Publications (54)142.98 Total impact
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ABSTRACT: Recently [Europhys. Lett. {\bf 98}, 37006 (2012)], based on heuristic arguments, it was conjectured that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(qq')D_q]^{1}$, $1\le q \le 2$. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to $q<1/2$ and also to deterministic models producing multifractal eigenstates. We also demonstrate, for the scattering version of the powerlaw banded random matrix model at criticality, that the scaling exponents $\sigma_q$ of the inverse moments of Wigner delay times, $\bra \tau_{\tbox W}^{q} \ket \propto N^{\sigma_q}$ where $N$ is the linear size of the system, are related to the level compressibility $\chi$ as $\sigma_q\approx q(1\chi)[1+q\chi]^{1}$ for a limited range of $q$; thus providing a way to probe level correlations by means of scattering experiments.  [Show abstract] [Hide abstract]
ABSTRACT: The localization of oneelectron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a nonmonotonic behavior as a function of energy owing to anomalous behavior of fewsite localization. The twosite approximation is solved analytically and shown to capture the essential features found in numerical simulations on one, two and threedimensional systems. Further improvement has been obtained by solving a threesite model. 
Article: KondoAnderson Transitions
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ABSTRACT: Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metalinsulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperaturedependent spinflip scattering rate. Accordingly, we name them KondoAnderson transitions (KATs).  [Show abstract] [Hide abstract]
ABSTRACT: Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(qq')D_q]^{1}$, $1\le q \le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $\chi$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1\chi)[1+(q1)\chi]^{1}$, thus generalizing existing relations with relevance to the disorder driven Andersontransition.  [Show abstract] [Hide abstract]
ABSTRACT: At the Anderson metalinsulator transition the eigenstates develop multifractal fluctuations. Therefore their properties are intermediate between being extended and localized. As a result these wave functions are powerlaw correlated, which causes a substantial suppression of the local density of states at some random positions, resembling random local pseudogaps at the Fermi energy. Consequently the Kondo screening of magnetic moments is suppressed when a magnetic impurity happens to be at such a position. Due to these unscreened magnetic moments the critical exponents and multifractal dimensions at the metalinsulator transition take their smaller, unitary ensemble values for exchange couplings not exceeding a certain critical value J* ≈ .3D, where D is the band width. Here we present numerical calculations of the distribution of Kondo temperatures for the critical Powerlaw Band Random Matrix (PBRM) ensemble, whose properties are similar to that of the Anderson transition with the advantage of using a continuous parameter for tuning the generalized multifractal dimensions of the eigenstates. 
Article: Quantum chaos in one dimension?
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ABSTRACT: In this work we investigate the inverse of the celebrated BohigasGiannoniSchmit conjecture. Using two inversion methods we compute a onedimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N→∞ the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.  [Show abstract] [Hide abstract]
ABSTRACT: We study numerically the conductance statistics of the onedimensional (1D) Anderson model with random longrange hoppings described by the Powerlaw Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M singlemode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT)~TM2/2, for T  [Show abstract] [Hide abstract]
ABSTRACT: We study numerically scattering and transport statistical properties of the onedimensional Anderson model at the metalinsulator transition described by the powerlaw banded random matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of singlechannel attached leads. We observe a smooth crossover from localized to delocalized behavior in the averagescattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying b (the effective bandwidth of the PBRM model) from small (b⪡1) to large (b>1) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit b→∞. We also compare our results for the PBRM model with those for the threedimensional (3D) Anderson model at criticality, finding that the PBRM model with b∊[0.2,0.4] reproduces well the scattering and transport properties of the 3D Anderson model.  [Show abstract] [Hide abstract]
ABSTRACT: Excitonic spectra of weakly disordered semiconductor heterostructures are simulated on the basis of a onedimensional tightbinding model. The influence of the length scale of weak disorder in quantum wells on the redshift of the excitonic peak and its linewidth is studied. By calculating twodimensional Fouriertransform spectra we are able to determine the contribution of disorder to inhomogeneous and also to homogeneous broadenings separately. This disorderinduced dephasing is related to a Fanotype coupling and leads to contributions to the homogeneous linewidth that depends on energy within the inhomogeneously broadened line. The model includes heavyand lighthole excitons and yields smaller inhomogeneous broadening for the lighthole exciton if compared to the heavyhole exciton, which agrees qualitatively with the experiment.  [Show abstract] [Hide abstract]
ABSTRACT: Localization of the centerofmass (com) motion of an exciton in a disordered semiconductor structure is studied theoretically by focusing on nonlinear optical spectroscopy. A onedimensional tightbinding model with diagonal disorder is applied and the Coulomb interaction is treated consistently. In the ordered situation the centerofmass momentum (K) selection rule leads to only the lowest transition for K = 0. The break down of the comKselection rule produces the well known asymmetric excitonic lines of disordered semiconductors. The coupling between the lowest dominant transition to this modified comcontinuum yields Fanolike features in the nonlinear spectra.  [Show abstract] [Hide abstract]
ABSTRACT: We study numerically the conductance distribution function w(T) for the onedimensional Anderson model with random longrange hopping described by the Powerlaw Banded Random Matrix model at criticality. We concentrate on the case of two singlechannel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/Ttyp) is scale invariant, where Ttyp = exp 〈 ln T 〉 is the typical value of T. Moreover, we find that for T < Ttyp, w(ln T/Ttyp) shows a universal behavior proportional to (T/Ttyp)1/2.  [Show abstract] [Hide abstract]
ABSTRACT: We study numerically the statistical properties of some scattering quantities for the Powerlaw Banded Random Matrix model at criticality in the absence of timereversal symmetry, with a small number of singlechannel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating to metalliclike behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.  [Show abstract] [Hide abstract]
ABSTRACT: It is well known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and timereversal symmetry. At low temperature, these symmetries can be restored by Kondo screening. It is also known that at the Anderson metalinsulator transition, wave functions develop multifractal fluctuations with powerlaw correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. When the exchange coupling J is smaller than a certain value J;{*}, the metalinsulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states.  [Show abstract] [Hide abstract]
ABSTRACT: In a recent publication [Phys. Rev. Lett. 97, 227402 (2006)], it has been demonstrated numerically that a longrange disorder potential in a semiconductor quantum well can be reconstructed reliably via singlephoton interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent twolevel systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters, such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angleresolved singlephoton correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.  [Show abstract] [Hide abstract]
ABSTRACT: Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tightbinding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a oneelectron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.  [Show abstract] [Hide abstract]
ABSTRACT: We study the relaxation of a nonequilibrium carrier distribution under the influence of the electronelectron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a twoparticle part accounting for the Coulomb interaction. We apply the equationofmotion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequlibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder.  [Show abstract] [Hide abstract]
ABSTRACT: The system size dependence of the conductance in a class of tightbinding quasiperiodic potentials V0cos(παnν), where 0 < ν < 1, has been investigated numerically. It has been shown that at the metalinsulator transition (MIT), V0c = 2−E, the conductance follows a clear power law decay vs. system size, g ~ N−δ, which corroborates the existence of a pronounced power law localization at the MIT.  [Show abstract] [Hide abstract]
ABSTRACT: Based on differences of generalized R?nyi 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 twomeasure 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.  [Show abstract] [Hide abstract]
ABSTRACT: 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.  [Show abstract] [Hide abstract]
ABSTRACT: A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the manybody Coulomb interaction. As a case study, the light emission of a correlated plasma is investigated numerically for a onedimensional twoband tightbinding model. The band structure of the underlying ordered system is assumed to correspond to either a direct or an indirect semiconductor. In particular, luminescence and absorption spectra are computed for various levels of disorder and sample temperature to determine thermodynamic relations, the Stokes shift, and the radiative lifetime distribution.
Publication Stats
488  Citations  
142.98  Total Impact Points  
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Institutions

19972012

PhilippsUniversität Marburg
 Faculty of Physics
Marburg, Hesse, Germany 
Hungarian Academy of Sciences
Budapeŝto, Budapest, Hungary


19902010

Budapest University of Technology and Economics
 • Department of Theoretical Physics
 • Institute of Physics
Budapest, Budapest fovaros, Hungary


19982000

University of Cologne
 Institute for Theoretical Physics
Köln, North RhineWestphalia, Germany


1987

Keio University
 Department of Physics
Edo, Tōkyō, Japan
