Relaxation of negative-temperature states in the discrete nonlinear Schrodinger chain · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title
Relaxation of negative-temperature states in the discrete nonlinear Schrodinger chain
Plain
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.
Precise · changed · core
Revision 1: For the DNLS chain $H = \sum_n [ (\psi_n* \psi_{(n+1)} + \mathrm{c.c.}) + (g/2)\left|\psi_n\right|^4 ]$ with conserved norm density $a$ and energy density $h$ above the infinite-temperature line h_inf = g a^2, determine whether isolated dynamics from generic initial data relaxes to the microcanonical equilibrium (one breather holding a macroscopic fraction of the norm on an infinite-temperature background), and give the scaling of the relaxation time with chain length $N$ and with h - h_inf. An answer is the asymptotic law, or a proof that the relaxation time diverges with $N$.
Revision 2: For the DNLS chain $H = \sum_n [ (\psi_n* \psi_{(n+1)} + \mathrm{c.c.}) + (g/2)\left|\psi_n\right|^4 ]$ with conserved norm density $a$ and energy density $h$ above the infinite-temperature line $h_{\mathrm{inf}} = g a^2$, determine whether isolated dynamics from generic initial data relaxes to the microcanonical equilibrium (one breather holding a macroscopic fraction of the norm on an infinite-temperature background), and give the scaling of the relaxation time with chain length $N$ and with $h - h_{\mathrm{inf}}$. An answer is the asymptotic law, or a proof that the relaxation time diverges with $N$.
Settled by
Simulations at increasing N that follow breather and background statistics to the predicted microcanonical state, with a theory of breather growth rates that reproduces the measured times.
Kind
well-posed
Answer type
value
References
(empty)
Literature status
partially-resolved
Status note
The microcanonical equilibrium above the line was derived in 2021 (Gradenigo, Iubini, Livi, Majumdar, J. Stat. Mech. 023201, arXiv:1910.07461), and an adiabatic invariant of tall breathers was shown to make relaxation extremely slow (Iubini et al., Phys. Rev. Lett. 122, 084102, 2019); the large-N law is not established.
Posed since
2000

Decisions