Thermalization of nearly integrable lattices (FPUT)

4 problems

• Endless spreading of wave packets in disordered nonlinear lattices

  Contested

  In a disordered lattice without interactions, waves stay trapped in place (Anderson localization). Weak nonlinearity lets a packet slowly spread, and it is unknown whether the spreading continues forever or eventually stops.

• Relaxation of negative-temperature states in the discrete nonlinear Schrodinger chain

  Partially resolved

  A chain of coupled nonlinear wave sites can be given so much energy per particle that its temperature formally becomes negative, and energy then gathers into a few tall localized peaks called breathers. Whether the chain ever settles into equilibrium from there, and how long it takes, is not known.

• Universal scaling of the FPUT equipartition time

  Partially resolved

  Recent work claims that the time to reach equal sharing of energy grows as the inverse square of the nonlinearity strength in large lattices. Whether this law is universal, and from which system size it applies, needs independent confirmation.

• Role of Toda integrals in the FPUT metastable state

  Partially resolved

  The FPUT chain is close to the Toda chain, a solvable model with as many conserved quantities as particles. The question is whether the long-lived non-thermal state of FPUT is the equilibrium of the Toda chain, and how fast its conserved quantities drift.