Probabilistic Study of the Speed of Approach to Equilibrium for an Inelastic Kac Model

This paper deals with a one-dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter p>0. In particular, the paper provides bounds for certain distances—such as specific weighted χ-distances and the Kolmogorov distance—between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent α=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, close to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function. Research partially supported by Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR grant 2006/134526).     

Electronic Structure and Conductivity of a Disordered A1 – xBx Binary Alloy in the Cluster Approach for the Hubbard Model

Journal of Experimental and Theoretical Physics - We propose a method for calculating the electronic band structure of disordered systems with strong electron correlations. Various approaches to...     

Mean—Field Calculations for the Three—Dimensional Holstein Model

The electron-phonon Holstein model is studied in three spatial dimensions.It is argued that this model can be used to account for major features of the high-Tc BaPb1-xBixO3 and BaxK1-xBiO3 systems.Mean-field calculations are performed via a path integral representation of the model.Charge-density-wave order parameters and transition temperatures are obtained.     

Constraints on an asymptotic safety scenario for the Wess–Zumino model

Using the nonrenormalization theorem and Pohlmeyer's theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess–Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kähler potential.     

πNN and ΔπN Couplings in a Relativistic Quark Model Approach

Based on a relativistic quark model approach,the decay of Δ^ →π^ p,and the coupling constants of gΔπN and gπNN are studied.Our results are compared with data and empirical values.     

Transient and Stationary Simulations for a Quantum Hydrodynamic Model

The transient and stationary characteristics of a one-dimensional quantum hydrodynamic model are comparatively studied for semiconductor charge transport in a resonant tunnelling diode. When the bias is not small, our numerical results show a deviation of the asymptotic transient solutions from the stationary ones. A dynamic instability accounts for such deviation. The stationary quantum hydrodynamic model is therefore unsuitable in general for simulating quantum devices.     

The Analytical Approach for the Two-dimensional O(3) Non-linear σ Model

In the lattice gauge theory,by using the variational cumulant expansion,we calculate the internal energy and specific heat for the two-dimensional O(3) non-linear σ model.A comparison with Monte Carlo data is also presented.     

StureGate：a Data Model for the ATLAS Software Architecture

ATLAS[1] has recently joined Gaudi,an open project to develop a data processing framework for HEP experiments[2],The data model is one of the areas where ATLAS has extended more the original Gaudi design to meet the experiment‘s own requirments.This paper describes StoreGate,the first implementation of the ATLAS Data Model.     

Towards a measurement of the two-photon decay width of the Standard Model Higgs boson at a Photon Collider

A study of the measurement of the two photon decay width times the branching ratio of the Standard Model Higgs boson with a mass of 120 GeV in photon–photon collisions is presented, assuming a γ γ integrated luminosity of 80 fb⁻¹ in the high energy part of the spectrum. The analysis is based on the reconstruction of the Higgs events produced in the γ γ→H process, followed by the decay of the Higgs into a pair. A statistical error of the measurement of the two-photon width, Γ(H→γ γ), times the branching ratio of the Higgs boson, BR is found to be 2.1% for one year of data taking.     

Searching for Constraints on Starobinsky’s Model with a Disappearing Cosmological Constant on Galaxy Cluster Scales

Predictions of the f(R)-gravity model with a disappearing cosmological constant (Starobinsky’s model) on scales characteristic of galaxies and their clusters are considered. The absence of a difference in the mass dependence of the turnaround radius between Starobinsky’s model and General Relativity accessible to observation at the current accuracy of measurements has been established. This is true both for small masses (from 10⁹M_Sun) corresponding to an individual galaxy and for masses corresponding to large galaxy clusters (up to 10¹⁵M_Sun). The turnaround radius increases with parameter n for all masses. Despite the fact that some models give a considerably smaller turnaround radius than does General Relativity, none of the models goes beyond the bounds specified by the observational data.     

Analytical Structure Matching and Very Precise Approach to the Coulombic Quantum Three—Body Problem

A powerful approach to solve the Coulombic quantium three-body problem is proposed.The approach is expeonentially convergent and more efficient than the hyperspherical coordinate method and the correlaion-function hyperspherical harmonic method.This approach is numerically competitive with the variational methods.Such as that using the Hylleraas-type basis functions,Numerical comparisons are made to demonstrate the efficiency of this approach,by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom.The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in thuis paper and the true wavefunction.This full matching was not reached by most other methods.For example,the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock.Two important approaches are proposed in this work to reach this full matching:the coordinate transfomation method and the asymptotic series method.Besides these,this work makes use of the least square method to substitute complicated numerical integrations in solving the Schroedinger equation without much loss of accuracy,which is routinely used by people to fit a theoretical curve with discrete experimental data,but here is used to simplify the computation.     

Entanglement in the Extended XY Spin Model with Three Spin Interaction and External Field

We investigate the pairwise thermal entanglement of the extended XY model with three spin interactions and external filed on zig-zag lattice. The influences of three spin interactions J ₂ and external field λ on the thermal entanglement of the nearest neighbor (NN) and next nearest neighbor (NNN) spins are considered. It is found that J ₂ and λ suppress both the maximal value and the critical temperature of the NN entanglement C ₁₂. However, when it comes to the NNN entanglement C ₁₃, there exists a critical value of J ₂ above which both the maximal entanglement and the critical temperature can be enhanced by J ₂ for a fixed external field. With J ₂ fixed, the effect of λ on C ₁₃ are different for different values of J ₂. For J ₂<1, λ suppresses both T _C and the maximal values of C ₁₃. For J ₂≥1, λ enhances the maximal values of C ₁₃ while decreases the critical temperature. These results show that one is able to get the entanglement wanted by properly controlling the values of the three spin interactions J ₂ and the external field λ.     

Grain Crush and Its Evolution in Granular Material： a Two-Dimensional Distinct Element Model Approach

A crush criterion and a simplified post-crush process for spherical grains are introduced into the traditional distinct element model (DEM). The crush criterion is based on Herzian comtact, and it indicates a negative relation between critical force Fcr and radius R via Fcr ∝ R^-3/2. Effects of grain crush on deformation pattern and statistical features of crush evolution for samples under uniaxial strain load are intensively investigated. Influences of maximum crush times and particle size distribution (PSD) are also discussed. It is found that: (1) Grain crush will blur the localization of deformation. (2) Crush is prone to occur in larger grains, due to force concentration and lower critical force Fcr for larger grains. (3) Grain crush only temporarily reduces contact force, which results in the most rapid increase of the number of grains with maximum crush time.     

Brick Wall Model and the Spectrum of a Schwarzschild Black Hole

The quantum entropy of a scalar field near a Schwarzschild black hole is investigated by employing the brick-wall model in the grand canonical ensemble. A positive chemical potential is introduced if the cutoff is set to be of order of the Planck length. We also discuss the relation between the chemical potential and the mass quantum of the black hole.     

A Universal Amplitude Ratio for the q≤4 Potts Model from a Solvable Lattice Model

The universal amplitude ratio R for the (q4)-state Potts model in two dimensions is determined by using results for the dilute A model in regime 1. The nature of the relationship between the Potts model and the dilute A model is discussed.     

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.     

Calculation of Be in an α-α-Λ Three-Body Model Using the Faddeev Equations

 The hypernucleus Be is investigated in an α-α-Λ three-body model using the Faddeev formalism. We use an α-α interaction in which the Pauli-forbidden states are correctly taken into account and we employ some phenomenological potentials between the α and Λ particles. We obtained two bound states for and , and three resonance states of . We studied the properties of these states by calculating the components and the expectation values of the potential for each partial wave. It is found that a few channels dominate in the α (α, Λ) and states, so that the alpha-clusters or the ⁸Be core are still alive in the nucleus. In a case where the two alpha particles are fixed on an axis the contour plots of the distribution of the Λ particle are shown. With the assistance of these plots one can visually understand that some of them are shell-model-like states while others are well developed cluster-model-like states. For the structure of Be, it is concluded that the Λ particle is loosely coupled in S- and P-wave orbits about the ⁸Be(0⁺) and ⁸Be(2⁺) core states. Finally, we discuss a redundant state in the Faddeev amplitude which could arise from the treatment of symmetrization. Received June 25, 1998; revised April 13, 1999; accepted for publication December 29, 1999     

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising–Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal D_z and transverse D_x crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second-and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.     

Calculation of Ratios of μ and π Masses to the e Mass for a Simplified Model with a Square-Well Potential

In the present paper, the feasibility of constructing a model of elementary and particles based on the Poincaré model of the electron [1] is examined with allowance for schemes of particle decay. The muon and pion in stopped states are considered as spherical resonators for virtual neutrino quanta excited inside an elastic lepton shell; the number of these quanta is determined by the scheme of the corresponding particle decay. In the model, the muon differs from the electron by two additional quanta of the neutrino field. The e, , and masses are calculated with the help of a single parameter. The ratio of and e masses is about (6c/e ²)^2/3, and the ratio of ° and e masses is (3/2)^2/3. The calculated e, , and ° masses are in the 0.547:105.71:134.963 ratios, which is in good agreement with the available experimental data. The calculated electromagnetic radius of the charged pion (±) = 0.5f is close to that calculated from the experimental data. The neutrino mass _e is found to be m( _e ) 0.02 eV.     

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on?Lattice Strips

We determine the general structure of the partition function of the q-state Potts model in an external magnetic field, Z(G,q,v,w) for arbitrary q, temperature variable v, and magnetic field variable w, on cyclic, M?bius, and free strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices with width L _y and arbitrarily great length L _x . For the cyclic case we prove that the partition function has the form Z(L,L_y×L_x,q,v,w)=?_d=0^L_y[(c)tilde]^(d)Tr[(T_Z,L,Ly,d)^m]Z(Lambda,L_{y}times L_{x},q,v,w)=sum_{d=0}^{L_{y}}tilde{c}^{(d)}mathrm{Tr}[(T_{Z,Lambda,L_{y},d})^{m}] , where Λ denotes the lattice type, [(c)tilde]^(d)tilde{c}^{(d)} are specified polynomials of degree d in q, T_Z,L,Ly,dT_{Z,Lambda,L_{y},d} is the corresponding transfer matrix, and m=L _x (L _x /2) for Λ=sq,tri (hc), respectively. An analogous formula is given for M?bius strips, while only T_Z,L,Ly,d=0T_{Z,Lambda,L_{y},d=0} appears for free strips. We exhibit a method for calculating T_Z,L,Ly,dT_{Z,Lambda,L_{y},d} for arbitrary L _y and give illustrative examples. Explicit results for arbitrary L _y are presented for T_Z,L,Ly,dT_{Z,Lambda,L_{y},d} with d=L _y and d=L _y −1. We find very simple formulas for the determinant det(T_Z,L,Ly,d)mathrm{det}(T_{Z,Lambda,L_{y},d}) . We also give results for self-dual cyclic strips of the square lattice.