Configuration Path Integral Monte Carlo

A novel path integral Monte Carlo (PIMC) approach for correlated many‐particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N ‐particle density operator in a basis of (anti‐)symmetrized N ‐particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M → ∞, where M is the number of high‐temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photon transport in thin disordered slabs

We examine using Monte Carlo simulations, photon transport in optically ‘thin’ slabs whose thickness L is only a few times the transport mean free path l*, with particles of different scattering anisotropies. The confined geometry causes an auto-selection of only photons with looping paths to remain within the slab. The results of the Monte Carlo simulations are borne out by our analytical treatment that incorporates directional persistence by the use of the Ornstein-Uhlenbeck process, which interpolates between the short time ballistic and long time diffusive regimes.     

Quantum virial coefficients of molecular nitrogen

We report virial coefficients up to third order in density for molecular nitrogen, investigating 103 temperatures in the range (15 K, 3000 K). All calculations are based on an ab initio-based potential taken from the literature. Path-integral Monte Carlo (PIMC) is applied to account for nuclear quantum effects, and these results are compared to a more approximate but faster semiclassical treatment. Additionally, we examine a PIMC approach that employs semiclassical beads for the path-integral images, but find that it offers marginal advantage. A recently developed orientation sampling algorithm is used in conjunction with Mayer sampling to compute precise virial coefficients. We find that, within the precision of our calculations of the second-order coefficient (B₂), semiclassical methods are adequate for temperatures greater than 250 K, and are needed to correct classical behaviour for temperatures as high as 800 K. For the third-order coefficient (B₃), the semiclassical methods are adequate above 150 K, and are required up to the highest temperature examined (3000 K) in order to correct the classical treatment within the precision of the calculations. However, three-body contributions to the potential are much more significant than nuclear quantum effects for the evaluation of B₃.     

Molecular simulation of chemical reaction equilibria by Kinetic Monte Carlo

ABSTRACT

We describe a new algorithm for the molecular simulation of chemical reaction equilibria, which we call the Reactive Kinetic Monte Carlo (ReKMC) algorithm. It is based on the use of the equilibrium Kinetic Monte Carlo (eKMC) method (Ustinov et al., J. Colloid Interface Sci., 2012, 366, 216–223) to generate configurations in the underlying nonreacting system and to calculate the species chemical potentials at essentially zero marginal computational cost. We consider in detail the typical case of specified temperature, T and pressure, P, but extensions to other thermodynamic constraints are straightforward in principle. In the course of this work, we also demonstrate an alternative method for calculating simulation box volume changes in NPT ensemble simulations to achieve the specified P. We consider two sets of example reacting systems previously considered in the literature, and compare the ReKMC results and computational efficiencies with those of different implementations of the REMC algorithm (Turner et al., Molec. Simulation, 2008, 34, 119–146).     

液态~4He系统对关联函数的路径积分蒙特卡罗模拟

利用路径积分蒙特卡罗(PIMC)模拟方法研究了由256个4He原子组成的系统在不同条件下的对关联函数g(r).在标准大气压下(SVP),分别在1.38K,1.67K,2.50K和4.24K等四个温度时对系统不同势能的情况的对关联函数进行了计算;另外还讨论了系统的温度和密度对对关联函数的影响.结果发现,系统的势能变化及密度变化都或大或小影响对关联函数,而温度对其影响不是很大.虽然PIMC方法存在有限尺度效应,但是由128和256个4He原子组成系统的对关联函数存在极小的差异,因此可以得到:随着模拟系统尺度的增大,所模拟的有限尺度的系统已逐渐接近于真实系统.所以所得的256原子系统的性质可近似说明液态系统性质.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

Computation of partial molar properties using continuous fractional component Monte Carlo

ABSTRACT

An alternative method for calculating partial molar excess enthalpies and partial molar volumes of components in Monte Carlo (MC) simulations is developed. This method combines the original idea of Frenkel, Ciccotti, and co-workers with the recent continuous fractional component Monte Carlo (CFCMC) technique. The method is tested for a system of Lennard–Jones particles at different densities. As an example of a realistic system, partial molar properties of a [NH₃, N₂, H₂] mixture at chemical equilibrium are computed at different pressures ranging from P = 10 to 80 MPa. Results obtained from MC simulations are compared to those obtained from the PC-SAFT Equation of State (EoS) and the Peng–Robinson EoS. Excellent agreement is found between the results obtained from MC simulations and PC-SAFT EoS, and significant differences were found for PR EoS modelling. We find that the reaction is much more exothermic at higher pressures.     

Analysis of diffuse scattering of single crystals using monte carlo methods

While conventional crystal structure analysis using Bragg intensities reveals only information about the average structure of the crystal, diffuse scattering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approaches to the analysis of diffuse scattering based on Monte Carlo methods are described in this paper: the direct Monte Carlo (MC) simulation technique and the Reverse Monte Carlo (RMC) method. The MC method requires the construction of a model for the disorder based on physical and chemical considerations and the selection of a set of near-neighbour interactions. The given model is realized by minimizing the total energy of the crystal via MC simulations. Next, the corresponding diffraction pattern is calculated and compared with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative “match” between observed and calculated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensities directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a chemically sensible structure or further insight into the particular disorder problem.

The first example given in this paper demonstrates the viability of the RMC method by refining diffuse scattering data calculated from simulated structures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffuse scattering of stabilized zirconias (CSZ) are shown, modelling occupational disorder as well as displacements.     

Design of a neutron polarizer using polarizing super mirrors for the TOF-SANS instrument at the J-PARC

Small-angle neutron scattering technique using polarized neutrons is powerful for studying structures in the range between nm and μm of magnetic materials. In addition, they have been used for the incident beam of focusing-geometry SANS instruments using a magnetic neutron lens, where a high polarization degree of about 99.9% is necessary because the imperfectness of the neutron polarization increases the background level. We are going to install such a magnetic focusing system on the new time-of-flight SANS (TOF-SANS) instrument at the J-PARC so as to make q_min smaller than 10⁻³ Å⁻¹ and improve the resolution of the conventional TOF-SANS at low q. As a polarizing device of the instrument, two V-shaped polarizing super mirrors arranged in crossed geometry to enhance the polarization degree has been considered. In this paper, we present the concept and the detailed design of this device and its performance estimated by Monte Carlo simulations.     

Finite Size Effect in Path Integral Monte Carlo Simulations of 4He Systems

Path integral Monte Carlo (PIMC) simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ⁴He. We determine the energy as a function of temperature at saturated-vapor-pressure (SVP) conditions in the temperature range of T∈[1.0 K, 4.0 K], and the equation of state (EOS) in the ground state for systems consisted of 32, 64 and 128 ⁴He atoms, respectively. We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T∈[2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

Benchmarking and validation of a Geant4–SHADOW Monte Carlo simulation for dose calculations in microbeam radiation therapy

Microbeam radiation therapy (MRT) is a synchrotron‐based radiotherapy modality that uses high‐intensity beams of spatially fractionated radiation to treat tumours. The rapid evolution of MRT towards clinical trials demands accurate treatment planning systems (TPS), as well as independent tools for the verification of TPS calculated dose distributions in order to ensure patient safety and treatment efficacy. Monte Carlo computer simulation represents the most accurate method of dose calculation in patient geometries and is best suited for the purpose of TPS verification. A Monte Carlo model of the ID17 biomedical beamline at the European Synchrotron Radiation Facility has been developed, including recent modifications, using the Geant4 Monte Carlo toolkit interfaced with the SHADOW X‐ray optics and ray‐tracing libraries. The code was benchmarked by simulating dose profiles in water‐equivalent phantoms subject to irradiation by broad‐beam (without spatial fractionation) and microbeam (with spatial fractionation) fields, and comparing against those calculated with a previous model of the beamline developed using the PENELOPE code. Validation against additional experimental dose profiles in water‐equivalent phantoms subject to broad‐beam irradiation was also performed. Good agreement between codes was observed, with the exception of out‐of‐field doses and toward the field edge for larger field sizes. Microbeam results showed good agreement between both codes and experimental results within uncertainties. Results of the experimental validation showed agreement for different beamline configurations. The asymmetry in the out‐of‐field dose profiles due to polarization effects was also investigated, yielding important information for the treatment planning process in MRT. This work represents an important step in the development of a Monte Carlo‐based independent verification tool for treatment planning in MRT.     

Simulations of germanium epitaxial growth on the silicon (1 0 0) surface incorporating intermixing

We present kinetic lattice Monte Carlo simulations of Ge deposition onto a reconstructed Si (1 0 0) surface. We account for the exchange of Ge with Si atoms in the substrate, considering two different exchange mechanisms: a dimer exchange mechanism whereby Ge–Ge dimers on the surface become intermixed with substrate Si atoms, and the exchange of Ge atoms below the surface to relieve misfit strain. We examine how Si–Ge exchange affects the interface between the materials when the growth simulations are done at different temperatures.     

Alternative Oblique-Incidence Reflectometry for Measuring Tissue Optical Properties

To deduce the optical properties, the absorption coefficient SmU_aand reduced scattering coefficient μ’_s, of turbid medium, Lin et al. (Appl. Opt. 34 (1995) 2362) proposed an oblique incidence reflectometry in which the diffusion approximation was assumed. In this paper we propose an alternative method which does not assume the diffusion approximation but uses a Monte Carlo light propagation model. Two features are extracted from the diffuse reflectance distribution detected on the medium surface, and optical properties are then estimated by looking up the predetermined table generated by Monte Carlo simulations. The validity of the proposed method has been confirmed by computer simulations.     

Quantum Monte Carlo simulation of exciton–exciton scattering in a GaAs/AlGaAs quantum well

We present a computer simulation of exciton–exciton scattering in a quantum well. Specifically, we use quantum Monte Carlo techniques to study the bound and continuum states of two excitons in a 10 nm wide GaAs/Al_0.3Ga_0.7As quantum well. From these bound and continuum states we extract the momentum-dependent phase shifts for s-wave scattering. A surprising finding of this work is that a commonly studied effective-mass model for excitons in a 10 nm quantum well actually supports two bound biexciton states. The second, weakly bound state may dramatically enhance exciton–exciton interactions. We also fit our results to a hard-disk model and indicate directions for future work.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Monte Carlo modeling of gold nanoparticles detection limits of benchtop three-dimensional L- and K-shell X-ray fluorescence mapping systems

This study aims to investigate the detection limits of gold nanoparticle (GNP) concentrations by Monte Carlo (MC) modeling of benchtop polychromatic K- and L-shell X-ray fluorescence mapping system. In Monte Carlo N-Particle (MCNP version 6.1) simulations, a 0.25-cm-diameter cylinder containing GNPs of various concentrations (i.e., 0.005%–1.0% gold by weight, wt%) was assumed to be located at the center of a cylindrical water phantom of various diameters (1.0–10 cm). Two different sets of incident pencil beam X-rays and detectors were modeled to stimulate X-ray fluorescence (XRF) of GNPs: (1) 62 kVp and silicon drift detector for L-XRF, (2) 105 kVp and cadmium telluride detector for K-XRF. The detection limits were calculated for given radiation doses to the center of phantom (375–1500 mGy). When the diameter of the phantom was 1 cm, the detection limits for L-XRF and K-XRF were an order of 0.001 wt% and of 0.01 wt%, respectively. The detectability of K-XRF turned out to be superior to that of L-XRF for the phantoms greater than or equal to 3 cm in diameter. The MC results will provide a guide for developing an optimal benchtop XRF imaging system for in vivo preclinical imaging, depending on the sizes of GNP-loaded objects, GNP concentrations, and radiation doses.     

Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin-resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi-Tosi-Land-Sjölander scheme with the QMC data to remove finite-size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110 , 146405 (2013)] and configuration path integral Monte Carlo/permutation-blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117 , 115701 (2016)].     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

Role of hot electron transport in scintillators: A theoretical study

Despite recent intensive study on scintillators, several fundamental questions on scintillator properties are still unknown. In this work, we use ab‐initio calculations to determine the energy dependent group velocity of the hot electrons from the electronic structures of several typical scintillators. Based on the calculated group velocities and optical phonon frequencies, a Monte‐Carlo simulation of hot electron transport in scintillators is carried out to calculate the thermalization time and diffusion range in selected scintillators. Our simulations provide physical insights on a recent trend of improved proportionality and light yield from mixed halide scintillators. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.