Collective-Coordinate Fluctuations of Driven-Dissipative Solitons

TL;DR

This paper develops a stochastic collective-coordinate theory for driven-dissipative solitons, revealing how internal fluctuation pathways shape observable noise spectra and distinguishing direct stochastic effects from deterministic transfer among soliton parameters.

Contribution

It introduces a pathway-resolved stochastic theory that explicitly models internal fluctuation transfer in driven-dissipative solitons, enhancing understanding of noise origins in these systems.

Findings

Timing jitter is mainly due to frequency-to-timing conversion.

Phase noise is often dominated by amplitude-to-phase transfer.

Raman response introduces additional fluctuation pathways.

Abstract

Fluctuations of nonequilibrium localized waves are shaped not only by direct stochastic forcing but also by deterministic transfer among coupled collective degrees of freedom. We develop a pathway-resolved stochastic collective-coordinate theory that makes this transfer explicit for stationary driven-dissipative solitons of the generalized Lugiato--Lefever equation with Raman response. The reduction yields a refined stationary phase-locking relation, providing a fixed point for the subsequent stochastic theory. Projecting field-level fluctuations onto four soliton coordinates: amplitude, frequency shift, temporal position, and global phase, yields a reduced Langevin model and, after linearization about a stable stationary state, an analytic power-spectral-density matrix. This framework separates direct stochastic injection from deterministic inter-coordinate conversion and thereby resolves how each observable spectrum is assembled from distinct internal fluctuation pathways. It shows that timing jitter is governed primarily by Gordon--Haus-type frequency-to-timing conversion, while phase noise is often dominated by amplitude-to-phase transfer rather than by direct phase diffusion. Raman response opens additional cascaded pathways, and the low-detuning hump in the intensity and phase spectra is traced to the driven response of an underdamped amplitude--phase subsystem preceding the breathing instability. Comparisons with stochastic simulations of both the reduced model and the full generalized Lugiato--Lefever equation show good agreement throughout most of the stable stationary single-soliton regime, with systematic deviations mainly near the Hopf boundary. The theory provides a general route for connecting internal fluctuation-transfer mechanisms of dissipative solitons to measurable noise observables.