An effective Monte Carlo calculation of the radial distribution function of hard spheres on a minicomputer

An algorithm that utilizes the advantage of a machine language and integer arithmetic is proposed for the Monte Carlo simulations of the radial distribution function of fluid hard spheres. The influence of integer arithmetic upon the accuracy of results is discussed. The method can be easily adapted for more complicated potentials.     

Monte Carlo values for the radial distribution function of a system of fluid hard spheres

The perturbation theory recently developed by Weeks, Chandler, and Andersen is applied to the solid phase of a rare gas near its melting line. The potential is separated into two parts: a reference part containing all the repulsive forces and a perturbation part containing all the attractions. We show that the expansion of the free energy in the perturbation potential is, as in the liquid phase, rapidly convergent for a temperature of the order of the triple-point temperature. On the contrary, the representation of the reference system by hard spheres with an appropriate diameter is less accurate than in the liquid phase. This representation requires the knowledge of the radial distribution functions of the hard-sphere solid for which we give a tabulation as well as an analytical representation. The perturbation theory is applied to the determination of the fluid-solid transition.     

A Monte Carlo study of dipolar hard spheres The pair distribution function and the dielectric constant

This paper is a systematic investigation of the effects of boundary conditions upon Monte Carlo calculations for dipolar fluids. Results are reported for the minimum image (MI), spherical cut-off (SC) and uniform reaction field methods. All three approximations are shown to give different pair distribution functions, g(12), and none yields the infinite system result. It is concluded that theories giving g(12) for an infinite system should not be evaluated by direct comparison with Monte Carlo results. Two alternative methods by which meaningful comparisons can be made are described in the text. The dependence of the thermodynamic properties upon boundary conditions is important only at large values of the dipole moment. For small to moderate dipoles both MI and SC are found to give reasonable estimates of the dielectric constant.     

First quantum correction to the radial distribution function and to the thermodynamic properties for a fluid of hard spheres

Dealing with the positions and orientations of the molecules as independent stochastic processes, the authors investigate the influence of translational and rotational fluctuations of anisotropically polarizable microsystems on the evolution in time of the second-order intensity correlation tensor of Rayleigh scattered light as well as on its spectral density. The notion of second-order depolarization is introduced and is shown to be a useful quantity for obtaining information on the translational and rotational motions of microsystems and their optical anisotropy.     

Improvement of the grand canonical quantum Monte Carlo method at low temperatures

We introduce an improvement of the algorithm for the simulation of correlated fermi systems in the grand canonical ensemble. Using this new method the computer time grows no more with the square but essentially linearly with the inverse temperature. At low temperatures the number of operations is diminished by a factor typically between 5 and 20. We present results for correlation functions of the one-dimensional Hubbard model at various band fillings.     

Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study

In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.     

Monte Carlo study of the equimolar mixture of hard spheres and spherocylinders

Using the Monte Carlo simulation technique the behaviour of the equimolar mixture of hard spheres and prolate spherocylinders of the length-to-breadth ratio equal to two was studied for the case in which both components had the same breadth. The surface-to-surface and the center-to-center correlation functions and the compressibility factor were computed and the results compared with theoretical predictions. Effect of non-sphericity of one component is shortly discussed.     

Perturbation calculation of the distribution functions of mixtures of hard spheres

The distribution functions for a mixture of additive hard spheres of diameter σ_ii are calculated by means of an expansion in powers of σ _ij ⁿ - dⁿ , using an unperturbed single-component hard-sphere fluid of diameter d. Although the expansion converges only when the hard spheres in the mixture are nearly equal in size, it is useful because it is the only practical scheme available for obtaining the distribution functions of multicomponent hard-sphere mixtures.     

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.     

Monte Carlo data of dilute solutions of large spheres in binary hard sphere mixtures

Monte Carlo (MC) simulation data for additive binary hard sphere mixtures are reported for dilute concentrations of the large sphere. Using a single occupancy linked cell method, binary hard sphere solutions with a size ratio of 5 are simulated at high reduced density and low concentration of the large sphere. Data for the solute-solvent pair distribution function show that at the lowest concentrations of the large sphere simulated, the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation underestimates the contact value; whereas the recently proposed Henderson-Chan (HC) equation gives a good prediction. For the solute-solute contact value at the colloidal limit, the MC data lie between the two predictions. The BMCSL equation underestimates, while the HC equation overestimates, the correct solute-solute contact value.     

An expansion method for the Monte Carlo distribution function

We present and test an expansion method for calculating the distribution function of mobile electrons in semiconductors in a drifting homogeneous electric field. This expansion represents an extension of the drifted Maxwellian method and correctly reproduces the exact Monte Carlo distribution function even in high fields.     

Monte Carlo study of three-dimensional QCD at finite temperature

Three-dimensional QCD at finite temperature is analyzed using Monte Carlo calculations. It is shown that confinement at low temperature is lost through a second-order phase transition. At high temperature, static quarks are liberated and screened and it is argued that timelike (A₀) gluons are liberated. Just above the critical temperature electric correlation functions seem to be dominated by a resonance of two timelike gluons, whose existence is suggested by perturbation theory. The influence of an external magnetic field close to the critical point is considered.     

The triplet distribution function in a fluid of hard spheres

The distribution functions of a fluid can be expressed as a series in powers, of the density. The coefficient of the fourth power of the density in the expansion of the triplet distribution function is obtained as a function of the separations of the molecules for a fluid of hard spheres. The coefficient is negative. It is used to estimate the amount by which the true triplet distribution function is less than the value attributed to it by the superposition approximation.     

Lennard-Jones chain mixtures: radial distribution functions from Monte Carlo simulation

Radial distribution functions are calculated for binary Lennard-Jones chain mixtures from Monte Carlo simulation. Average and end-to-end inter- and intrachain radial distribution functions are calculated, ten for a binary mixture and four for a pure component. The effects of density, concentration, temperature, chain length, Lennard-Jones size and energy parameters are investigated. It is found that intrachain radial distribution functions are largely independent of density except at very high densities, where they start to take on a structure tending towards that of a crystal lattice. In addition, the effect of using different distribution functions to calculate the associating contribution in statistical associating fluid theory (SAFT) is examined. Further, the effect of using short chain fluids rather than the monomer unit as the reference system in the calculation of the pressure and free energy of chain fluids in first-order thermodynamic perturbation theory (TPT) is examined. It is found that the choice of reference radial distribution function has a marked effect on the calculation of thermodynamic properties through the use of SAFT and TPT.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work (Phys. Rev. B 74 195414 (2006)), we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper,we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature.Unlike the proof given in our previous work(Phys.Rev.B 74 195414(2006)),we take a different approach,which does not exploit the explicit expression of the Gibbs distribution function.Instead,we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable.As a result,we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability.Furthermore,the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.