Exact lattice calculations of dispersion coefficients in the presence of external fields and obstacles

We present a study of the field-dependent dispersion coefficient of point-like particles in various 2D overdamped systems with obstructions (periodic, percolating, and trapping distributions of obstacles). These calculations profit from the synthesis of a newly proposed Monte Carlo algorithm --the first such algorithm that correctly reproduces the free dispersion coefficient in the presence of finite external fields-- and an asymptotically exact calculation technique. The resulting method efficiently produces algebraic and numerical results without the need to actually perform Monte Carlo simulations. When compared to such simulations, our exact method features a negligible computational cost and exponentially small errors. Utilizing the power of this numerical method, we engage in comprehensive parametric analysis of several model systems, revealing very subtle effects that would otherwise be swamped by statistical errors or incur prohibitive computational costs. The unified framework presented here serves as a template for further applications of lattice random-walk models of biased diffusion.Received: 27 July 2004, Published online: 1 October 2004PACS: 87.15.Vv Diffusion - 82.20.Wt Computational modeling; simulation - 05.10.Ln Monte Carlo methods     

Grand Canonical Ensemble Monte Carlo Simulation of Depletion Interactions in Colloidal Suspensions

Depletion interactions in colloidal suspensions confined between two parallel plates are investigated by using acceptance ratio method with grand canonical ensemble Monte Carlo simulation. The numerical results show that both the depletion potential and depletion force are affected by the confinement from the two parallel plates. Furthermore, it is found that in the grand canonical ensemble Monte Carlo simulation, the depletion interactions are strongly affected by the generalized chemical potential.     

QCD studies with e+e− annihilation data at 161 GeV

We have studied hadronic events produced at LEP at a centre-of-mass energy of 161 GeV. We present distributions of event shape variables, jet rates, charged particle momentum spectra and multiplicities. We determine the strong coupling strength to be α_s(161 GeV) = 0.101±0.005(stat.)±0.007(syst.), the mean charged particle multiplicity to be 〈n _ch〉(161 GeV) = 24.46 ± 0.45(stat.) ± 0.44(syst.) and the position of the peak in the ξ_p = ln(1/x _p) distribution to be ξ₀(161 GeV) = 4.00 ±0.03(stat.)±0.04(syst.). These results are compared to data taken at lower centre-of-mass energies and to analytic QCD or Monte Carlo predictions. Our measured value of α_s(161 GeV) is consistent with other measurements of α_s. Within the current statistical and systematic uncertainties, the PYTHIA, HERWIG and ARIADNE QCD Monte Carlo models and analytic calculations are in overall agreement with our measurements. The COJETS QCD Monte Carlo is in general agreement with the data for momentum weighted distributions like Thrust, but predicts a significantly larger charged particle multiplicity than is observed experimentally.     

Molecular dynamical simulation of the canonical ensemble

We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the one-dimensional jellium.     

The grand canonical ensemble Monte Carlo method applied to electrolyte solutions

A grand canonical ensemble Monte Carlo method is developed for application to electrolyte solutions.

The method proves to be of comparable accuracy and speed to the conventional NVT Monte Carlo method for electrolytes but has the added advantage of being able to fix the chemical potential. This latter point is vital for the study of surface phenomena. Application of the method to 1:1 and 2:2 primitive model electrolytes is made as is a comparison with the results of approximate statistical mechanical treatments.     

Temperature and density extrapolations in canonical ensemble monte carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.     

A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble

A grand canonical Monte Carlo (GCMC) simulation method is presented for the determination of the phase equilibria of mixtures. The coexistence is derived by expanding the pressure into a Taylor series as a function of the temperature and the chemical potentials that are the independent intensive variables of the grand canonical ensemble. The coefficients of the Taylor series can be calculated from ensemble averages and fluctuation formulae that are obtained from GCMC simulations in both phases. The method is able to produce the equilibrium data in a certain domain of the (T, p) plane from two GCMC simulations. The vapour-liquid equilibrium results obtained for a Lennard-Jones mixture agree well with the corresponding Gibbs ensemble Monte Carlo data.     

多π关联对π发射源相干性的分析

对高能重离子碰撞中不同相于性程度π源产生的多π关联事件进行了蒙特卡罗模拟,比较了不同多重数子事件中的多π关联对π源相于性程度依赖的敏感性.对Bevalac流光室2.1A GeV Ne+Pb和1.2A GeV Ar+KCl中心碰撞产生的π源的相干性程度进行了分析,并与以往的2π干涉学的结果进行了比较.     

QCD analyses and determinations of \alpha_s in {\rm e}^+{\rm e}^- annihilation at energies between 35 and 189 GeV

We employ data taken by the JADE and OPAL experiments for an integrated QCD study in hadronic ee annihilations at c.m.s. energies ranging from 35 GeV through 189 GeV. The study is based on jet-multiplicity related observables. The observables are obtained to high jet resolution scales with the JADE, Durham, Cambridge and cone jet finders, and compared with the predictions of various QCD and Monte Carlo models. The strong coupling strength, , is determined at each energy by fits of calculations, as well as matched and NLLA predictions, to the data. Matching schemes are compared, and the dependence of the results on the choice of the renormalization scale is investigated. The combination of the results using matched predictions gives The strong coupling is also obtained, at lower precision, from fits of the c.m.s. energy evolution of some of the observables. A qualitative comparison is made between the data and a recent MLLA prediction for mean jet multiplicities. Received: 13 December 1999 / Published online: 26 July 2000     

Probability-changing cluster algorithm for Potts models

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, p = 1-e(-J/k(B)T), in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.     

Disorder-induced stabilization of the pseudogap in strongly correlated systems

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two nonperturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and quantum Monte Carlo simulations. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder, and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

Statistical hadronization and hadronic microcanonical ensemble I

We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas starting from a quantum-mechanical formulation which is appropriate for the statistical model of hadronization. By using a suitable transition operator for hadronization we are able to recover the results of the statistical theory, particularly the expressions of the rates of different channels. Explicit formulae are obtained for the phase space volume or density of states of the ideal relativistic gas in quantum statistics as a cluster decomposition, generalizing previous ones in the literature. The problem of the computation of averages in the hadron gas microcanonical ensemble and the comparison with canonical ones will be the main subject of a forthcoming second paper.Received: 8 July 2003, Revised: 17 October 2003, Published online: 5 May 2004     

Application of the kinetic Monte Carlo method in the microscopic description of argon adsorption on graphite

We present an application of kinetic Monte Carlo (kMC) in the canonical ensemble to a calculation of vapour liquid equilibrium and to describe the adsorption of argon on a flat graphite surface and in a slit-like graphitic pore. Simulations at 77 and 87.3?K accurately describe the experimental data. The kMC method is simple to implement and, unlike conventional Monte Carlo, no rejection trials are necessary. The only move is a uniform sampling of the volume space, which makes the determination of the chemical potential straightforward using real particles in the simulation, in the same spirit as the Widom inverse potential distribution. This avoids the need to freeze the real particles before the trial insertion of test particles as is necessary in other methods, such as the Widom method and its variants.     

Monte Carlo Hamiltonian:Inverse Potential

The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system, using Monte Carlo (MC) algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applied to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.     

Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems

We apply the multicanonical Monte Carlo (MMC) method to compute the probability distribution of the received voltage in a chirped return-to-zero system. When computing the probabilities of very rare events, the MMC technique greatly enhances the efficiency of Monte Carlo simulations by biasing the noise realizations. Our results agree with the covariance matrix method over 20 orders of magnitude. The MMC method can be regarded as iterative importance sampling that automatically converges toward the optimal bias so that it requires less a priori knowledge of the simulated system than importance sampling requires. A second advantage is that the merging of different regions of a probability distribution function to obtain the entire function is not necessary in many cases.     

A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble

We propose to compute the thermodynamic properties of many-body systems using a path-sampling Monte Carlo scheme implemented in a generalized path ensemble. Trial paths are generated through an expanded ensemble using a reversible discretization of Langevins equation of motion. We also show how the systematic errors resulting from the use of a finite time step can rigorously be taken into account in the path-sampling scheme. We find that the degree of convergence of the estimated thermodynamic quantity towards the exact value correlates with the mean acceptance rates of the path-sampling scheme. An application of the path method for simulating glassy systems is finally suggested.Received: 28 January 2004, Published online: 8 June 2004PACS: 82.60.Lf Thermodynamics of solutions - 07.05.Tp Computer modeling and simulation - 64.70.Pf Glass transitions     

Next-to-leading order jet cross sections in polarized hadronic collisions

We present a next-to-leading order computation in QCD of one-jet and two-jet cross sections in polarized hadronic collisions. Our results are obtained in the framework of a general formalism that deals with soft and collinear singularities using the subtraction method. We construct a Monte Carlo programme that generates events at the partonic level. We use this code to give phenomenological predictions for pp collisions at √S = 500 GeV, relevant for the spin physics programme at RHIC. The possibility of using jet data to constrain the poorly known polarized parton densities is examined.