gas model to incorporate radial flow. Experimental data are used to set the magnitude of radial flow. This flow is then included in the Lattice Gas Model in a microcanonical formalism. For magnitudes of flow seen in experiments, the main effect of the flow on observables is a shift along the $E^*/A$ axis.Comment: Version accepted for publication in Phys. Rev. C, Rapid Communicatio

Influence of measurement on the life-time and the line-width of unstable systems

We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schr\"odinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time-development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse life-time -- it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.Comment: 13 pages, 8 figures, comments and references added; to appear in Phys. Rev.

Effect of the measurement on the decay rate of a quantum system

We investigated the electron tunneling out of a quantum dot in the presence of a continuous monitoring by a detector. It is shown that the Schr\"odinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time-development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, $\exp (-\Gamma t)$, contrary to expectations based on the Quantum Zeno effect . However, the width of the energy distribution of the tunneling electron is no more $\Gamma$, but increases due to the decoherence, generated by the detector.Comment: Additional explanations are added. Accepted for publications in Phys. Rev. Let