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HarmonicBalance.jl

Mar 1, 2024 1 min read

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HarmonicBalance.jl
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HarmonicBalance.jl is a Julia package implementing multi-frequency Floquet expansions to find and analyse steady states of driven nonlinear (quantum) systems. I am a maintainer of the package since March 2024.

The textbook example is the Duffing oscillator. Harmonic balance turns its equation of motion into an algebraic condition on the response amplitude, and as the drive grows the resonance bends over into a region with two stable states and an unstable one between them.

Duffing frequency response: the resonance peak bends towards higher drive frequency as the drive grows, with an unstable middle branchdrive frequency ωω0amplitude
Duffing response from harmonic balance as the drive strength rises and falls; the dashed branch is unstable.
Julia Floquet Expansion
Orjan Ameye
Orjan Ameye
Physicist
Postdoctoral researcher in the Quest research group (Prof. Oded Zilberberg) at the University of Konstanz, working on non-equilibrium physics from Floquet engineering to many-body systems. On the side I enjoy coding and contributing to scientific open-source software.