Showing papers on "Cluster expansion published in 2001"
TL;DR: In this article, a local cluster expansion is proposed to describe the configuration dependence of activation barriers and a kinetically resolved activation barrier is introduced, which can be used to obtain the activation barrier for migration in any configuration.
Abstract: Many multicomponent materials exhibit significant configurational disorder Diffusing ions in such materials migrate along a network of sites that have different energies and that are separated by configuration dependent activation barriers We describe a formalism that enables a first-principles calculation of the diffusion coefficient in solids exhibiting configurational disorder The formalism involves the implementation of a local cluster expansion to describe the configuration dependence of activation barriers The local cluster expansion serves as a link between accurate first-principles calculations of the activation barriers and kinetic Monte Carlo simulations By introducing a kinetically resolved activation barrier, we show that a cluster expansion for the thermodynamics of ionic disorder can be combined with a local cluster expansion to obtain the activation barrier for migration in any configuration This ensures that in kinetic Monte Carlo simulations, detailed balance is maintained at all times and kinetic quantities can be calculated in a properly equilibrated thermodynamic state As an example, we apply this formalism for an investigation of lithium diffusion in ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ A study of the activation barriers in ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{x}$ within the local density approximation shows that the migration mechanism and activation barriers depend strongly on the local lithium-vacancy arrangement around the migrating lithium ion By parametrizing the activation barriers with a local cluster expansion and applying it in kinetic Monte Carlo simulations, we predict that lithium diffusion in layered ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ is mediated by divacancies at all lithium concentrations Furthermore, due to a strong concentration dependence of the activation barrier, the predicted diffusion coefficient varies by several orders of magnitude with lithium concentration x
405 citations
TL;DR: In this article, a fully relativistic particle-in-cell code is used to simulate atomic clusterexplosions following the interaction with ultrashort high-intensity laser pulses, investigating the dynamics of a 1 μm hydrogen cluster explosion and providing information about the time-resolved position, momentum, and energy of electrons and ions, for different laser intensities.
Abstract: A fully relativistic particle-in-cell code is used to simulate atomic clusterexplosions following the interaction with ultrashort high-intensity laser pulses, investigating the dynamics of a 1 μm hydrogen cluster explosion and providing information about the time-resolved position, momentum, and energy of electrons and ions, for different laser intensities. The results indicate that the mechanism responsible for cluster expansion is Coulombic explosion producing MeV ions and electrons.
39 citations
TL;DR: In this paper, the authors consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure, and the uniqueness of the Gibbs measure for two cases is shown.
Abstract: We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour, the degree of mixing and some further properties are derived. We use cluster expansion in the small coupling parameter.
38 citations
TL;DR: In this article, a method based on cluster expansion was proposed to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field, including infinite range simply integrable interactions.
Abstract: We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field. By this method we study the spin–spin truncated correlations of various systems, including the case of infinite range simply integrable interactions, and we show how suitable boundary conditions and/or external fields may improve the decay of the correlations.
27 citations
TL;DR: In this article, it was shown that the fixed-node approximation does not describe the thermodynamic properties of strongly coupling fermions rather well at weak and moderate degeneracy, and that the exact Fermi function with index 3/2 describing the logarithm of the grand partition function of ideal Fermions cannot be reproduced in the fixednode approximation.
Abstract: Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3/2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.
21 citations
TL;DR: In this paper, the authors used coupled cluster (CC) methods with inclusion of connected clusters through pentuple excitations to study several small molecules containing triple bonds, and found that both for the bond lengths and for the harmonic frequency, they observed a slow convergence of the studied property with respect to the cluster expansion.
Abstract: Several small molecules containing triple bonds have been studied using coupled cluster (CC) methods with inclusion of connected clusters through pentuple excitations. The calculations were performed with a recently developed CC approach that adds noniterative contributions due to the T 5 operator to the connected triples and quadruples evaluated in standard CC methods. The results indicate that both for the bond lengths and for the harmonic frequency we observe a slow convergence of the studied property with respect to the cluster expansion. For N 2 , NO + and CN − the frequency corrections due to the T 4 and T 5 clusters at the DZP level are: 20, 5; 19, 7, 10 and 3 cm −1 , respectively.
17 citations
TL;DR: In this article, a non-perturbative cumulant expansion method for computing the grand partition function of quantum systems is presented, which embeds the classical component of the partition function exactly and treats the quantum contributions by a systematic cluster expansion of the Boltzmann operator.
15 citations
TL;DR: In this article, the first step towards proving that a three dimensional interacting system of Fermions is a Fermi liquid in the sense of Salmhofer was taken.
Abstract: In this paper we complete the first step, namely the uniform bound on completely convergent contributions, towards proving that a three dimensional interacting system of Fermions is a Fermi liquid in the sense of Salmhofer. The analysis relies on a direct space decomposition of the propagator, on a bosonic multiscale cluster expansion and on the Hadamard inequality, rather than on a Fermionic expansion and an angular analysis in momentum space, as was used in the recent proof by two of us of Salmhofer's criterion in two dimensions.
14 citations
TL;DR: In this article, a linked-cluster expansion technique for the high-temperature expansion of spin modes is reviewed and a new algorithm for the computation of three-point and higher Green's functions is presented.
Abstract: The linked-cluster expansion technique for the high-temperature expansion of spin modes is reviewed. A new algorithm for the computation of three-point and higher Green's functions is presented. Series are computed for all components of two-point Green's functions for a generalized 3D Ising model, to 25th order on the bcc lattice and to 23rd order on the sc lattice. Series for zero-momentum four-, six-, and eight-point functions are computed to 21st, 19th, and 17th order respectively on the bcc lattice.
13 citations
TL;DR: The tetranuclear platinum cluster complexes [Pt4(μ-CO)3 (μ-dppm)3(PPh3) as mentioned in this paper ] have butterfly structures and are fluxional.
Abstract: The tetranuclear platinum cluster complexes [Pt4(μ-CO)3(μ-dppm)3(PPh3)]2+ and [Pt4(μ-H)(μ-CO)2(μ-dppm)3(PPh3)]+ have been prepared by cluster expansion They have butterfly structures and are fluxional
12 citations
TL;DR: In this paper, the statistical mechanics of a one-dimensional system of bosons with repulsive delta-function interaction was studied and explicit calculations of the partition function and the cluster integrals were carried out.
Abstract: Statistical mechanics of a one-dimensional system of bosons with repulsive delta-function interaction is studied. Explicit calculations of the partition function and the cluster integrals are carried out. The results coincide with those by the thermal Bethe ansatz (TBA) method. Thermodynamic quantities such as the pressure, the chemical potential and the energy are given both for large and small coupling limits.
TL;DR: A systematic cluster expansion for dilute systems in the highly dilute phase is developed, which proves the exactness of the RS ansatz below the percolation threshold and the free energy of the Viana-Bray model in the paramagnetic phase.
Abstract: We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the control parameter, the average connectivity, that is identical to the one obtained by using the replica approach with a replica symmetric (RS) ansatz, when the order parameter is calculated via a perturbative expansion in the control parameter. As a second application we compute the free energy of the Viana-Bray model in the paramagnetic phase. The cluster expansion allows one to compute finite-size corrections in a simple manner, and these are particularly important in optimization problems. Importantly enough, these calculations prove the exactness of the RS ansatz below the percolation threshold, and might require its revision between this and the easy-to-hard transition.
TL;DR: In this paper, a non-empirical equation of state of a crystal is found in the framework of the finite-deformation theory, and the adiabatic potential is calculated from first principles by using a set of localized functions which are exactly orthogonalized to one another, with the orthogonomizing matrix being calculated by the cluster expansion method.
Abstract: A nonempirical equation of state of a crystal is found in the framework of the finite-deformation theory. The adiabatic potential is calculated from first principles by using a set of localized functions which are exactly orthogonalized to one another, with the orthogonalizing matrix being calculated by the cluster expansion method. The most essential part of the equation of state which corresponds to short-range repulsion involves no experimentally determined parameters. Comparison of the theory and experimental data in the range of large compressive deformations shows that the terms of higher orders in the overlap integral are of importance for neon, whereas it suffices to use the quadratic approximation for xenon. The reason for this is discussed.
TL;DR: In this article, strong coupling expansion of a spin-half Heisenberg chain coupled to Einstein phonons and a frustrating next-nearest-neighbor spin interaction was studied.
Abstract: We report results from a systematic strong-coupling expansion of a spin-½ Heisenberg chain coupled to Einstein phonons and a frustrating next-nearest-neighbor spin interaction. It is not obvious which interaction dominates in the regime of small coupling constants. In the non-adiabatic regime (Ω ≈ J) this model is used to describe the zero-temperature properties of CuGeO3. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly, in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO3. The ground-state magnetic correlations are found to be hardly affected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO3.
TL;DR: In this paper, it was rigorously proved that the exact Fermi function with index 5/2 in grand ensemble can not be reproduced in FNA, so FNA has not the correct limit to ideal fermions.
Abstract: Results of the direct path integral Monte Carlo simulation (DPIMCS) have shown that the “fixed node approximation” (FNA) rather well describes thermodynamic properties of the strongly coupled fermions at “weak and moderate” degeneracy. To explain the increasing difference for highly degenerate fermions it is rigorously proved that the exact Fermi function with index 5/2 in grand ensemble can not be reproduced in FNA, so FNA has not the correct limit to ideal fermions.
TL;DR: In this paper, a coupled cluster method was used to study the lattice massive Schwinger model with staggered fermions, and the vacuum energy and mass gaps were calculated. Good agreement was found between these calculations, the exact results in the continuum limit, and other approximation methods.
Abstract: The coupled cluster method is used to study the lattice massive Schwinger model with staggered fermions. The vacuum energy and mass gaps are calculated. Good agreement is found between these calculations, the exact results in the continuum limit, and the results obtained by other approximation methods.
01 Apr 2001
TL;DR: In this paper, an extension of the Gaussian model of the stochastic vacuum is presented, which consists of including higher cumulants than just the second one in the cluster expansion in QCD.
Abstract: In this work an extension of the Gaussian model of the stochastic vacuum is presented. It consists of including higher cumulants than just the second one in the cluster expansion in QCD. The influence of nonabelian fourth cumulants on the potential of a static quark-antiquarkpair is examined and the formation of flux tubes between a static q q -pair is investigated. It is found that the fourth cumulants can contribute to chromomagnetic flux tubes. Furthermore the contribution of fourth cumulants to the total cross section of soft high energy hadron-hadron scattering is examined and it is found that the fourth cumulants do not change the general picture obtained in the Gaussian model.
TL;DR: In this article, a steady-state perturbation theory for arbitrary excited multiply degenerate states of a normal Fermi system in the statistical limit was studied, and the perturbations were proved solvable in the space of quasinormal form operators.
Abstract: This paper is a study in a possible steady-state perturbation theory for arbitrary excited multiply degenerate states of a normal Fermi system in the statistical limit. An operator technique has been developed to transform the relevant Hamiltonian into an operator that is a function of occupation number operators only. The perturbation theory equations have been proved to be solvable in the space of quasinormal form operators and their formal solutions have been derived. It is shown that the operator series of perturbation theory can be transformed to a linked cluster expansion with the nonphysical powers of volume eliminated. Elimination of nonphysical terms is effected without use of the diagrams technique.
TL;DR: In this paper, the authors extended their previous work to cover weakly interacting chains for a quantitative description of three dimensional materials like PHCC and KCuCl_3, and showed the gradual transition between the minimum of the dispersion at wavevector 0 and wavevector Pi within this region.
Abstract: We have studied dimerized spin systems by realizing the cluster expansion to high order. We have extended our previous dimer expansion for one-dimensional systems to cover weakly interacting chains for a quantitative description of three dimensional materials like PHCC and KCuCl_3. By comparison with recent inelastic neutron scattering data we are able to determine the exchange energies between individual spins. We have further investigated the incommensurate region of zigzag chains with isotropic exchange coupling constants near the disorder-line where the dispersion curve exhibits a minimum at a finite wavevector. Our approach clearly shows the gradual transition between the minimum of the dispersion at wavevector 0 and wavevector Pi within this region. The extent of the incommensurate regime is given analytically in an expansion in the coupling constants.
TL;DR: In this article, the model of the atom-vacancy solid solution is studied in terms of cluster expansion formalism and effective interaction of vacancies is formally included in the energy of vacancy formation.
Abstract: Vacancies in metal are studied in the model of the atom-vacancy solid solution Vacancy formation energy is discussed in terms of cluster expansion formalism It is shown that effective interaction of vacancies is formally included in the energy of vacancy formation The cluster expansion method illustrates that pairwise and nonpairwise interactions between atoms and vacancies are responsible for the interaction of vacancies in the atom-vacancy solid solution © 2001 John Wiley & Sons, Inc Int J Quantum Chem, 2001
TL;DR: The computational behaviour of the proposed m -step algorithms is investigated by solving matrix eigenproblems up to the order 3600 by using the m - step algorithms for m =2, 3, 4, 5.
TL;DR: By using a high-temperature cluster expansion, the authors constructed the evolution operator of the BBGKY-type gradient diffusion hierarchy for plane rotators that interact via a summable pair potential in a Banach space containing the Gibbs correlation functions.
Abstract: By using a high-temperature cluster expansion, we construct the evolution operator of the BBGKY-type gradient diffusion hierarchy for plane rotators that interact via a summable pair potential in a Banach space containing the Gibbs (stationary) correlation functions. We prove the convergence of this expansion for a sufficiently small time interval. As a result, we prove that weak solutions of the hierarchy exist in the same Banach space. If the initial correlation functions are locally perturbed Gibbs correlation functions, then these solutions are defined on an arbitrary time interval.