| Summary: | The state of a deformed crystal is highly heterogeneous, with plasticity localised into linear and point defects such as dislocations, vacancies and interstitial clusters. The motion of these defects dictate a crystal's mechanical behaviour, but defect dynamics are complicated and correlated by external applied stresses, internal elastic interactions and the fundamentally stochastic influence of thermal vibrations. This thesis is concerned with establishing a rigorous, modern theory of the stochastic and dissipative forces on crystal defects, which remain poorly understood despite their importance in any temperature dependent micro-structural process such as the ductile to brittle transition and irradiation damage. From novel molecular dynamics simulations we parametrise an efficient, stochastic and discrete dislocation model that allows access to experimental time and length scales. Simulated trajectories of thermally activated dislocation motion are in excellent agreement with those measured experimentally. Despite these successes in coarse graining, we find existing theories unable to explain stochastic defect dynamics. To resolve this, we define crystal defects through projection operators, without any recourse to elasticity. By rigorous dimensional reduction we derive explicit analytical forms for the stochastic forces acting on crystal defects, allowing new quantitative insight into the role of thermal fluctuations in crystal plasticity.
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