Search results for "statistical [methods]"
showing 10 items of 1664 documents
Quantum effects on the herringbone ordering ofN2on graphite
1993
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
Reply to “Comment on ‘Elastic constants from microscopic strain fluctuations’ ”
2010
We agree with Coupier et al. [Phys. Rev. E 81, 013101 (2010)] that their technique for extracting elastic constants from microscopic strain fluctuations improves upon ours because of a more accurate computation of the integral of the elastic correlation function over sub-blocks. However, we believe that their interpretation of the physical relevance of the elastic correlation length extracted from the fits is misleading.
Monte Carlo simulation of dimensional crossover in the XY model.
1993
We report Monte Carlo simulations of Villain's periodic Gaussian XY model on ${\mathit{L}}^{2}$\ifmmode\times\else\texttimes\fi{}N lattices of film geometry (L\ensuremath{\gg}N) with up to N=16 layers, employing the single-cluster update algorithm combined with improved estimators for measurements. The boundary conditions are periodic within each layer and free at the bottom and top layer. Based on data for the specific heat, the spin-spin correlation function, and the susceptibility in the high-temperature phase we study the crossover from three- to two-dimensional behavior as criticality is approached. For the transition temperatures, determined from Kosterlitz-Thouless fits to the correl…
Collective atomic effects in resonance fluorescence
1977
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incid…
Test of the semischematic model for a liquid of linear molecules
1998
We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].
Probing slow fluctuations in nonergodic systems: Interleaved sampling technique
2007
We present a new dynamic light scattering scheme to obtain ensemble-averaged correlation functions of slow fluctuations in non-ergodic systems in an efficient way. On a rotating sample, a large set of separate correlation functions is measured in parallel, for each independent orientational component of the sample’ density fluctuations. The ensemble-averaged correlation function spans a lag time range from 1 to 104 s. We describe our first implementation of this technique, discuss its statistical accuracy and show first results. Compared to plain ensemble averaging over a series of N measurements, the total measurement time is usualy reduced by a factor N without significant degradation of …
REMARKS ON THE METHODS OF INVESTIGATIONS OF ALIGNMENT OF GALAXIES
2011
In the 1975 Hawley and Peebles gave the proposal to use three statistical tests for investigations of the galaxies orientation in the large structures. Nowadays, it has been considered as the standard method of searching for galactic alignments. In the present paper we analyzed the tests in details and proposed a few improvements. Basing on the improvements, the new method of analysis of the alignment of galaxies in clusters is proposed. The power of this method is demonstrated on the sample of 247 Abell clusters with at least 100 objects in each. The distributions of the position angles for galaxies in each cluster are analyzed using statistical tests: $\chi^2$, Fourier, autocorrelation an…
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
2005
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the ch…
Some aspects of the nonperturbative renormalization of the phi^4 model
2007
A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamiltonian under the integration over a shell Lambda - d Lambda < k < Lambda, where d Lambda -> 0. We show that the known Wegner--Houghton equation is consistent with the assumption of a simple superposition of the integration results for +/- q. The renormalized action can be expanded in powers of the phi^4 coupling constant u in the high temperature phase at u -> 0. We compare the expansion coefficients with those exactly calculated by the…
Theory of bound polarons in oxide compounds
2001
We present a multilateral theoretical study of bound polarons in oxide compounds MgO and \alpha-Al_2O_3 (corundum). A continuum theory at arbitrary electron-phonon coupling is used for calculation of the energies of thermal dissociation, photoionization (optically induced release of an electron (hole) from the ground self-consistent state), as well as optical absorption to the non-relaxed excited states. Unlike the case of free strong-coupling polarons, where the ratio \kappa of the photoionization energy to the thermal dissociation energy was shown to be always equal to 3, here this ratio depends on the Froehlich coupling constant \alpha and the screened Coulomb interaction strength \beta.…