Search results for "Path Integral"
showing 10 items of 80 documents
Correction: “On-the-fly” coupled cluster path-integral molecular dynamics: impact of nuclear quantum effects on the protonated water dimer
2015
We present an accelerated ab initio path-integral molecular dynamics technique, where the interatomic forces are calculated “on-the-fly” by accurate coupled cluster electronic structure calculations. In this way not only dynamic electron correlation, but also the harmonic and anharmonic zero-point energy, as well as tunneling effects are explicitly taken into account. This method thus allows for very precise finite temperature quantum molecular dynamics simulations. The predictive power of this novel approach is illustrated on the example of the protonated water dimer, where the impact of nuclear quantum effects on its structure and the 1H magnetic shielding tensor are discussed in detail.
Nuclear quantum effects in liquid water from path-integral simulations using anab initioforce-matching approach
2014
We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterized by force-matching to density functional theory-based molecular dynamics simulations. The resulting effective potentials provide an inexpensive replacement for direct ab inito molecular dynamics simulations and allow efficient simulation of nuclear quantum effects. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals…
Rollio delle navi in presenza di onde modellate come processi gaussiani e poissoniani agenti simultaneamente.
2008
Obiettivo del presente lavoro è l’estensione del metodo della path integral solution (PIS) per lo studio della dinamica del rollio delle navi in presenza di onde modellate come processi gaussiani e poissionani agenti simultaneamente. Si è proceduto dapprima a mostrare come la PIS consenta di valutare l’evoluzione temporale della funzione densità di probabilità (PDF) del processo di risposta, applicando il metodo ad equazioni differenziali stocastiche soggette a forzanti esterne gaussiane e poissoniane. Successivamente si è trattato il caso di un sistema non lineare soggetto ad entrambi i rumori gaussiano e poissoniano agenti contestualmente. Si è infine affrontato sia analiticamente che num…
Nucleon and delta masses in QCD
1992
Using the positivity of the path integral measure of $QCD$ and defining a structure for the quark propagator in a background field according to the fluxon scenario for confinement, we calculate and compare the correlators for nucleon and delta. From their shape we elucidate about the origin of their mass difference, which in our simplified scenario is due to the tensor structure in the propagator. This term arises due to a dynamical mechanism which is responsible simultaneously for confinement and spontaneous chiral symmetry breaking. Finally we discuss, by comparing the calculated correlators with the Lehmann representation, the possibility that a strong CP and/or P violation occurs as a c…
On new efficient algorithms for PIMC and PIMD
2002
Abstract The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number P . A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with P . Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propaga…
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.
An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems
2015
The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…
Direct Evaluation of Path Integrals
2001
Every time τ n is assigned a point y n . We now connect the individual points with a classical path y(τ). y(τ) is not necessarily the (on-shell trajectory) extremum of the classical action. It can be any path between τ n and τn−1 specified by the classical Lagrangian \(L(y,\dot{y},t).\)
First-passage problem for nonlinear systems under Lévy white noise through path integral method
2016
In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
2002
Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method, originally proposed by Takahashi and Imada, is based on a higher-order approximation (HOA) of the quantum mechanical density operator. The other method is based upon an effective propagator (EPr). This propagator is constructed such that it produces correctly one and two-particle imaginary time correlation functions in the limit of small densities even for finite Trotter numbers P. We discuss the conceptual differences between both methods and compare the convergence rate of both approaches. While th…