Simple approximate solutions to continuous-time random-walk transport

We present a procedure for obtaining simple approximate solutions to the continuous-time random walk (CTRW) as it applies to charge transport in amorphous materials. Application of this procedure to a particularly simple trial function leads to an approximate solution that is in excellent agreement with the exact solution for the case in which it is known. The approximate solutions have proved to be very useful in applications of the CTRW theory to observable transport processes such as transient charge relaxation, following exposure to pulsed ionizing radiation, in thin films of amorphous insulators used in metal-insulator-semiconductor capacitors.