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costco cracker jacks boxes crack any serial number Supervisors: Prof. Mike Finnis (Physics/Materials, Imperial), Dr Eva-Maria Graefe (Mathematics, Imperial)
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2014 fifa world cup printable bracket Feynman's path-integral formulation of quantum mechanics establishes an isomorphism between a quantum particle and a ring of classical particles connected via harmonic springs: in the limit of infinite beads the ring reproduces the equilibrium statistical properties of the quantum particle exactly. This correspondence enables to calculate statistical quantities for quantum systems by means of techniques well known in classical mechanics, such as molecular dynamics or Monte Carlo methods, where the accuracy of the classical approximation improves with higher phase space dimensions. Recently these computational methods have been employed also to solve for non-equilibrium statistical mechanical properties of quantum systems, for example to study the diffusion of hydrogen in metals. While these calculations have so far yielded encouraging results, it is yet to be understood why this theory should work in the dynamical context and what is the error involved with using it in such cases. My project aims to answer these questions and to apply the insight gained on the theory to real-life simulations of hydrogen in iron.