PhD Dissertation Defense

We study the Schwinger effect, which is the non-perturbative production of e^-e⁺ pairs from the vacuum by an external electric field.  Basic quantitative analysis consists of extracting pair production probabilities which could be done exactly for only few cases. Thus, as far as realistic electric fields are concerned, application of numerical methods becomes essential for the analysis. We present two well known numerical methods which are developed for the electric fields varying only in one dimension, and we give the treatment for the electric fields varying in time. The first methods employs a Riccati type equation and relates the reflection probability of the associated scattering problem to the produced particle density. The second approach makes use of a time-dependent number operator whose evolution given by the quantum Vlasov equation, and its asymptotic value gives the density of the produced pairs. We show that these two methods are equivalent and the evolution equations can be reduced to a second order nonlinear differential equation. In the following, we present a detailed semiclassical analysis both within the framework of Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation and worldline instanton formalism.  In the former method analytical continuation rules for the approximate JWKB solutions are introduced and the reflection amplitude is obtained for a generic time dependent potential. In conjunction with the experimental studies, we compute the momentum spectra for realistic laser pulses with subcycle structure which might be relevant for
the planned laser facilities.