In the pursuit of designing complex materials with desired properties, un- derstanding their design parameter space is crucial. However, this space’s convolution often hinders comprehension of...Show moreIn the pursuit of designing complex materials with desired properties, un- derstanding their design parameter space is crucial. However, this space’s convolution often hinders comprehension of complex materials’ responses as a function of their design parameters. Machine Learning has recently emerged as a promising tool for capturing patterns in complex design spaces, although this performance often comes at the cost of interpretabil- ity. This thesis aims to explore the design parameter space of interact- ing hysterons using interpretable Machine Learning, specifically Decision Tree inspired methods. Despite the complexity of the design parameter space of even small systems of interacting hysterons, interpretable Ma- chine Learning can classify coarse-grained properties of the system effec- tively. Introducing the Support Vector Classifier (SVC) inspired Decision Tree, we achieve almost perfect isolation of these properties. This model preserves interpretability while effectively probing the statistical structure of design parameter space of systems of interacting hysterons.Show less
We compute the quantum back reaction of Schwinger pair production in the context of spinor QED. Using path integral and Schwinger’s proper time methods, we employ a WKB approximation to find the...Show moreWe compute the quantum back reaction of Schwinger pair production in the context of spinor QED. Using path integral and Schwinger’s proper time methods, we employ a WKB approximation to find the current-current correlation function and relate it to the current expectation value in a manner analogous to fluctuation-dissipation theory. The same expression for the current expectation value in terms of the electric field is derived using point-splitting to cure UV divergences. We use this current value to compute the back reaction on the electric field via Maxwell’s equation, obtaining a non-linear complex differential equation. A stable numerical solution is found, whose real part is the electric field. The field, initially just below the Schwinger limit, undergoes a sharp drop followed by exponential-like decay. Further analysis on the behavior of the current, production rate, and the energy density is performed using numerical integration.Show less
