Permutation blocking path integral Monte Carlo simulations of degenerate electrons at finite temperature

We analyse the simulation of strongly degenerate electrons at finite temperature using the recently introduced permutation blocking path integral Monte Carlo (PB‐PIMC) method [T. Dornheim et al., New J. Phys. 17 , 073017 (2015)]. As a representative example, we consider electrons in a harmonic confinement and carry out simulations for up to P = 2000 so‐called imaginary‐time propagators – an important convergence parameter within the PIMC formalism. This allows us to study the P‐dependence of different observables of the configuration space in the Monte Carlo simulations and of the fermion sign problem. We find a surprisingly persisting effect of the permutation blocking for large P, which is explained by comparing different length scales. Finally, we touch upon the uniform electron gas in the warm dense matter regime.     

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.     

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.     

Kirkwood–Buff integrals of finite systems: shape effects

The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.     

Shear viscosity of pseudo hard-spheres

We present molecular dynamics simulations of pseudo hard sphere fluid (generalized WCA potential with exponents (50, 49) proposed by Jover et al. [J. Chem. Phys 137, (2012)] using GROMACS package. The equation of state and radial distribution functions at contact are obtained from simulations and compared to the available theory of true hard spheres (HS) and available data on pseudo hard spheres. The comparison shows agreements with data by Jover et al. and the Carnahan–Starling equation of HS. The shear viscosity is obtained from the simulations and compared to the Enskog expression and previous HS simulations. It is demonstrated that the PHS potential reproduces the HS shear viscosity accurately.     

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in ?001? by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)] we calculate the cross-coupling term between elastic field due to gravity and that due to a Shockley partial dislocation. The cross-term is an increasing function of the linear dimension R over which the elastic field expands, showing that a driving force arises for the partial dislocation moving toward the upper boundary of a grain.     

An efficientmethod to determine chemical potential of mixtures in the isothermal and isobaric bulk phase with kineticMonte Carlo simulation

A kinetic Monte Carlo (kMC) scheme in the NPT ensemble (constant number of molecules, pressure and temperature) has been developed to determine accurate chemical potentials for all components in a homogeneous mixture. The simulation requires two moves: (1) a displacement move and (2) a volume change move. In the former, the mobility rate of a selected molecule is determined by its interaction with all the other molecules in the system and is moved to a random position within the simulation box, according to the Rosenbluth algorithm, without any rejections (entropic sampling). The volume change move is decided by a comparison between either the instant pressure or the partial average pressure (with long-range correction) and the specified pressure and is carried out much less frequently than the displacement move. We applied this NPT scheme to a number of mixtures in both the gaseous and liquid phases, and show that the derived chemical potentials are accurate and reproducible. The method is recommended for obtaining chemical potentials in mixtures that are required as input in a grand canonical ensemble simulation.     

Rovibrational laser control targeting a dark state in acetylene. Simulation in the Ns = 1, Nr = 5 polyad

Optimal control theory in the Liouville space is used to perform rovibrational control by means of a laser pulse in a polyad of acetylene in order to populate a dark vibrational state. The initial mixed state is a truncated Boltzmann distribution of rotational levels from J=27 to J=31 of the ground vibrational state. The target state is a rotational equidistribution of levels ranging from J=28 to J=32 of the first excited vibrational dark state including quanta of energy in each bending modes, with positive vibrational angular momenta. The simulation is performed by using a manifold of eigenstates of a full-dimensional Hamiltonian calibrated by high precision spectroscopy known as the global acetylene Hamiltonian [B. Amyay et al., J. Chem. Phys. 131, 114301 (2009)]. The control is successful as an Uhlmann's fidelity of 0.98 is reached.     

Efficient determination of Hugoniot states using classical molecular simulation techniques

We present a methodology for the efficient calculation of the shock Hugoniot using standard molecular simulation techniques. The method is an extension of an equation of state methodology proposed by Erpenbeck [1992, Phys. Rev. A, 46, 6406] and is considered as an alternative to other methods that generate Hugoniot properties. We illustrate the methodology for shocked liquid N₂ using two different simulation methods: (a) the reactive Monte Carlo method for a reactive system; and (b) the molecular dynamics method for a non-reactive system. The method is shown to be accurate, stable and generally independent of the algorithm parameters. We find excellent agreement with results calculated by other previous simulation studies. The results show that the methodology provides a simulation tool capable of determining points on the shock Hugoniot from a single simulation in an efficient, straightforward manner. Further applications and extensions of the method are briefly discussed.     

A hierarchically constrained kinetic Ising model

A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric kinetic constraint, allowing a spin to flip only if its neighbour to the right is in the up spin state. The spin autocorrelation function is obtained by numerically exact calculation for finite chain length up toL=9 and by Monte Carlo simulation for effectively infinite chain length. The Kohlrausch-Williams-Watts formula is found to fit the results only with limited accuracy, and within limited time intervals. We also performed an analytical calculation using an effective-medium approximation. The approximation leads to a spurious blocking transition at a critical up spin concentrationc=0.5.     

Recoil growth algorithm for chain molecules with continuous interactions

The recoil growth (RG) scheme is a dynamic Monte Carlo algorithm that has been suggested as an improvement over the configurational bias Monte Carlo (CBMC) method (Consta, S., Wilding, N. B., Frenkel, D. and Alexandrowicz, Z., 1999, J. chem. Phys., 110, 3220). The RG method had originally been tested for hard core polymers on a lattice, and it was found that RG outperforms CBMC for dense systems and long chain molecules. In the present paper, the RG scheme is extended to the practically more relevant case of off-lattice chain molecules with continuous interactions. It is found that for longer chain molecules RG becomes over an order of magnitude more efficient than CBMC. However, other schemes are better suited to the computation of the excess chemical potential. Moreover, it is more difficult to parallelize RG than CBMC.     

Simulation of MCAO on (extremely) large telescopes

In this article, we describe the different methods to simulate Multi-Conjugate Adaptive Optics (MCAO) systems. First, analytical (error-budget type) and semi-analytical (Fourier) methods are described. We then describe the different modules required to make end-to-end (Monte Carlo) simulations of these systems. Finally, we present some of the computational challenges associated with the simulation of MCAO on Extremely Large Telescopes (ELTs). To cite this article: M. Le Louarn et al., C. R. Physique 6 (2005).     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

Virial-bias Monte Carlo methods

A new sampling technique is proposed for the isothermal-isobaric (T, P, N) ensemble Monte Carlo computer simulation. The new method selects the volume perturbations by using the partial derivative of the volume with respect to the internal energy. Test calculations on the Lennard-Jones fluid show significant improvements over the conventionally used method.     

Lattice simulations for light nuclei: Chiral effective field theory at leading order

We discuss lattice simulations of light nuclei at leading order in the chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.     

Distribution of the conductance of a linear chain of tunnel barriers with fractal disorder

Distributions of the conductance G of a long quantum wire with the fractal distribution of barriers have been obtained in the successive incoherent tunneling regime. The asymptotic behavior (in the limit L → ∞) of moments 〈G ^k (L)〉, average power of the shot noise 〈S(L)〉, and Fano factor agree with the results of the work [C. W. J. Beenakker et al., Phys. Rev. B 79, 024204 (2009)], and the distributions themselves describe well the Monte Carlo simulation results. The equation that has been obtained for the distributions of the resistance and conductance agrees with the recent fractional differential generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the quasi-one-dimensional multichannel disordered semiconductors with a self-similar distribution of scatterers.     

Electron density characteristics and charge transfer effect of hydrogen bond O–H···Pt(II): atoms in molecules study and natural bond orbital analysis

In this report, we extended the works of Rizzato et al. [Angew. Chem. Int. Ed. 49, 7440 (2010)] on the nature of O–H···Pt hydrogen bond in trans-[PtCl₂(NH₃)(N–glycine)]·H₂O(1·H₂O) complex, by computational study of O–H···Pt interaction in [NBu₄][Pt(C₆F₅)₃(8-hydroxyquinaldine)], with emphasis on charge transfer effect in this interaction of platinum(II) and hydrogen atom. According to the crystallographic geometry reported by José María Casas et al., [NBu₄][Pt(C₆F₅)₃(8-hydroxyquinaldine)] possesses one O–H···Pt hydrogen bridging interaction, similar to the case in trans-[PtCl₂(NH₃)(N–glycine)]·H₂O(1·H₂O) complex. On the basis of topological criteria of electron density, we characterised this O–H···Pt interaction. Charge transferred between platinum(II) and σ^*_O–H orbital in this complex was calculated by using NBO method. The stabilised energy associated to charge transfer was estimated using a direct proportionality, that is 2–3 eV per electron transferred. Charge transfer effects in O–H···Pt hydrogen bonds were studied for these two complexes. Our results indicate that the interaction of O–H···Pt is closed–shell in nature with significant charge transfer, and that charge transfer effect is not negligible in the interaction of O–H···Pt. The second conclusion is different from the result of Rizzato et al.     

Direct molecular-level Monte Carlo simulation of Joule—Thomson processes

We present an application of the recently developed constant enthalpy-constant pressure Monte Carlo method [SMITH, W. R., and LÍSAL, M., 2002, Phys. Rev. E, 66, 01114] for the direct simulation of Joule-Thomson expansion processes using a molecular-level system model. For the alternative refrigerant HFC-32 (CH_{2F 2}), we perform direct simulations of the isenthalpic integral Joule-Thomson effect (temperature drop) resulting from Joule-Thomson expansion from an initial pressure to the representative final pressure of 1 bar. We consider representative expansions from single-phase states yielding final states in both single-phase and two-phase regions. We also predict the dependence of T(P, h) and of the Joule-Thomson coefficient, μ (P, h), on pressure along several representative isenthalps, as well as points on the Joule-Thomson inversion curve. HFC-32 is modelled using a five-site potential taken from the literature, with parameters derived from ab initio calculations and vapour-liquid equilibrium data. The simulated results show excellent agreement with those calculated from an international standard equation of state.     

Risk analysis in investment appraisal based on the Monte Carlo simulation technique by A. Hacura, M. Jadamus-Hacura and A. Kocot

Comment on Eur. Phys. J. B 20, 551 (2001) Since Hertz major work on investment appraisal using the Monte Carlo Simulation technique, the so called “Risk Analysis” has become a standard tool for supporting investment decisions [1,2]. A main problem in investment appraisal is to consider and specify the risk of investment projects in an appropriate way, for enabling consistent project evaluation. In calculating a risky project's net present value (NPV) the major difficulty is to quantify the project's risk for quantifying an appropriate risk adjusted discount rate (RADR). Theoretically not founded risk adjusted discount rates face a lot of critique. Furthermore it is discussed that the incorporation of a constant risk factor into the discount rate makes a certain assumption about the resolution of uncertainty over time [3] and finally that a single net present value could not in general reflect risk properly. Especially in consequence of the last point the proponents of simulation argue that a whole distribution of net present values shows a project's risk better than a single number. In the special issue “Econophysics” of this journal Hacura et al. tried to describe the methodology and use of Monte Carlo Simulation in investment appraisal [4]. The purpose of this comment is to point out three fundamental flaws in that article. Received 29 April 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: robert.obermaier@wiwi.uni-regensburg.de