On the Complexity of a Charged Quantum Oscillator

Abstract

In this paper, we study the effect of both the electric and the magnetic fields on the rate of complexity growth. Our system is a charged quantum oscillator and over a period of time, we study the maximum dynamic evolution of quantum states which might lead to a strong bound on the rate of computation. We show that by turning on the electric field, the rate of complexity decreases whereas this rate has increasing behavior when the magnetic field is turned on. In this regard, we also find a critical value of the magnetic field, beyond which this rate changes its behavior drastically.