We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation describing the system’s evolution on slow time scales. For this purpose, we start from the corresponding path integral representation of the stochastic system...

The internal energy of high-density hydrogen plasmas in the temperature range T = 10, 000 . . . 50, 000K is calculated by two different analytical approximation schemes (method of effective ion-ion interaction potential EIIP and Padé approach within the chemical picture PACH) and compared with path integral Monte Carlo results. Reasonable agreement between the results obtained from the three in...

Atomically thin 4 He lms of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T=0.5 K, using path integral Monte Carlo. We compute the binding energy of 4 He to the H 2 substrate as a function of 4 He coverage and obtain evidence of the prewetting transition. Density pro les perpendicular to the 4 He-H 2 interface are obtained, as well as the zero point motion and e e...

We report path-integral Monte Carlo calculations of the kinetic energy of condensed lithium for several temperatures in both the solid and liquid phases. The excess kinetic energy of lithium decreases from about 10.4% of the classical value at 300 K to 3.2% at 520 K indicating a very slow decay with temperature. A Wigner-Kirkwood perturbation treatment of quantum effects to order \ gives a sati...

Path-integral Monte Carlo simulations of liquid helium at negative pressure have been carried out for a temperature range from the critical temperature to below the superfluid transition. We have calculated the temperature dependence of the spinodal line as well as the pressure dependence of the isothermal sound velocity in the region of the spinodal. We discuss the slope of the superfluid tran...

The (1,1,1)-surfaces of bulk solid molecular hydrogen have been studied at temperatures between 0.5K and 1.3K, using path integral Monte Carlo. A general method is introduced for constructing an external potential to represent the tail correction for an arbitrary heterogeneous layered bulk substrate-adsorbate system. We compute density pro les parallel and perpendicular to the free H 2 surface,...

Previous heat capacity estimators useful in path integral simulations have variances that grow with the number of path variables included. In the present work a new specific heat estimator for Fourier path integral Monte Carlo simulations is derived using methods similar to those used in developing virial energy estimators. The resulting heat capacity estimator has a variance that is roughly in...

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between 10 −1 and 10 2 Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. C...

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouville operator in the sense of the norm. Spectral Galerkin and Petrov-Galerkin methods for tempered fractional advection problems and tempered ...

The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values, A specific numerical scheme is presented for antiplane strain problems and a numerical example is given,