Quantum mechanical evolution of electron’s Landau state in the dissipative magnetic field

Physicists have long studied Landau states and energy levels of electrons in a stable magnetic field. However, when the magnetic field dissipates, the question of how Landau states evolve remains unanswered. This study investigates the magnetic dissipative effect from a quantum mechanics perspective. We establish a quantum master equation that describes a dissipative magnetic field. Subsequently, we solve the master equation using an entangled state representation. Consequently, we found that the Landau state evolves into a binomial quantum state (mixed state) when the magnetic field dissipated. This is in sharp contrast to the case where the Landau state becomes a negative binomial state when an additional harmonic oscillator potential is applied. We hope that this finding will be helpful for the evolution of quantized plasma physics.