Imre Varga
University of Marburg
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Publication
Featured researches published by Imre Varga.
Physical Review E | 2003
Imre Varga; János Pipek
We discuss some properties of the generalized entropies, called Rényi entropies, and their application to the case of continuous distributions. In particular, it is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e., to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e., no classical limit can be defined. Numerical simulations on a one-dimensional disordered system corroborate our expectations.
Physical Review B | 2002
Imre Varga
The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.
International Journal of Quantum Chemistry | 1997
János Pipek; Imre Varga
It is known that in numerous interesting systems one-electron states appear with multifractal internal structure. Physical intuition suggest, however, that electron densities should be smooth both at atomic distances and close to the macroscopic limit. Multifractal behavior is expected at intermediate length scales, with observable non-trivial statistical properties in considerably, but far from macroscopically sized clusters. We have demonstrated that differences of generalized Renyi entropies serve as relevant quantities for the global characterization of the statistical nature of such electron densities. Asymptotic expansion formulas are elaborated for these values as functions of the length scale of observation. The transition from deterministic electron densities to statistical ones along various length of resolution is traced both theoretically and by numerical calculations.
Physical Review Letters | 2002
Philippe Jacquod; Imre Varga
We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U= infinity eigenstates bases, respectively. This implies the existence of a duality point U(d) where the eigenstates have the same spreading in both bases. U(d) is surrounded by an interval of finite width which is characterized by a non-Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.
Physical Review B | 2002
V. S. Filinov; Peter Thomas; Imre Varga; T. Meier; M. Bonitz; V. E. Fortov; S. W. Koch
The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path-integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering, as an application, a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.
Physical Review Letters | 2006
P. Bozsoki; P. Thomas; M. Kira; W. Hoyer; T. Meier; S. W. Koch; K. Maschke; Imre Varga; H. Stolz
The method of angular photonic correlations of spontaneous emission is introduced as an experimental, purely optical scheme to characterize disorder in semiconductor nanostructures. The theoretical expression for the angular correlations is derived and numerically evaluated for a model system. The results demonstrate how the proposed experimental method yields direct information about the spatial distribution of the relevant states and thus on the disorder present in the system.
EPL | 1996
Imre Varga; János Pipek; Martin Janssen; Krystian Pracz
Based on differences of generalized Renyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two-measure random Cantor set are calculated exactly and finally, using the results of numerical simulations, the distribution of the eigenvector components calculated in the critical region of the lowest Landau band is analyzed.
Physical Review B | 2006
J. A. Mendez-Bermudez; Imre Varga
We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times
European Physical Journal B | 1999
D. Brinkmann; J.E. Golub; S. W. Koch; P. Thomas; K. Maschke; Imre Varga
\tau
Physica Status Solidi B-basic Solid State Physics | 2000
P. Thomas; Imre Varga; T. Lemm; J.E. Golub; K. Maschke; T. Meier; S. W. Koch
and resonance widths