0000000000037595
AUTHOR
Michael Schreiber
showing 39 related works from this author
Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian
1993
A method to describe the metal-insulator transition (MIT) in disordered systems is presented. For this purpose the statistical properties of the eigenvalue spectrum of the Anderson Hamiltonian are considered. As the MIT corresponds to the transition between chaotic and nonchaotic behavior, it can be expected that the random matrix theory enables a qualitative description of the phase transition. We show that it is possible to determine the critical disorder in this way. In the thermodynamic limit the critical point behavior separates two different regimes: one for the metallic side and one for the insulating side.
A Monte Carlo Study of the Low-Temperature Properties of Strongly Correlated Localized Particles in Disordered Systems
1993
A computer simulation method is presented, which yields the ground state as well as the low-energy excitations for disordered systems of many interacting particles. The efficiency of the method is demonstrated by the application to the Coulomb glass, i.e. many localized electrons with long-range interaction. The obtained knowledge about the specific configurations of a large number of excited states is only the starting point for further investigations. First results are presented which shed a new light on old controversies about the behaviour of correlated electrons within the Coulomb gap regime.
MULTIFRACTAL ELECTRONIC WAVE FUNCTIONS IN THE ANDERSON MODEL OF LOCALIZATION
1992
Investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.
Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
1994
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.
Excitons and nonlinear optical spectra in conjugated polymers.
1992
Excitons in conjugated polymers are studied theoretically in the Su-Schrieffer-Heeger model supplemented by long-range Coulomb interactions. The relationship between exciton energies and basic interaction parameters is clarified. Linear and third-order nonlinear optical susceptibilities (two-photon absorption, electroabsorption, and third-harmonic generation) have been calculated, elucidating the significance of singlet and triplet excitons and unbound electron-hole pairs. Using only moderate interaction strength, various experiments in polydiacetylene can be interpreted in a consistent way
Polarons in thet-J model
1991
A convenient form of the Peierls-Hubbard Hamiltonian is obtained for the case when the Hubbard repulsion is the largest energy parameter. It allows to consider in the spin-wave approximation the properties of the one-hole low-lying excitations of a 2d lattice. For the parameters approximately corresponding to La2CuO4 it is shown that the hole polarons in the CuO2 planes of lightly doped samples are of large size with a solitonlike-shaped highly asymmetric wave function oriented along the diagonals of the planes or of small size depending on the value of the electron-phonon coupling. In both cases the cooperative effect of the electron-phonon and electron-magnon interactions leads to a large…
How Universal is the Scaling Theory of Localization?
1991
The numerical implementation of the one-parameter scaling theory of localization is reviewed for the Anderson model of disordered solids. A finite-size scaling procedure is used to derive the 3D localization length and d.c.-conductivity from the raw data computed for quasi-1D systems by the strip-and-bar method. While a common scaling function can be unambiguously obtained for different distributions of the diagonal disorder in the Anderson model, discrepancies appear between the box and the Gaussian distribution with regard to the derived critical exponents. To discuss these effects, new results are presented for a triangular distribution, and a new method for the computation of the critic…
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Fractal eigenstates in disordered systems
1990
Abstract The wave functions of the non-interacting electrons in disordered systems described by a tight-binding model with site-diagonal disorder are investigated by means of the inverse participation ratio. The wave functions are shown to be fractal objects. In three-dimensional samples, a critical fractal dimension can be defined for the mobility edge in the band centre, which yields the mobility edge trajectory in the whole energy range in good agreement with previous calculations based on the investigation of the exponentially decaying transmission coefficient.
Nonlinear optical susceptibilities of polysilanes: exciton effect
1992
Abstract Third-order nonlinear optical susceptibilities of σ-conjugated one-dimensional polymers have been calculated in a tight-binding model by taking account of the formation of excitons due to long-range Coulomb interactions. The spectrum of third-harmonic generation (THG) exhibits peaks due to excitons as well as unbound electron—hole states, in contrast to the linear absorption spectrum which is dominated by the lowest exciton state. The results are in excellent agreement with recent experiments in polysilanes not only for THG but also for linear absorption, two-photon absorption, and electroabsorption in a mutually consistent way.
Fluctuations in mesoscopic systems
1992
Abstract Electronic wavefunctions in weakly disordered systems have been studied within the Anderson model of localization. The eigenstates calculated by means of the Lanczos diagonalization algorithm display characteristic spatial fluctuations that can be described by a multifractal analysis. For increasing disorder or energy the observed curdling of the wavefunction reflects the stronger localization, but no exponential decay can be observed. This is reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.
Energy spectrum and transport properties of the two-dimensional t-J model
1992
Abstract The formation of a ferromagnetically ordered region around a hole in the two-dimensional t-J model is investigated. The energy bands characterized by different values of the z-component of the total spin are analysed. A strong anisotropy of the lower-energy bands is found. For intermediate coupling of additionally included optical phonons, this anisotropy leads to a large polaronic state with an anisotropic envelope oriented along the plane diagonals. In the strong-coupling case the competition between the hole-magnon and the hole-phonon interactions prevents the formation of ferrons. Owing to the large effective mass in both cases, the hole transport takes place via hopping, with …
Coherent and incoherent electron transport along a disordered chain
1992
Abstract The Landauer-Buttiker approach is used to describe electron transport along a chain of scatterers which allow elastic as well as inelastic processes. The inelastic scattering takes place via side branches, coupling the chain to electron reservoirs which serve as a heat bath. In this approach, coherent and dissipative transport can be treated in a unified manner, and the suppression of quantum coherence effects for increasing coupling to the heat bath can be described. The influence of disorder on the transmission properties can be characterized by an appropriate coherence length in addition to the decay of the coherence due to dissipation.
Nonlinear optical spectra of conjugated polymers: Effect of long-range coulomb interactions
1993
Abstract Nonlinear optical spectra of conjugated polymers are theoretically studied in the Su-Schrieffer-Heeger model supplemented by long-range Coulomb interactions. Excitonic correlation for electron-hole excitations in explicitly taken into account by a standard method. Nonlinear susceptibilities χ (3) are calculated numerically with a standard sum-over-states method for finite chains (up to 1000 sites). Using moderate interaction strength, our calculations can reproduce many distinct features observed in the linear and nonlinear spectra (two-photon absorption, third-harmonic generation, and electroabsorption) of polydiacetylenes and some other polymers. Especially, a hump in the spectru…
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.
Vers une historiographie des politiques des traductions en Belgique durant la période française
2014
The language policy of the French Revolution is known today especially for the imposition of the national language and the oppression of dialects and regional languages in France. This pilot study focuses on a less-known phenomenon of that period: translation policy. From 1790 on, several decrees stipulated the translation of national laws and decrees into the regional languages of France and some languages of other European countries. We will illustrate this translation policy focusing on translations of political and administrative texts from French into Flemish in Belgium (which was annexed by the French Republic in 1795 and remained French until the end of the Napoleonic era). We will n…
Emerging Standards and the Hybrid Model for Organizing Scientific Events During and After The COVID-19 Pandemic
2020
AbstractSince the beginning of 2020, the coronavirus disease (COVID-19) pandemic has dramatically influenced almost every aspect of human life. Activities requiring human gatherings have either been postponed, canceled, or held completely virtually. To supplement lack of in-person contact, people have increasingly turned to virtual settings online, advantages of which include increased inclusivity and accessibility and a reduced carbon footprint. However, emerging online technologies cannot fully replace in-person scientific events. In-person meetings are not susceptible to poor Internet connectivity problems, and they provide novel opportunities for socialization, creating new collaboratio…
The multifractal character of the electronic states in disordered two-dimensional systems
1995
The nature of electronic states in disordered two-dimensional (2D) systems is investigated. With this aim, we present our calculations of both density of states and d.c. conductivity for square lattices modelling the Anderson Hamiltonian with on-site energies randomly chosen from a box distribution of width W. For weak disorder (W), the eigenfunctions calculated by means of the Lanczos diagonalization algorithm display spatial fluctuations reflecting their (multi)fractal behaviour. For increasing disorder the observed increase of the curdling of the wavefunction reflects its stronger localization. However, as a function of energy, the eigenstates at energy mod E mod /V approximately=1.5 are…
Multifractal wave functions at the Anderson transition.
1991
Electronic wave functions in disordered systems are studied within the Anderson model of localization. At the critical disorder in 3D we diagonalize very large (103 823\ifmmode\times\else\texttimes\fi{}103 823) secular matrices by means of the Lanczos algorithm. On all length scales the obtained strong spatial fluctuations of the amplitude of the eigenstates display a multifractal character, reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure. An analysis of 1D systems shows multifractality too, in contrast to previous claims.
Determination of the mobility edge in the Anderson model of localization in three dimensions by multifractal analysis.
1995
We study the Anderson model of localization in three dimensions with different probability distributions for the site energies. Using the Lanczos algorithm we calculate eigenvectors for different model parameters like disorder and energy. From these we derive the singularity spectrum typically used for the characterization of multifractal objects. We demonstrate that the singularity spectrum at the critical disorder, which determines the mobility edge at the band center, is independent of the employed probability distribution. Assuming that this singularity spectrum is universal for the metal-insulator transition regardless of specific parameters of the model we establish a straightforward …
Parametrization of scatterers in the Landauer-Büttiker transport theory.
1993
Electronic dc transport along a finite chain of scatterers that allow for elastic as well as inelastic processes is described within the Landauer-Buttiker approach. The transport channels in the chain are locally coupled via (current-conserving) side channels to electron reservoirs or heat baths that provide the phase randomization. Different choices for the parameters describing the inelastic coupling as well as the elastic (transmission and reflection) coefficients are compared. The scattering matrix of the chain is calculated with a recursive method. We show that the most general individual scatterer can be characterized by five parameters only, and that it can be represented by a subset…
Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model
1995
We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.…
Monte Carlo simulation of correlated electrons in disordered systems
1992
Abstract The properties of many-electron states in disordered systems with long-range electron-eletron interaction are investigated by means of a Monte Carlo simulation. Using the Metropolis algorithm, three-dimensional systems up to 512 sites are systematically analysed. The low-lying excitations are investigated in order to distinguish between one-particle and many-particle hopping. In the interesting regime in which disorder and correlation effects are equally important we find that variable-range hopping is insignificant for electron transfer when compared with the contribution from nearest-neighbour one-electron hopping processes as well as variable-number hopping.
Spatial multifractal properties of wave packets in the Anderson model of localization.
1993
The multifractal properties of electronic wave functions in disordered samples are investigated. In a given energy range all eigenstates are determined for the same disorder configuration in the Anderson model of localization. It is shown that the singularity spectrum and the generalized dimensions change only slowly with energy, aside from statistical fluctuations. More important, the wave packet constructed by linear combination of the eigenstates shows quantitatively the same multifractal properties. Consequences for the transport properties of electronic states in disordered systems are discussed.
Quantum Coherence Effects in One-Dimensional Chains with Inelastic Scattering
1991
To describe the ballistic transport in a 1 D chain Landauer [1] has calculated the resistance R of a series of elastic scatterers from their transmission coefficient T $$R = \frac{h}{{{e^2}}}\frac{{1 - T}}{T}$$ (1) This relation implies complete quantum coherence between incident and all backscattered waves. Dephasing due to irreversible processes has been introduced into this model by Buttiker [2] who added inelastic scatterers coupled to an external heat bath to the chain. In this way it is possible to describe also certain dissipative aspects of electron transport. However, his approach does not allow to study the gradual transition from coherent to incoherent transport with increasing s…
Dissipation of vibronic energy in a dimer
1992
Abstract The density matrix theory is used for the study of the dissipative quantum dynamics of electron transfer in a dimer. The vibrational modes of the dimer are divided into a single interaction coordinate coupling to the transfered electron and the remaining modes which form a dissipative environment. To correlate the dissipative dynamics with the exact eigenlevels computed for the model system without dissipative environment we analyse the time dependence of the expectation value of the number of vibrational quanta. We analyse the renormalisation of the eigenvalues due to the damping and the relaxation of an excitation into these states.
SPATIAL MULTIFRACTALITY OF ELECTRONIC STATES AND THE METAL-INSULATOR TRANSITION IN DISORDERED SYSTEMS
1993
For the investigation of the spatial behavior of electronic wave functions in disordered systems, we employ the Anderson model of localization. The eigenstates of the corresponding Hamiltonian are calculated numerically by means of the Lanczos algorithm and are analyzed with respect to their spatial multifractal properties. We find that the wave functions show spatial multifractality for all parameter cases not too far away from the metal-insulator transition (MIT) which separates localized from extended states in this model. Exactly at the MIT, multifractality is expected to exist on all length scales larger than the lattice spacing. It is found that the corresponding singularity spectrum…
Multifractal electronic wave functions in disordered systems
1992
Abstract To investigate the electronic states in disordered samples we diagonalize very large secular matrices corresponding to the Anderson Hamiltonian. The resulting probability density of single electronic eigenstates in 1-, 2-, and 3-dimensional samples is analysed by means of a box-counting procedure. By linear regression we obtain the Lipschitz-Holder exponents and the corresponding singularity spectrum, typical for a multifractal set in each case. By means of a Legendre transformation the mass exponents and the generalized dimensions are derived. Consequences for spectroscopic intensities and transport properties are discussed.
Electron-transfer dynamics in a donor—acceptor complex
1991
Abstract Density matrix theory is used for the study of the dissipative quantum dynamics of electron transfer in a donor—acceptor complex. The vibrational modes of the complex are divided into a single interaction coordinate coupling to the transferred electron and the remaining modes which form a dissipative environment. With increase of the coupling of the interaction coordinate to the environment and, thus, of the corresponding damping rate of the vibrational quanta, the results of the numerical calculations display a change from the coherent to the incoherent transfer regime. In contrast to the case of small values of the damping, the transfer dynamics become independent of the number o…
Band Tails in a Disordered System
1993
In crystalline solids electronic excitations have a band structure. Energy intervals, in which excitations occur, are separated by band gaps, where the density of electronic states vanishes. At the band edge the density-of-states (DOS) has power law singularities, so-called van Hove singularities.
Non-linear optical spectra of excitons in polydiacetylene
1992
Abstract Adding long-range Coulomb interactions to the Su-Schrieffer-Heeger model makes it possible to investigate excitonic states in conjugated polymers. Various characteristic features due to these states as well as due to the electron-hole continuum can be found in the calculated non-linear optical susceptibilities. In particular the electroabsorption spectrum and the third harmonic generation intensity and its dependence on the system size are examined. Using only moderate interaction strength, various experiments in polydiacetylene can be interpreted in a consistent way.
Electronic States in Mesoscopic Systems
1992
Abstract Electronic states in disordered systems are studied within the Anderson model of localization. By means of the Green's function technique we derive the transmission coefficient for electronic states through mesoscopic samples. The transmission coefficient is shown to be not self-averaging due to strong spatial fluctuations of the amplitude of the eigenstates, which are obtained by direct diagonalization of the respective secular matrices. The wave functions display a multifractal behaviour, characterized by the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.
Identification of spatially confined states in two-dimensional quasiperiodic lattices.
1995
We study the electronic eigenstates on several two-dimensional quasiperiodic lattices, such as the Penrose lattice and random-tiling lattices, using a tight-binding Hamiltonian in the vertex model. The infinitely degenerate states at E=0 are especially investigated. We present a systematic procedure which allows us to identify numerically the spatially strongly localized so-called confined states.
Magnetic excitations of a doped two-dimensional antiferromagnet
1993
Magnetic excitations of the two-dimensional (2D) t-J model are considered in the presence of a small concentration of holes c. The spin-wave approximation used implies long-range antiferromagnetic ordering from the beginning. Migdal's theorem is shown to be valid for the model considered. The energy spectrum of the magnons is determined with the help of the one-pole approximation for the hole Green's function. If the concentration of mobile holes is larger than a critical value an additional branch of overdamped magnons arises near the \ensuremath{\Gamma} and M points of the Brillouin zone. This is connected with the generation of electron-hole pairs (the Stoner excitations) by magnons. The…
Quantum fluctuations of the conductance in the hopping regime
1992
Abstract The results of the numerical scaling approach for localization are used to discuss the statistical behaviour of the zero-temperature conductance of disordered systems of finite size. In the asymptotic regime of strong localization, where transport is dominated by hopping processes, explicit expressions for the temperature dependence of the fluctuations of the conductance and the resistance are obtained by assuming that the phase coherence length is given by the Mott hopping law. It is shown that the temperature dependence of the fluctuations of the logarithm of the conductance/resistance does not depend on the assumptions concerning the statistics of the hopping processes. The resu…
Dynamic Aspects of Quasi-Particle Transfer in Molecular Electronic Devices
1993
Abstract The importance of the dissipative quantum dynamics of molecular systems for possible future device applications is emphasized. The necessity to study in detail the respective quasi-particle transfer phenomena is discussed. As a specific example charge transfer in a molecular dimer and a molecular chain is investigated in order to demonstrate how the quantum dynamical features can be controlled by different intrinsic nonlinearities.
Spatial fluctuations of the chemical potential in case of nearly coherent transport along an ordered chain
1991
The Landauer-Buttiker approach is used to describe electron transport along a chain of scatterers which allow elastic as well as inelastic processes. The inelastic scattering takes place via side branches coupling the chain to electron reservoirs which serve as a heat bath. For small inelastic coupling of the scatterers to the heat bath strong interference effects lead to spatial fluctuations of the charge density. The corresponding oscillations of the chemical potential are discussed in view of phase-sensitive experiments measuring the four-probe resistance.
dc transport in dissipative disordered one-dimensional systems
1995
We present a numerical study of the dc transport properties of dissipative disordered chains which are described by linear ensembles of interconnected scatterers. The elastic-scattering amplitudes are derived from an Anderson Hamiltonian with diagonal (site) disorder. Inelastic scattering is accounted for by connecting the sites of the Anderson chain to separate external electron reservoirs. The calculated wave-vector-dependent transmission probabilities are discussed for chains with different lengths and for different degrees of dissipation. Using the Landauer-B\"uttiker approach we obtain the dc resistance of the considered samples. Our results demonstrate the rather intricate competition…
Themenheft: Translation & Linguistik
2020
International audience