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Jonathan Lloyd-WilliamsTheory of Condensed Matter GroupCavendish Laboratory 19, J. J. Thomson Avenue Cambridge CB3 0HE United Kingdom Email: jhl50 at cam.ac.uk Room: 545, Mott Building Tel: +44 (0)1223 337275 |
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I am an EPSRC funded PhD student working in the Theory of Condensed Matter (TCM) group in the Cavendish Laboratory at the University of Cambridge. My research is in the area of Quantum Monte Carlo (QMC) simulations of real materials. I am currently working on the further development of the Cambridge CASINO code and applying QMC techniques to a range of systems.
The term Quantum Monte Carlo refers to a large class of numerical algorithms that aim to solve the many-body Schrödinger equation using stochastic methods. QMC research is carried out in the TCM group using two particular algorithms, the so-called Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC) methods. VMC is a simple application of Monte Carlo integration to obtain the expectation value of the Hamiltonian of a system with respect to a given trial wave function. The variational principle guarantees that this expectation value is an upper bound of the ground-state energy of the system. One can also optimize the parameters of the trial wave function to minimize a given cost function (usually the energy or its variance), thus obtaining a more accurate description of the system. DMC is a more sophisticated method which solves the imaginary-time Schrödinger equation to project out the lowest-energy component of a trial wave function and in principle gives the exact ground state energy of the system.
Currently I am implementing a wave function for solid hydrogen in CASINO that fully takes into account the zero-point motion of the protons.
The Kinetic Monte Carlo (KMC) method is a stochastic technique used to simulate the time evolution of processes occurring in nature. Typically these are processes that occur at known rates which are given as inputs to the KMC algorithm. As part of my MSci project at Imperial College London working with Bartomeu Monserrat, Dimitri Vvedensky, and Andrew Zangwill, we carried out a KMC study of submonolayer epitaxial growth with a mobile intermediate cluster species, inspired by observations of graphene epitaxy on metals. We supposed that deposited atoms diffuse on the surface and collide to form four-atom clusters, or tetramers, which also diffuse on the surface, and that immobile islands are only formed upon the collision of a certain number of tetramers. Our model was able to qualitatively explain many of the findings of the graphene epitaxy study. For example, unlike all other growth scenarios, the density of atoms adsorbed on the surface at the onset of island nucleation was found to increase as a function of temperature when a large enough number of tetramers are needed to collide to form an immobile island.
Epitaxial kinetics with an intermediate polyatomic species
J. H. Lloyd-Williams, B. Monserrat, D. D. Vvedensky, and A. Zangwill
Phys. Rev. B 85, 161402(R) (2012)
A VMC study of the isotopologues of H2
and H2+
Theory of Condensed Matter Group, University of Cambridge, UK.
April 24th 2013
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