Related papers: Path integral Monte Carlo ground state approach: F…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We present a novel Exchange Monte Carlo (EMC) method designed for application in continuous-space Path Integral Monte Carlo (PIMC) simulations at finite temperature. Traditional PIMC methods for bosonic systems suffer from long…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feyman-Kac path integral and can be estimated using Monte Carlo sampling. In this contribution we review path…
Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate…
The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…
We describe a path-integral ground-state quantum Monte Carlo method for light nuclei in continuous space. We show how to efficiently update and sample the paths with spin-isospin dependent and spin-orbit interactions. We apply the method to…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed…
We present in detail a formulation of the shell model as a path integral and Monte Carlo techniques for its evaluation. The formulation, which linearizes the two-body interaction by an auxiliary field, is quite general, both in the form of…
We carry out highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) simulations to directly estimate the free energy of various warm dense matter systems including the uniform electron gas and hydrogen without any nodal…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis…
Thermodynamics of dissipative quantum systems with double-well potentials is studied by the path-integral Monte Carlo (PIMC) method without truncation to the two-state model. For efficient simulation at low temperatures, we develop a new…
Ground state properties of condensed Helium are calculated using the Path Integral Ground State (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other…
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the epxerimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high…
We investigate the thermal expansion of crystalline SiO$_2$ in the $\beta$-- cristobalite and the $\beta$-quartz structure with path integral Monte Carlo (PIMC) techniques. This simulation method allows to treat low-temperature quantum…
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
We have simulated the ground states of quantum harmonic oscillators driven either by constant forces of different magnitudes or time-dependent driving forces. The expectation values of position for various combinations of mass, natural…
With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are…