Related papers: A Monte Carlo method for solving the NEGF equation…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
Monte Carlo simulations are performed to study the in-plane transport of spin-polarized electrons in III-V semiconductor quantum wells. The density matrix description of the spin polarization is incorporated in the simulation algorithm. The…
We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…
The diffusion quantum Monte Carlo method is extended to solve the old theoretical physics problem of many-electron atoms and ions in intense magnetic fields. The feature of our approach is the use of adiabatic approximation wave functions…
We explore a self-learning Markov chain Monte Carlo method based on the Adversarial Non-linear Independent Components Estimation Monte Carlo, which utilizes generative models and artificial neural networks. We apply this method to the…
We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
Experimental studies on two-dimensional (2D) materials are still in the early stages, and most of the theoretical studies performed to screen these materials are limited to the room-temperature carrier-mobility in the free standing 2D…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
Here we present the derivation, description and results of a Monte Carlo-based algorithm for simulating inelastic scattering of photo-electrons when passing through some scattering medium, such as a gas atmosphere or a solid material. The…
Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using…
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods…
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
An effective mass based model accounting for the conduction band quantization in a high aspect ratio semiconductor nanotip is developed to describe injected electron transport and subsequent electron emission from the nanotip. A transfer…
In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest…