Mathematical Physics at the Crossings, VirginiaTech, Virginia, USA
The electrons in a metal can be extracted from the metal by a variety of processes: for instance by applying a strong electric field (field emission), or shining an intense laser pulse (photoemission). In the case of field emission, the celebrated and widely used Fowler-Nordheim equation predicts a value for the current of electrons outside the metal. In this talk, I will show that the Fowler-Nordheim equation emerges as the long-time asymptotic solution of a Schrodinger equation with a realistic initial condition, thereby justifying the use of the Fowler Nordheim equation in real setups. As for photoemission, the expression for the current has been predicted by Faisal et al, and I will discuss ongoing work to show that this prediction emerges as the long-time asymptotic solution of a Schrodinger equation. In both cases, I will discuss the time scale of the convergence.
This presentation is based on