An Open Quantum System of Coupled Rotors

TL;DR

This paper investigates a quantum system of two coupled rotors, analyzing their entanglement and dynamics using Mathieu functions, and derives a Lindblad master equation for the reduced system under certain approximations.

Contribution

It provides explicit eigenvalue calculations using Mathieu functions and develops a master equation approach for the open quantum system of coupled rotors.

Findings

Eigenvalues expressed via Mathieu functions

Von Neumann entropy computed from Fourier coefficients

Derived Lindblad master equation for the system

Abstract

A quantum mechanical system of two coupled rotors (particles constrained to move on a circle) is studied from an open quantum systems point of view. One of the rotors is integrated out and the reduced density operator of the other rotor is studied. It's eigenvalues are worked out explicitly using the properties of Mathieu functions, and the von Neumann entropy, which is a standard measure of entanglement, is computed in terms of the Fourier coefficients defining the Mathieu functions. Furthermore, upon introducing a time-periodic delta kick and making one of the rotors much heavier than the other, the two-rotor system can be interpreted as a system-bath model, allowing us to introduce a series of approximations to derive a master equation of the Lindblad type describing the time-evolution of the reduced density operator.