Search results for "Matrix"
showing 10 items of 3205 documents
The dynamics of sodium in sodium disilicate: Channel relaxation and sodium diffusion
2001
We use molecular dynamics computer simulations to study the dynamics of amorphous (Na_2O)2(SiO_2). We find that the Na ions move in channels embedded in a SiO_2 matrix. The characteristic distance between these channels gives rise to a prepeak in the structure factor at around q=0.95 A^-1. The dynamics of sodium is given by a fast process which can be seen in the incoherent scattering function and a slow process which is seen in the coherent function. The relaxation time of the latter coincides with the alpha-relaxation time of the matrix. The Kohlrausch exponent of the fast process for q>1.6 A^1 is the same as the von Schweidler exponent for the slow one, demonstrating that the two proc…
Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions
2004
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase 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 (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity …
XXZ-like phase in the F-AF anisotropic Heisenberg chain
2008
By means of the Density Matrix Renormalization Group technique, we have studied the region where $XXZ$-like behavior is most likely to emerge within the phase diagram of the F-AF anisotropic extended ($J-J'$) Heisenberg chain. We have analyzed, in great detail, the equal-time two-spin correlation functions, both in- and out-of- plane, as functions of the distance (and momentum). Then, we have extracted, through an accurate fitting procedure, the exponents of the asymptotic power-law decay of the spatial correlations. We have used the exact solution of $XXZ$ model ($J'=0$) to benchmark our results, which clearly show the expected agreement. A critical value of $J'$ has been found where the r…
Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit
2013
We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). The competition among the interactions ($U$, $V_1$, and $V_2$) generates a plethora of T=0 phases in the whole range of fillings. $U$, $V_1$, and $V_2$ are the intensities of the local, NN and NNN interactions, respectively. We report the T=0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit $T\…
Validity of power functionals for a homogeneous electron gas in reduced-density-matrix-functional theory
2016
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,n')=(n n')^\alpha$ for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $\alpha$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlatio…
Generation of robust entangled states in a non-hermitian periodically driven two-band Bose-Hubbard system
2016
A many-body Wannier-Stark system coupled to an effective reservoir is studied within a non-Hermitian approach in the presence of a periodic driving. We show how the interplay of dissipation and driving dynamically induces a subspace of states which are very robust against dissipation. We numerically probe the structure of these asymptotic states and their robustness to imperfections in the initial-state preparation and to the size of the system. Moreover, the asymptotic states are found to be strongly entangled making them interesting for further applications.
New methods of evaluation of the flavor composition in e+ e- annihilation by double hemisphere tagging at LEP / SLC energies
1995
Two new methods are proposed to extract the flavour contents of the events produced at LEP/SLC, together with the classification matrix of a tagging by hemispheres. By utilising the tagging obtained in both hemispheres, the efficiencies, backgrounds and flavour compositions are directly obtained by fitting the data. A minimal dependence on modelling and a consistent treatment of systematic errors are achieved by applying these methods. The choice of the tagging algorithm is irrelevant in the methods, provided that similar efficiencies are reached. As an example, a multivariate analysis technique combining the tracking information given by a microvertex detector has been applied to extract t…
Backtracing particle rays through magnetic spectrometers: avoiding systematic errors in the reconstruction of target coordinates
1993
Abstract The procedures used to model [J. Friedrich, Nucl. Instr. and Meth. A 293 (1990) 575] or to determine [N. Voegler et al., Nucl. Instr. and Meth. A 249 (1986) 337, H. Blok et al., ibid., vol. A 262 (1987) 291, and E.A.J.M. Offermann et al., ibid., vol. A 262 (1987) 298] the mapping properties of a magnetic spectrometer are based on a minimization of the variance of target coordinates . We show that backtracing with matrix elements, determined in this way, may contain systematic errors. As alternative, we propose to minimize the variance of the detector coordinates . This procedure avoids these systematic errors.
WIGNER TRANSFORM METHODS IN INCLUSIVE ELECTRON SCATTERING FROM NUCLEI
1984
A multiple scattering series for deep inelastic leptoninduced reactions is derived by using semiclassical Wigner transform methods. In contrast to the usual Glauber theory there is no limitation for the energy loss since a time-dependent formulation is used throughout. A simple parametrization of the generalized profile function yields a closed analytical expression for the longitudinal and transverse response function of p-shell nuclei. Comparison is made with the Saclay data for -'• C. I Introduction It is common knowledge that geometrical optics is valid if the wavelength of the scattering wave is small compared to the dimensions of the scatterer. Under these conditions the phase-space d…
A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems
2012
One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum s…