Accurate momentum distributions from computations on 3He and 4He
01 Nov 1987-Canadian Journal of Physics (NRC Research Press Ottawa, Canada)-Vol. 65, Iss: 11, pp 1409-1415
TL;DR: In this paper, the momentum distribution and condensate fraction of liquid and solid 4He determined from Green's function Monte Carlo calculations using the HFDHE2 pair potential are described.
Abstract: The momentum distribution and condensate fraction of liquid and solid 4He determined from Green's function Monte Carlo calculations using the HFDHE2 pair potential are described. The one-body density matrix and the momentum distribution for liquid 3He derived from variational and fixed-node Green's function Monte Carlo calculations are also reported.
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TL;DR: In this paper, the authors introduce a picture of a boson superfluid and show how superfluidity and Bose condensation manifest themselves, showing the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution.
Abstract: One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.
1,908 citations
TL;DR: In this article, the authors present a review of the theoretical issues and numerical techniques used to describe dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties.
134 citations
TL;DR: In this article, the self-consistency between the ladders and the self energy is established for the quasi-particle energy, and a careful study of the complete momentum and energy dependence of the resulting self-energy is made for various densities.
109 citations
TL;DR: This simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.
Abstract: The formation of a superfluid when 4He is cooled below the characteristic lambda transition temperature is accompanied by intricate quantum mechanical phenomena, including the emergence of a Bose condensate. A combination of path integral and semiclassical techniques is used to calculate the single-particle velocity autocorrelation function across the normal-to-superfluid transition. We find that the inclusion of particle exchange alters qualitatively the shape of the correlation function below the characteristic transition temperature but has no noticeable effect on the dynamics in the normal phase. The incoherent structure factor extracted from the velocity autocorrelation function is in very good agreement with neutron scattering data, reproducing the width, height, frequency shift, and asymmetry of the curves, as well as the observed increase in peak height characteristic of the superfluid phase. Our simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.
62 citations
TL;DR: In this paper, a self-consistent Green function approach for the many-body theory of interacting fermions is presented and its application to nuclear systems is presented. But the authors focus on the consistent inclusion of short-range and long-range correlations induced by realistic nucleon-nucleon interactions.
Abstract: Recent developments in the many-body theory of interacting fermions are discussed employing a self-consistent Green function approach. This scheme is outlined and its application to nuclear systems is presented. Special attention is paid to the consistent inclusion of short-range and long-range correlations induced by realistic nucleon-nucleon interactions. Such correlations lead to occupation probabilities which deviate from the simple mean-field or shell-model description. The scheme is extended to incorporate relativistic effects. Also applications of field theoretical models for hadrons in a nuclear medium and their relation to QCD are discussed.
57 citations
References
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Book•
01 Jan 1979
TL;DR: This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods.
Abstract: This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods. The material covered includes methods for both equilibrium and out of equilibrium systems, and common algorithms like the Metropolis and heat-bath algorithms are discussed in detail, as well as more sophisticated ones such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering. Data analysis techniques are also explained starting with straightforward measurement and error-estimation techniques and progressing to topics such as the single and multiple histogram methods and finite size scaling. The last few chapters of the book are devoted to implementation issues, including discussions of such topics as lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. At the end of the book the authors give a number of example programmes demonstrating the applications of these techniques to a variety of well-known models.
2,765 citations