Search results for "singularity."
showing 10 items of 346 documents
Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice
2005
We study the sound velocity in cubic and non-cubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothened by interactions and eventually vanishes when interactions are strong enough. For non-cubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the 1D and 2D limits.
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.
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.
Stationary models of magnetized viscous tori around a Schwarzschild black hole
2020
We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field, and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equations of motion. The stationary models are constructed by numerically solving the general relativis…
Singularities in L^p-quasidisks
2021
We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities. We give, in a connection of quasidisks, a sharp integrability condition for the distortion function to answer this question. peerReviewed
Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
2010
Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help ration…
Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations.
2010
The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducin…
Tetra and pentaquarks from the molecular perspective
2019
We present results for the analysis of the B+ → J/ψϕK+ which shows the contribution of two resonances, the X(4140) and X(4160) and a cusp at the $D_s^*\bar D_s^*$ threshold tied to the molecular character of the X(4160) resonance. In the second part we present the results for the theoretical approach to the new Ωcstates from the molecular perspective. In both cases we compare with results of the LHCb collaboration.
Analysis of the "Unusual" Vibrational Components of Triply Degenerate Vibrational Mode nu(6) of Mo(CO)(6) Based on the Classical Interpretation of th…
2001
Rotational structure of the triply degenerate vibrational state nu(6)(F(1u)) of the octahedral molecule Mo(CO)(6) is analyzed qualitatively on the basis of classical mechanics. We show that the energy level redistribution between the vibrational components of nu(6)(F(1u)) occurs due to rotational excitation and is related to the formation of singular points of classical rotational energy surfaces. The singularity is stable under small variations of parameters of the effective rovibrational Hamiltonian. Parameters responsible for the persistence of this phenomenon are specified. Comparison with quantum calculations demonstrates the high qualitative and quantitative accuracy of our classical …
Natural occupation numbers: When do they vanish?
2013
The non-vanishing of the natural orbital occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' Theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wave function leads, in general, to a power law decay of the natural occupations, whe…