Search results for "Model theory"
showing 10 items of 681 documents
Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover w…
2013
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-d…
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.
Calculations of the ground and excited states ofF-type centers in corundum crystals
1994
The semiempirical intermediate neglect of differential overlap method was used for calculating optical properties of ${\mathit{F}}^{+}$ and F centers (oxygen vacancy trapped one and two electrons, respectively) embedded into large quantum clusters, ${\mathrm{Al}}_{26}$${\mathrm{O}}_{39}$. The geometry was optimized for both the ground and excited states of defects. Calculated absorption and luminescence energies obtained for ${\mathit{F}}^{+}$ and F centers are in good agreement with experimental data. Their energy levels lie in the gap between the upper valence band and conduction band, like for similar centers in MgO and alkali halides. It is shown that the oxygen vacancy in corundum crys…
Spin-restricted coupled-cluster theory with triple excitations
2002
Working equations for a spin-restricted coupled-cluster (SR-CC) ansatz with full inclusion of triple excitations are presented. The equations have been derived using a new formulation of the SR-CC theory that is equivalent to the original one but much easier processed and also provides a new interpretation of the underlying concepts of the SR-CC approach. Test calculations with a preliminary SR-CC singles, doubles, triples (SR-CCSDT) implementation indicate that spin-restriction has a rather small effect on the computed energies and that the effects are—as expected—less pronounced than in the case of the CC singles, doubles approximation. The corresponding partially spin-adapted scheme turn…
Ising Spins on 3D Random Lattices
1999
We perform single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices of Voronoi/Delaunay type with up to 128 000 sites. For each lattice size quenched averages are computed over 96 realizations. From a finite-size scaling analysis we obtain strong evidence that the critical exponents coincide with those on regular cubic lattices.
Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator
2003
We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics often mislead or misunderstood. We compare two different approximations both referred to as Rotating Wave Approximation. Using a specific example, we clarify some issues related to non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the density matrix.
SPECIAL HPERBOLIC TYPE APPROXIMATION FOR SOLVING OF 3-D TWO LAYER STATIONARY DIFFUSION PROBLEM
2019
In this paper we examine the conservative averaging method (CAM) along the vertical z-coordinate for solving the 3-D boundary-value 2 layers diffusion problem. The special parabolic and hyperbolic type approximation (splines), that interpolate the middle integral values of piece-wise smooth function, is investigated. With the help of these splines the problems of mathematical physics in 3-D with respect to one coordinate are reduced to problems for system of equations in 2-D in every layer. This procedure allows reduce also the 2-D problem to a 1-D problem and the solution of the approximated problem can be obtained analytically. As the practical application of the created mathematical mode…
Colle-Salvetti-type local density functional for the exchange-correlation energy in two dimensions
2010
We derive an approximate local density functional for the exchange-correlation energy to be used in density-functional calculations of two-dimensional systems. In the derivation we employ the Colle-Salvetti wave function within the scheme of Salvetti and Montagnani [Phys. Rev. A 63, 052109 (2001)] to satisfy the sum rule for the exchange-correlation hole. We apply the functional for the two-dimensional homogeneous electron gas as well as to a set of quantum dots and find a very good agreement with exact reference data.
Extended SUSY quantum mechanics, intertwining operators and coherent states
2009
Abstract We propose an extension of supersymmetric quantum mechanics which produces a family of isospectral Hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau–Klauder type associated to our Hamiltonians.
Diluted Heisenberg Ferromagnets with Competing Ferro- and Antiferromagnetic Interactions: Evidence for a New Universality Class?
1993
The site-diluted classical face-centered cubic (fee) Heisenberg model with exchange between nearest and (J nn > 0) next nearest (J nnn =-J nn /2) neighbors is studied by Monte Carlo simulations using the heatbath algorithm in conjunction with histogram reweighting techniques. Finite size scaling analysis suggests that the diluted system crosses over to a new type of critical behavior, different from that of the pure system, in contrast to the prediction of the Harris criterion. But this model possibly can explain related experimental findings in Eu x Sr 1-x S.