A problem of interest in theoretical physics is the issue of the evaporation of black holes via Hawking radiation subject to a fixed background. We approach this problem by considering an electromagnetic analogue, where we have substituted Hawking radiation with the Schwinger effect. We treat the case of massless QED in 1+1 dimensions with the path integral approach to quantum field theory, and discuss the resulting Feynman diagrams from our analysis. The results from this thesis may be useful to find a version of the Schwinger effect that can be solved exactly and perturbatively, as this version may provide insights to the gravitational problem of Hawking radiation.

Mechanical properties (e.g. deformability or stiffness) are critical to a cancer cell's ability to maneuver through and exert forces upon the extracellular matrix, and thus affect its ability to metastasize. §3.1 introduces the experimental method combining atomic force microscope (AFM) based indentation and confocal laser scanning microscopy (CLSM). §3.2 presents a method combining AFM and confocal microscopy (AFM stiffness nanotomography), and results on normal and pre-cancerous esophageal cells which indicate that even in the earliest stages, cancer cells exhibit increased deformability. §3.3 presents experimental results on weakly metastatic breast cancer cells that compare well with values obtained from other experimental methods and demonstrates that the mechanical response of cells to sharp and mesoscale probes differ significantly. §3.4 presents experimental results indicating that metastatic breast cancer cells are more deformable than normal counterparts, and demonstrates that indentation measurements with sharp probes are capable of identifying mechanical differences between cytoplasmic, nuclear and nucleolar regions of the cell. §3.5 presents results on weakly metastatic breast cancer cells sensitive and resistant to tamoxifen (an estrogen antagonist), and demonstrate that estrogen has a significant effect on cell stiffness. §3.6 applies stiffness nanotomography to study metastatic breast cancer cells allowed to invade 3D collagen gels, demonstrating the ability to use AFM indentation on heterogeneous samples, and shows that cell stiffness increases during the invasion process for partially and fully embedded metastatic breast cancer cells.