A Classical Switched LC/LR Circuit Modeling the Quantum Zeno and Anti-Zeno Effects

Abstract

Generalizing a recent analysis, we model the quantum Zeno and anti-Zeno effects with a quickly switched, ideal LC/LR circuit, in the limiting case of it alternating very many times between its short LC and even shorter LR regime. If the initial current is arranged to be negligible, the capacitor turns out never to discharge. If the initial current is made dominant, this capacitor discharges, and faster than the exponential decay to which it limits. The existence and simplicity of these phases in such a rudimentary model indicates that the corresponding effects are ubiquitous throughout physics, both quantum and classical. In turn, the parameter space of this model contains intermediate phases in which the circuit exhibits behaviors that seem to foreshadow other quantum effects of some interest.