Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background

TL;DR

This paper investigates the quantum interaction between a charged particle in a magnetic field and a circularly polarized gravitational wave, revealing quantum resonance effects analogous to classical predictions.

Contribution

It provides a quantum mechanical analysis of the Landau system's response to circularly polarized gravitational waves, extending classical resonance results to the quantum domain.

Findings

Quantum resonance behavior observed for circularly polarized GWs

Time-evolution of particle's position and momentum computed

Quantum analogue of classical resonance confirmed

Abstract

Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the classical Hamiltonian following \cite{speli}. The rotating polarization vectors of the circularly polarized GW are employed to form a unique directional triad which served as the coordinate axes. The Schrodinger equations for the system are cast in the form of a set of coupled linear differential equations. This system is solved by iterative technique. We compute the time-evolution of the position and momentum expectation values of the particle. The results show that the resonance behaviour obtained earlier\cite{emgw_classical} by classical treatements of the system has a quantum analogue not only for the linearly polarized GW \cite{emgw_1_lin}, but for circularly polarized GW as well.