The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These properties are determined by three complementary methods. One approach is via the time-integration of the velocity autocorrelation function. The second is via the mean-squared-displacement of thermal wavepackets subject to stochastic collapse via Lindblad jump operators. These two methods are applicable in the high-temperature regime, where the noise is temporally uncorrelated. In this regime the noise causes particle localization and the transport is diffusive. The third approach -- applicable in the low-temperature regime -- is weak-coupling Redfield theory. Here, static disorder causes particle localization. When the dynamics is diffusive, the diffusion coefficient is a non-monotonic function of temperature, increasing with temperature in the low-temperature Environment Assisted Quantum Transport regime and decreasing with temperature in the high-temperature quantum-Zeno regime. For any temperature, static and dynamic disorder decreases the diffusion coefficient. The dynamics is non-diffusive for thermal energies deep within the manifold of local-ground-states, where the sub-diffusive exponent decreases with increasing disorder and decreasing temperature.

The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the important connection between kinematics and dynamics - clarifies the role of rods and clocks in general relativity.

We state and prove a general result establishing that T-duality simplifies the bulk-boundary correspondence, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors, and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to String Theory and to the study of the quantum Hall effect and topological insulators with defects in Condensed Matter Physics.

In this expository article we present Rosenlicht's work on geometric class field theory, which classifies abelian coverings of smooth, projective, geometrically connected curves over perfect fields.

This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of convergence and particularly the effect of gradient discontinuities (i.e., the omni-present `kinks' in option payoffs) on this rate have not been fully analysed so far. This effect becomes important not least when using penalisation as a numerical technique. We use matched asymptotic expansions to characterise the boundary layers between exercise and hold regions, and to compute first order corrections for representative payoffs on a single asset following a diffusion or jump-diffusion model. Furthermore, we demonstrate how the viscosity theory framework in [Jakobsen, 2006] can be applied to this setting to derive upper and lower bounds on the value. In a small extension to [Bensoussan & Lions, 1982], we derive weak convergence rates also for option sensitivities for convex payoffs under jump-diffusion models. Finally, we outline applications of the results, including accuracy improvements by extrapolation.