FPUT Recurrence & Discrete Breathers in Anharmonic Lattices

The Fermi-Pasta-Ulam-Tsingou (FPUT) problem: energy initially in a single normal mode of an anharmonic lattice slowly flows to other modes, but nearly-periodically returns to the initial mode — the famous recurrence. Discrete breathers are time-periodic, spatially localized excitations that exist due to nonlinearity and discreteness.

Lattice displacements u_n(t). Color = local energy density.

Mode energies E_k vs time. FPUT recurrence: energy flows back to k=1.

Breather mode: spatial energy profile showing localization.

N particles: 32 Nonlinearity α: 0.25 Initial mode k₀: 1 Initial amplitude A: 0.5

Time t: 0

E(k₀)/E_total: —

Recurrence period: ~

Localization ξ: —

FPUT-α: V(r)=r²/2+αr³/3

Breather freq ω_b > ω_max (phonon band)

Current mode energy spectrum.