Biomedical subjects

D M Ceperley

Publications and source records attributed to D M Ceperley.

12 recordsLinked to original sources

PubMed2005

Accurate, efficient, and simple forces computed with quantum Monte Carlo methods.

Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H(2), LiH, CH(4), NH(3), H(2)O, and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for diatomics are also in good agreement with experiment. An antithetical sampling method is also discussed for additional reduction of the variance.

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PubMed2004

Ring exchanges and the supersolid phase of 4He.

Using path integral Monte Carlo simulations we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is, have a nonclassical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be observed in a perfect 4He crystal.

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PubMed2003

Backflow correlations for the electron gas and metallic hydrogen.

We justify and evaluate backflow three-body wave functions for a two-component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wave functions are used in variational and diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-three-body wave functions lead to energies nearly as low as those from using local density approximation orbitals in the trial wave function. However, compared to wave functions constructed from density functional solutions, backflow wave functions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.

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PubMed2003

Superfluidity in a doped helium droplet.

Path-integral Monte Carlo calculations of the superfluid density throughout 4He droplets doped with linear impurities are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the cylindrically symmetric region of the first solvation layer. The helium in this region has a superfluid transition temperature similar to that of a two-dimensional helium system and may be responsible for previously unexplained experimental Q-branch measurements.

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PubMed2002

Spin polarization of the low-density three-dimensional electron gas.

To determine the state of spin polarization of the three-dimensional electron gas at very low densities and zero temperature, we calculate the energy versus spin polarization using diffusion quantum Monte Carlo methods with backflow wave functions and twist averaged boundary conditions. We find a second-order phase transition to a partially polarized phase at r(s) approximately 50+/-2. The magnetic transition temperature is estimated using an effective mean-field method, the Stoner model.

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PubMed2002

Bose-Einstein condensation at a helium surface.

A path integral Monte Carlo method was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0.77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9 before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. Finally, a surface dispersion relation was calculated from imaginary-time density-density correlations.

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PubMed2001

Calculation of a deuterium double shock Hugoniot from ab initio simulations.

We calculate the equation of state of dense deuterium with two ab initio simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < or = rho < or = 1.60 g cm(-3). We derive the double shock Hugoniot and compare with the recent laser-driven double shock wave experiments by Mostovych et al. [Phys. Rev. Lett. 85, 3870 (2000)]. We find excellent agreement between the two types of microscopic simulations, but a significant discrepancy with the laser-driven shock measurements.

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PubMed2001

Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms.

We develop and test Quantum Monte Carlo algorithms that use a"twist" or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy and has the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.

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PubMed2001

Path integral Monte Carlo simulation of the low-density hydrogen plasma.

Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of 9.83 x 10(-4)</=rho</=0.153 g cm(-3) and 5000</=T</=250 000 K. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral, and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.

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PubMed2001

Simulation of flux lines with columnar pins: bose glass and entangled liquids.

Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto interacting bosons in (2+1)D. With increasing temperatures we find first order melting from an ordered solid to an entangled liquid signaled by a finite entropy jump and sharp discontinuities of the defect density and the structure factor S(G). For a particular density of strong columnar pins the crystal is transformed into a Bose glass phase with patches of crystalline order disrupted by the trapped vortices at the pinning sites but with no overall positional or orientational order. This glassy phase melts into a defected entangled liquid through a continuous transition.

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PubMed2001

Exchange frequencies in the 2D Wigner crystal.

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.

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PubMed2001

Single and paired point defects in a 2D Wigner crystal.

Using the path-integral Monte Carlo method, we calculate the energy to form single and pair vacancies and interstitials in a two-dimensional Wigner crystal of electrons. We confirm that the lowest energy point defects of a 2D electron Wigner crystal are interstitials, with a creation energy roughly 2/3 that of a vacancy. The formation energy of the defects goes to zero at melting, suggesting that point defects may be the melting mechanism and that the melting could be a continuous transition. In addition, we find that the interaction between defects is strongly attractive, so that most defects will exist as bound pairs.

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