Generalized Gelfand-Dikii equation for fermionic Schwinger pair production
arXiv:2205.15945 · doi:10.1088/1742-6596/2249/1/012020
Abstract
Schwinger pair creation in a purely time-dependent electric field can be reduced to an effective quantum mechanical problem using a variety of formalisms. Here we develop an approach based on the Gelfand-Dikii equation for scalar QED, and on a generalization of that equation for spinor QED. We discuss a number of solvable special cases from this point of view. In previous work, two of the authors had shown for the scalar case how to use the well-known solitonic solutions of the KdV equation to construct Pöschl-Teller like electric fields that do not pair create at some fixed but arbitrary momentum. Here, we present numerical evidence that this construction can be adapted to the fermionic case by a mere change of parameters.
arXiv comment7 pages, 5 figures, based on a talk given by C. S. at LPHYS'21
References in corpus (7)
- A quantum kinetic equation for particle production in the Schwinger mechanism
- Pair Production Beyond the Schwinger Formula in Time-Dependent Electric Fields
- On the Time Dependence of Adiabatic Particle Number
- On the kinetic equation approach to pair production by time-dependent electric field
- Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production
- On the Vlasov equation for Schwinger pair production in a time-dependent electric field
- The inverse problem for Schwinger pair production