Search results for "density of state"
showing 10 items of 187 documents
Propagation and localisation of vibrational modes in 3–dimensional disordered systems: the binary force constant model
1999
We consider a system of coupled harmonic oscillators on a cubic lattice. The force constants are supposed to take two distinct values at random according to a bond concentration x. The density of states (DOS) is evaluated both by numerical diagonalisation and in coherent-potential approximation (CPA). There is excellent agreement between the results of the two methods. Near the concentration, where the bonds with the larger force constants percolate, the DOS differs appreciably from the crystalline one and is anomalously enhanced at low frequencies as compared to Debye's ω2 law (“boson peak”). These features are shared with models with continuous distributions of force constants. The mean f…
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…
Model calculations for vibrational properties of disordered solids and the “boson peak”
1999
Abstract It is demonstrated that a disordered system of coupled classical harmonic oscillators with a continuous distribution of coupling parameters exhibits generally a low-frequency enhancement (“boson peak”) of the density of states, as compared with the Debye law. This phenomenon is most pronounced if the system is close to an instability. This is shown by means of a scalar model on a simple cubic lattice. The force constants are assumed to fluctuate from bond to bond according to a Gaussian distribution which is truncated at its lower end. The model is solved for the density of states and the one-phonon dynamic structure factor S(q, ω) by applying the two-site coherent potential approx…
Relaxation and phonons in viscous and glassy orthoterphenyl by neutron scattering
1993
We present an extended set of incoherent neutron scattering measurements on the van der Waals liquido-terphenyl, obtained by time-of-flight and backscattering spectroscopy. In the supercooled liquid regime, data from three instruments are combined and analysed in terms of the selfcorrelationS(Q, t). In the time range 1...100 ps, the crossover from α-to β-relaxation is well described by the masterfunction of mode coupling theory, and fitted parameters are consistent with the previously established critical temperatureT c [Z. Phys. B83, 175 (1991)]. In the glassy regime, vibrations are harmonic and can be described by a density of states. Deviations at lowQ are quantitatively explained by a m…
Dynamical mean-field theory calculation with the dynamical density-matrix renormalization group
2006
Abstract We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy approach to the DMFT. Using the dynamical density–matrix renormalization group method (DDMRG) we calculate the density of states (DOS) with a resolution ranging from 3% of the bare bandwidth W = 4 t at high energies to 0.01% for the quasi-particle peak. The DDMRG resolution and accuracy for the DOS is sup…
Vibrational excitations in systems with correlated disorder
2007
We investigate a $d$-dimensional model ($d$ = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's $\omega^{d-1}$ law (``boson peak'') as a result of disorder. This anomay becomes reinforced for increasing correlation length $\xi$. The theory predicts that $\xi$ times the width of the Brillouin line should be a universal …
Self-consistency conditions for localized magnetic moments in a free electron gas
1969
The self-consistent conditions for a localized magnetic moment in a metal are studied in the case where the density of states of the host metal is free electron like. A method is outlined which in principle allows to determine self-consistently in the Hartree-Fock approximation the relevant parameters of the magnetic ground state of the system. A numerical example is approximately worked out to show how the theory gives reasonable answers in spite of the crudeness of some of the approximations used.
Direct interpretation of near-field optical images.
2001
The interpretation of the detection process in near-field optical microscopy is reviewed on the basis of a discussion about the possibility of establishing direct comparisons between experimental images and the solutions of Maxwell equations or the electromagnetic local density of states. On the basis of simple physical arguments, it is expected that the solutions of Maxwell equations should agree with images obtained by collecting mode near-field microscopes, while the electromagnetic local density of states should be considered to provide a practical interpretation of illumination mode near-field microscopes. We review collecting mode near-field microscope images where the conditions to o…
Infinite single-particle bandwidth of a Mott–Hubbard insulator
2016
The conventional viewpoint of the strongly correlated electron metal-insulator transition is that a single band splits into two upper and lower Hubbard bands at the transition. Much work has investigated whether this transition is continuous or discontinuous. Here we focus on another aspect and ask the question of whether there are additional upper and lower Hubbard bands, which stretch all the way out to infinity — leading to an infinite single-particle bandwidth (or spectral range) for the Mott insulator. While we are not able to provide a rigorous proof of this result, we use exact diagonalization studies on small clusters to motivate the existence of these additional bands, and we discu…
Symmetry and Electronic Structure of Noble Metal Nanoparticles and the Role of Relativity
2004
High resolution photoelectron spectra of cold mass selected Cu_n-, Ag_n- and Au_n- with n =53-58 have been measured at a photon energy of 6.42 eV. The observed electron density of states is not the expected simple electron shell structure, but seems to be strongly influenced by electron-lattice interactions. Only Cu55- and Ag55- exhibit highly degenerate states. This is a direct consequence of their icosahedral symmetry, as is confirmed by density functional theory calculations. Neighboring sizes exhibit perturbed electronic structures, as they are formed by removal or addition of atoms to the icosahedron and therefore have lower symmetries. Gold clusters in the same size range show complet…