The Ginzburg-Landau model of Bose-Einstein condensation of magnons

TL;DR

This paper develops a phenomenological model combining features of Gross-Pitaevskii and Ginzburg-Landau equations to describe Bose-Einstein condensates of magnons, predicting stable localized states and their dynamics.

Contribution

It introduces a new set of coupled equations for magnon condensates, including localized sources, and analyzes their solutions and stability, bridging theory with experimental observations.

Findings

Analytical solutions for symmetric localized states.

Prediction of asymmetric states with unequal amplitudes.

Numerical simulations confirm stability and reveal pattern transitions.

Abstract

We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right-and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms, to represent the microwave magnon-pumping field. With the source represented by the $\delta $-functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitudes of the two components. Numerical simulations demonstrate that all analytically found solutions are stable. With the $\delta $-function terms replaced by broader sources, the simulations reveal a transition from the single-peak stationary symmetric states to multi-peak ones, generated by the modulational instability of extended nonlinear-wave patterns. In the simulations, symmetric initial conditions always converge to symmetric stationary patterns. On the other hand, asymmetric inputs may generate nonstationary asymmetric localized solutions, in the form of traveling or standing waves. Comparison with experimental results demonstrates that the phenomenological equations provide for a reasonably good model for the description of the spatiotemporal dynamics of magnon condensates.