Non-hermitian exact local bosonic algorithm for dynamical quarks

We present an exact version of the local bosonic algorithm for the simulation of dynamical quarks in lattice QCD. This version is based on a non-hermitian polynomial approximation of the inverse of the quark matrix. A Metropolis test corrects the systematic errors. Two variants of this test are presented. For both of them, a formal proof is given that this Monte Carlo algorithm converges to the right distribution. Simulation data are presented for different lattice parameters. The dynamics of the algorithm and its scaling in lattice volume and quark mass are investigated.     

Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model

To validate the ability of full configuration interaction quantum Monte Carlo(FCIQMC) for studying the 2 D Hubbard model near half-filling regime, the ground state energies of a 4 x 4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization(i.e., the exact values for a given basis set) when the population of psi particles(psips) is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2 D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.     

Finite temperature QCD in the presence of dynamical quarks

By using Monte Carlo (MC) methods we study the deconfining transition of QCD with color group SU(3) at finite temperature. The fermion polarization effects are kept in account by implementing the pseudo-fermion method. We use two different lattice volumes (6³ × 4, 8³ × 4) to check finite size effects. Even in the presence of light quarks we find a discontinuous transition. The existence of this transition is observed both creating metastable states and using mixed phase runs.     

Chiral phase transition in lattice QCD with dynamical quarks

The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 6³ × 2 lattice. The variation in the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory.     

First-passage Monte Carlo algorithm: diffusion without all the hops

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.     

Exchange monte carlo for molecular simulations with monoelectronic hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented.     

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     

Incorporating dynamical light quarks in lattice QCD at finite temperature

Using the pseudo-fermion Monte Carlo method we investigate the chiral and the deconfinement phase transitions in the SU(3) gauge theory with dynamical staggered fermions on a 6³ × 2 lattice. The energy density of the gluonic sector ε_G, the average thermal Wilson loop |L| and the order parameter are found to have a rapid variation in the same range of β (=6/g²). The variation is similar to that observed in the quenched theory but is at a smaller value of β.     

非定常粒子输运蒙特卡罗散射源分层抽样方法

定常粒子输运蒙特卡罗并行计算是成功的,因为粒子游动是独立的,可以把模拟的粒子数等分到每个处理器去.然而,对非定常问题,由于每个时间步涉及散射源和几何网格的通讯,它严重的制约了并行规模,导致并行不可扩展.研究了两种算法,采用自适应分配处理器,提高了加速比和处理器的利用率;采用蒙特卡罗分层抽样大大降低了处理器之间散射源的通讯量,并行可扩展性显著改善,取得了理想的加速比.     

Superlight small bipolarons in the presence of a strong Coulomb repulsion

We study a lattice bipolaron on a staggered triangular ladder and triangular and hexagonal lattices with both long-range electron-phonon interaction and strong Coulomb repulsion using a novel continuous-time quantum Monte Carlo algorithm to solve the two-particle Coulomb-Fr?hlich model. The algorithm is preceded by an exact integration over phonon degrees of freedom, and as such is extremely efficient. The bipolaron effective mass and radius are computed. Bipolarons on lattices constructed from triangular plaquettes have a novel crablike motion, and are small but very light over a wide range of parameters. We discuss the conditions under which such particles may form a Bose-Einstein condensate with high transition temperature, proposing a route to room temperature superconductivity.     

Investigation of nucleation and grain growth in 2-dimensional systems by using generalized Monte Carlo simulations

In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena.     

蜂窝状格子带有晶场作用的铁磁Ising混合自旋S=1和S=1/2的相图的Monte-Carlo研究

利用具有翻转单个自旋的Metropolis-Monte-Carlo算法,研究蜂窝状格子带有晶场作用的铁磁Ising混合自旋S=1和S=1/2的相图,所得相图与严格解相接近,好于关联有效场方法得出的结果。因此Metropolis-Monte-Carlo算法同样也可以用于研究混合自旋模型。     

A Markov-property Monte Carlo method: One-dimensional Ising model

In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.     

The SU(3) deconfining transition in the presence of quarks

We perform a Monte Carlo simulation of the full theory of QCD at finite temperature. The effect of closed quark loops is taken in account by employing the pseudo-fermion method. Our preliminary data, show that for three flavors the scenario given by the pure gauge theory is unchanged: the theory still undergoes a first order phase transition at the critical coupling β_c = 6/g_c² = 5.2 ± 0.1 (T_c/Λ_L = 171 ± 28). Increasing the number of flavors we observe stronger ordering effects and the critical coupling decreases.     

考虑中子泄漏修正的快堆蒙特卡罗少群截面参数制作与验证方法

一种基于B1均匀化方程的泄漏修正模型在连续能量蒙特卡罗程序TRIPOLI4中得以实现并且用于制作少群截面参数。此蒙卡泄漏修正模型通过在连续能量的蒙卡模拟以及求解B1均匀化方程之间迭代,最终得到蒙卡模拟下的临界状态。通过此方法得到的少群截面参数较其他蒙卡以及确定论方法有两点显著优势:用于求解B1均匀化方程的少群常数是用通过临界状态的通量谱得到的;考虑了泄漏效应的蒙卡模拟可以更真实地反映组件计算时的能谱状态。为验证此泄漏修正模型,一个由连续能量的TRIPOLI4模拟而得到的数值临界实验被用于分析与比较。通过与其他蒙卡程序SERPENT以及确定论程序ECCO进行结果对比,可证明此B1泄漏修正方法能够给出更精确的用于堆芯计算的少群截面参数。     

A dynamical monte carlo algorithm for master equations with time-dependent transition rates

A Monte Carlo algorithm for simulating master equations with time-dependent transition rates is described. It is based on a waiting time image, and takes into account that the system can become frozen when the transition rates tend to zero fast enough in time. An analytical justification is provided. The algorithm reduces to the Bortz-Kalos-Lebowitz one when the transition rates are constant. Since the exact evaluation of waiting times is rather involved in general, a simple and efficient iterative method for accurately calculating them is introduced. As an example, the algorithm is applied to a one-dimensional Ising system with Glauber dynamics. It is shown that it reproduces the exact analytical results, being more efficient than the direct implementation of the Metropolis algorithm     

Chiral symmetry restoration in baryon rich environments

Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illusstrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide one's expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2).     

Quantum-trajectory approach to time-dependent transport in mesoscopic systems with electron-electron interactions

It is proved that many-particle Bohm trajectories can be computed from single-particle time-dependent Schr?dinger equations. From this result, a practical algorithm for the computation of transport properties of many-electron systems with exchange and Coulomb correlations is derived. As a test, two-particle Bohm trajectories in a tunneling scenario are compared to exact results with an excellent agreement. The algorithm opens the path for implementing a many-particle quantum transport (Monte Carlo) simulator, beyond the Fermi liquid paradigm.     

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.     

Monte Carlo simulation of joint density of states in one-dimensional Lebwohl-Lasher model using Wang-Landau algorithm

Monte Carlo simulation using the Wang-Landau algorithm has been performed in an one-dimensional Lebwohl-Lasher model. Both one-dimensional and two-dimensional random walks have been carried out. The results are compared with the exact results which are available for this model.