Search results for "Path integral formulation"
showing 10 items of 60 documents
Path integral method for first-passage probability determination of nonlinear systems under levy white noise
2015
In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path Integral technique. Comparison with pertinent Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Stochastic ship roll motion via path integral method
2010
ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …
Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses
1998
Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…
Quantum simulations in materials science: molecular monolayers and crystals
1999
Low temperature properties and anomalies in crystals and molecular monolayers are studied by path integral Monte Carlo (PIMC) simulations. For light particles (H 2 , D 2 ) adsorbed on graphite anomalies in the transition to the low temperature √3-phases have been observed in experiments and are analyzed by PIMC. The computed thermal expansion of various crystalline materials (Si, N 2 ) is in much better agreement with experiments compared to the results obtained with purely classical simulations.
Elastic Constants of Quantum Solids by Path Integral Simulations
2000
Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the (NVT) ensemble using an estimator for elastic constants. The other method is based on simulations in the (NpT) ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good agreement with …
Quantum effects on the herringbone ordering ofN2on graphite
1993
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
Gradual freezing of orientational degrees of freedom in cubicAr1−x(N2)xmixtures
1995
The mixed crystal ${\mathrm{Ar}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ is studied by Monte Carlo (MC) methods for x=0.33, 0.67, and 1.0 over a wide range of temperatures. For x=1 we find first-order transition from ordered cubic to disordered cubic, while for x=0.33 and x=0.67 we find broad nonuniform distribution functions of the local quadrupole Edwards-Anderson order parameter at low temperature. The short-range order of the quadrupolar mass distribution of the ${\mathrm{N}}_{2}$ molecules in the mixed systems is different from that observed in the pure ${\mathrm{N}}_{2}$ crystal, although the fcc symmetry has been chosen for the translational degrees…
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Simplicial Wheeler-DeWitt equation in 2+1 spacetime dimensions.
1993
We introduce an equation which rue suggest to be a simplicial counterpart to the Wheeler-DeWitt equation in 2 + 1 spacetime dimensions. Our approach is based on the use of the Ashtekar variables
A simple microsuperspace model in 2 + 1 spacetime dimensions
1992
Abstract We quantize the closed Friedmann model in 2 + 1 spacetime dimensions using euclidean path-integral approach and a simple microsuperspace model. A relationship between integration measure and operator ordering in the Wheeler-DeWitt equation is found within our model. Solutions to the Wheeler-DeWitt equation are exactly reproduced from the path integral using suitable integration contours in the complex plane.