Numerical and Analytical Approach to the Quantum Dynamics of Two Coupled Spins in Bosonic Baths

TL;DR

This paper presents a combined numerical and analytical method to study the quantum dynamics of two coupled spins interacting with bosonic baths, validated by analytical solutions and simulations.

Contribution

It introduces a mixed Wigner-Heisenberg formalism for simulating spin-bath interactions and compares it with analytical solutions in the Born-Markov approximation.

Findings

The formalism accurately reproduces analytical results.

Numerical simulations match the analytical Born-Markov solutions.

The approach effectively models quantum spin dynamics in bosonic environments.

Abstract

The quantum dynamics of a spin chain interacting with multiple bosonic baths is described in a mixed Wigner-Heisenberg representation. The formalism is illustrated by simulating the time evolution of the reduced density matrix of two coupled spins, where each spin is also coupled to its own bath of harmonic oscillators. In order to prove the validity of the approach, an analytical solution in the Born-Markov approximation is found. The agreement between the two methods is shown.