Frozen dynamics of a breather induced by an adiabatic invariant

Antonio Politi, Paolo Politi, Stefano Iubini

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The discrete nonlinear Schrödinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In (Iubini et al 2019 Phys. Rev. Lett. 122 084102), it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is ‘forced’ by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with Lévy processes.
Original languageEnglish
Article number043206
Number of pages25
JournalJournal of statistical mechanics-Theory and experiment
Issue number4
Early online date29 Apr 2022
Publication statusPublished - 29 Apr 2022

Bibliographical note

P P acknowledges support from the MIUR PRIN 2017 project 201798CZLJ.


  • numerical simulations
  • slow relaxation
  • glassy dynamics
  • aging
  • diffusion
  • ergodicity breaking


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