Résultats de recherche pour « Monte Carlo methods »

We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling, the kinetic equation converges to an advection-diffusion equation in the limit of zero mean free path. Classical particle-based techniques suffer from a strict time-step restriction to maintain stability in this limit. Asymptotic-preserving schemes provide a solution to this time step restriction, but introduce a first-order error in the time step size. We demonstrate how the multilevel Monte Carlo method can be used as a bias reduction technique to perform accurate simulations in the diffusive regime, while leveraging the reduced simulation cost given by the asymptotic-preserving scheme. We describe how to achieve the necessary correlation between simulation paths at different levels and demonstrate the potential of the approach via numerical experiments.

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayesian analysis of imaginary time correlation functions.

We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis. The MC Hamiltonian allows to obtain energies and wave functions of low-lying states. It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero). We present examples from lattice field theory (Klein-Gordon model).

Monte Carlo event generators (MCEGs) are the indispensable workhorses of particle physics, bridging the gap between theoretical ideas and first-principles calculations on the one hand, and the complex detector signatures and data of the experimental community on the other hand. All collider physics experiments are dependent on simulated events by MCEG codes such as Herwig, Pythia, Sherpa, POWHEG, and MG5_aMC@NLO to design and tune their detectors and analysis strategies. The development of MCEGs is overwhelmingly driven by a vibrant community of academics at European Universities, who also train the next generations of particle phenomenologists. The new challenges posed by possible future collider-based experiments and the fact that the first analyses at Run II of the LHC are now frequently limited by theory uncertainties urge the community to invest into further theoretical and technical improvements of these essential tools. In this short contribution to the European Strategy Update, we briefly review the state of the art, and the further developments that will be needed to meet the challenges of the next generation.

In the last few years we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer (BO) approximation, the Coupled Electron-Ion Monte Carlo Method (CEIMC). Electronic properties in CEIMC are computed by Quantum Monte Carlo (QMC) rather than by Density Functional Theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT based ab initio dynamical methods. Application of the new method to high pressure metallic hydrogen has recently appeared. In this paper we present a new sampling algorithm that we have developed in the framework of the Reptation Quantum Monte Carlo (RQMC) method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show here that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.