Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.     

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.     

Exact treatment of exciton-polaron formation by diagrammatic Monte Carlo simulations

We develop an approximation-free diagrammatic Monte Carlo technique to study fermionic particles interacting with each other simultaneously through both an attractive Coulomb potential and bosonic excitations of the underlying medium. Exemplarily we apply the method to the long-standing exciton-polaron problem and present numerically exact results for the wave function, ground-state energy, binding energy and effective mass of this quasiparticle. Focusing on the electron-hole pair bound-state formation, we discuss various limiting cases of a generic exciton-polaron model. The frequently used instantaneous approximation to the retarded interaction due to the exchange of phonons is found to be of very limited applicability.     

The non-Markovian quantum behavior of open systems

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo wave function method that enables the stochastic treatment of the full non-Markovian behavior of open quantum systems. Numerical simulations are carried out which demonstrate that the method is applicable to open systems strongly coupled to a bosonic reservoir, as well as to the interaction with a spin bath. Full details of the simulation algorithms are given, together with an investigation of the dynamics of fluctuations. Several potential generalizations of the method are outlined.Received: 29 October 2003, Published online: 10 February 2004PACS: 03.65.Yz Decoherence; open systems; quantum statistical methods - 02.70.Ss Quantum Monte Carlo methods - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)     

The potential curve of the He-α-quartz surface interaction

One of the fundamental problems for gas-surface interaction physics is to relate the pairwise gas atom-surface atom interaction characteristics to that of the aggregate collision complex. One method of studying the problem on a microscopic scale is to model the surface lattice structure and calculate the interaction characteristics using the Monte Carlo technique. We describe the calculation of the He-α-quartz (SiO₂) interaction potential applying this method assuming pairwise He-surface atom Lennard-Jones (12, 6) potentials. The results show that the interaction potential follows a (13.5, 3.8) shape function in the gas-surface interaction range below 8 Å, and an asymptotic dependence with 3.8 < m < 6 for the region beyond 8 Å. This potential well shape function differs substantially from the (9, 3) function suggested by earlier work. The calculated potential curve shows a weak dependence on surface and gas temperature. The potential well depth of the gas-surface interaction shows a strong nonlinear relationship to the equilibrium internuclear distance of the HeSi pair potential applied to the calculation. We find that the empirically determined parameters for the HeSi pair potential provide resultant gas-surface potentials with well depth remarkably close to those required by the measured heat of adsorption.     

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.     

Pair correlations of an expanding superfluid Fermi gas

The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.     

The structure of the water dimer

A previously reported self consistent approximation for the pair distribution function is applied to inverse power potentials. Results are reported for the first six virial coefficients over the full range of such potentials. The thermodynamic properties and pair distributions functions are presented for the inverse sixth and twelfth power potentials and are shown to be in close agreement with the results of molecular dynamics and Monte Carlo calculations.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Relaxation kinetics of primary pairs of radiation defects in ionic crystals

The relaxation kinetics of primary pairs of radiation defects in ionic crystals with a face-centered lattice is investigated using the Monte Carlo method. The dependence of the relaxation kinetics of an F-H pair on the parameters of the interaction potential between the components of the pair is studied. The obtained kinetic dependences are analyzed to determine the factors responsible for the relaxation processes.     

Pair correlation functions obtained from very short structure factors,using Reverse Monte Carlo

Acta Physica Hungarica - It is shown that the Reverse Monte Carlo method [5] is able to provide the correct pair correlation function even if the structure factor is available over only very...     

The Fisher-Widom line for systems with low melting temperature

We present Monte Carlo results for the pair distribution function of three simple fluid models, with pairwise interactions, which have low triple point temperatures and mimic some aspects of Na and Hg liquid metals. The results are then used to get the direct correlation function, by numerical solution of the Ornstein-Zernike equation, and to characterize the decay modes of any density distribution towards the bulk fluid. The Fisher-Widom line is obtained from the crossing of the two lowest inverse decay lengths, associated to monotonic and to oscillatory decay modes. For the pair potential models with a soft repulsive core, the Fisher-Widom line appears well below the critical temperature and has positive slope of the temperature with respect to the density, contrary to previous results for the Lennard-Jones and square-well potentials which had located that line quite close to T _c and with negative slope.     

Computation of the effective potential for the two-dimensionalO(N) nonlinear σ-models

A Monte Carlo method for the computation of effective Hamiltonians for theO(N) nonlinear lattice σ-models is described. The procedure is based on simulations of auxiliary statistical mechanical systems with fixed block spins and thus avoids the simulation of systems with large correlation length. The method is applied to study the renormalization group flow of the effective potential for the Ising model, the XY model, and the Heisenberg ferromagnet in two dimensions. Some of the results are compared with second order high temperature expansions. For small block size a very good agreement is found in a large range of the inverse temperature β.     

High-pressure equation of state for solid krypton from interatomic potentials

The pressure-volume isotherm for krypton at 300 K is evaluated by the Monte Carlo method using pair and three-body potentials. The pair potentials used are that of Aziz and Slaman and a slightly modified version of their potential which gives better agreement with high-energy scattering data. The three-body potentials considered are the Axilrod-Teller interaction and the first-order three-body exchange interaction as parametrized by Loubeyre. The results are compared with recent measurements at pressures up to 300 kbar and the implications of the comparison are discussed. The best agreement with experiment is found using the Axilrod-Teller interaction as the only many-body interaction, indicating that the three-body exchange interaction is to a large extent canceled by higher many-body interactions, at least in the highly symmetrical environment of the crystal.This paper is dedicted to Howard Reiss on the occasion of his 66th birthday.     

An accurate equation of state of a hard convex body fluid mixture

A method enabling to calculate the contact-point values of the pair correlation function of convex body fluids from a semi-empirical equation of state is presented and the accurate Nezbeda equation of the pure hard convex body fluid is extended to mixtures. Comparison of results for one- and two-component systems with Monte Carlo simulation data shows excellent agreement.     

Stimulation of vapor nucleation on perfect and imperfect hexagonal lattice surfaces

Monte Carlo simulations of water vapor nucleation on a perfect crystal surface and on a surface with defects are performed. Mass exchange with the vapor phase is modeled by using an open ensemble. Cluster-substrate interaction is described in terms of conventional atom-atom potentials. The Hamiltonian of the system includes expressions for electrostatic, polarization, exchange, and dispersion interactions. The Gibbs free energy and work of adsorption are calculated by Monte Carlo simulation in the bicano?nical ensemble. The microscopic structure of nuclei is analyzed in terms of pair correlation functions. Periodic boundary conditions are used to simulate an infinite substrate surface. Molecule-substrate and molecule-molecule long-range electrostatic interactions are calculated by summing the Fourier harmonics of the electrostatic potential. Dispersion interactions are calculated by direct summation over layers of unit cells. Nucleation on a surface with matching structure follows a layer-by-layer mechanism. The work of adsorption per molecule of a monolayer on the substrate surface has a maximum as a function of nucleus size. The steady rate of nucleation of islands of supercritical size is evaluated. The work of adsorption per molecule for layer-by-layer film growth is an oscillating function of cluster size. As a function of layer number, it has a minimum depending on the vapor pressure. The electric field generated by a microscopic surface protrusion destroys the layered structure of the condensate and eliminates free-energy nucleation barriers. However, point lattice defects do not stimulate explosive nucleation.     

A simple effective pair potential for the molecular simulation of the thermodynamic properties of ammonia

A new optimized effective pair potential model is proposed, which is appropriate for the prediction of thermodynamic properties of fluid ammonia including vapour—liquid coexistence data. The phase behaviour is determined using a recently developed version of the Gibbs ensemble Monte Carlo method. Furthermore, liquid structure characteristics, the dielectric constant and supercritical properties are determined by Monte Carlo simulations in the isothermal—isobaric ensemble. The second virial coefficient of the pair potential model is calculated over a broad range of temperature. All properties are compared with experimental data or results of a multi-parameter equation of state for ammonia. The new model is found to yield coexistence properties and second virial coefficients in good agreement with experimental data and the results of the equation of state, respectively.     

Tensor optimized antisymmetrized molecular dynamics for relativistic nuclear matter

We apply a newly developed many-body theory, tensor optimized antisymmetrized molecular dynamics (TOAMD), to nuclear matter using a relativistic bare nucleon-nucleon interaction in the relativistic framework. It becomes evident that the tensor interaction plays an important role in nuclear many-body system due to the role of the pion in a strongly interacting system. We take the relativistic nuclear matter (RNM) wave function as a basic state and add tensor and short-range correlation operators in the form of pion and omega-meson correlation functions acting on the RNM wave function using the concept of TOAMD. We use the Monte Carlo (Metropolis) method based on the Gaussian integration and the second quantization method for antisymmetrization to calculate all the matrix elements of the many-body Hamiltonian. We write the whole formula of the TOAMD method for numerical calculations of the nuclear binding and saturation properties of nuclear matter using one-boson exchange potential.     

The convergence of chaotic integrals

We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential. (c) 1997 American Institute of Physics.     

Correlation properties of FeAs-based superconductors: Quantum trajectory Monte Carlo method

Pair correlation functions for two-dimensional FeAs clusters simulating iron-based superconductors have been calculated with the generalized quantum Monte Carlo algorithm within the full two-orbital model. The data obtained for clusters with dimensions up to 10 × 10 FeAs cells indicate the possibility of the effective attraction of charge carriers, which corresponds to symmetry A _1g , at certain interaction parameters. The dependences of pair correlations on the dimension of a cluster, temperature, interaction magnitude, and type of symmetry of the order parameter have been analyzed.