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The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a…
Simulating radiative transfer in the atmosphere with Monte Carlo ray tracing provides realistic surface irradiance in cloud-resolving models. However, Monte Carlo methods are computationally expensive because large sampling budgets are…
Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly…
A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model…
Effects of geometrical frustration and quantum fluctuation are theoretically investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded system, squaric acid crystal. We elucidate the phase diagram for an effective…
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
We present an efficient and exact Monte Carlo algorithm to simulate reversible aggregation of particles with dedicated binding sites. This method introduces a novel data structure of dynamic bond tree to record clusters and sequences of…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
We adapt the Quantum Monte Carlo method to the cascaded formalism of quantum optics, allowing us to simulate the emission of photons of known energy. Statistical processing of the photon clicks thus collected agrees with the theory of…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference…
We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their…
Quantum Monte Carlo (QMC) methods can very accurately compute ground state properties of quantum systems. We applied these methods to a system of boson hard spheres to get exact, infinite system size results for the ground state at several…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance…
Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms…
This work is motivated by the need to develop efficient tools for uncertainty quantification in subsurface flows associated with radioactive waste disposal studies. We consider single phase flow problems in random porous media described by…
We propose a new generalized-ensemble algorithm, which we refer to as the multibaric-multithermal Monte Carlo method. The multibaric-multithermal Monte Carlo simulations perform random walks widely both in volume space and in potential…
In this article, we present a method for computing accurate and scalable nuclear forces within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) framework. Our approach leverages automatic differentiation of the energy functional to…