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Tails of instability and decay: A hydrodynamic perspective

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Olalla A. Castro-Alvaredo, Cecilia De Fazio, Benjamin Doyon, Aleksandra A. Ziółkowska

Original languageEnglish
Article number115
JournalSciPost Physics
Issue number3
PublishedMar 2022

Bibliographical note

Funding Information: We are grateful to Frederik S. M?ller for answering our questions on the iFluid package. In 2020 two groups of courageous colleagues put together the conference ?Great Lessons from Exact Techniques and Beyond? held in Padova 20-25 September 2020 and the summer school on ?Clean and disordered systems out of equilibrium" held in Carg?se 14-18 September 2020. We thank the organisers of both, for their financial support, for giving us the opportunity to meet in person and discuss and, especially, for creating islands of normality in the midst of a global pandemic. Publisher Copyright: © Copyright O. A. Castro-Alvaredo et al.

King's Authors


In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and life-time of the particle, observed in scattering events. In this paper, we uncover new, dynamical signatures of unstable excitations and show that they have a strong effect on the non-equilibrium properties of QFT. Focusing on a 1+1D integrable model, and using the theory of Generalized Hydrodynamics, we study the formation and decay of unstable particles by analysing the release of hot matter into a low-temperature environment. We observe the formation of tails and the decay of the emitted nonlinear waves, in sharp contrast to the situation without unstable excitations. We also uncover a new phenomenon by which a wave of a stable population of unstable particles may persist without decay for long times. We expect these signatures of the presence of unstable particles to have a large degree of universality. Our study shows that the out-of-equilibrium dynamics of many-body systems can be strongly affected not only by the spectrum, but also by excitations with finite life-times.

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