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2019

Breathing modes, quartic nonlinearities and effective resonant systems

Evnin, Oleg

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A breathing mode in a Hamiltonian system is a function on the phase space whose evolution is exactly periodic for all solutions of the equations of motion.

Such breathing modes are familiar from nonlinear dynamics in harmonic traps or anti-de Sitter spacetimes, with applications to the physics of cold atomic gases, general relativity and high-energy physics.
We discuss the implications of breathing modes in weakly nonlinear regimes, assuming that both the Hamiltonian and the breathing mode are linear functions of a coupling parameter, taken to be small.
For a linear system, breathing modes dictate resonant relations between the normal frequencies.

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1903
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