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Tails of Instability and Decay: a Hydrodynamic Perspective

by Olalla A. Castro-Alvaredo, Cecilia De Fazio, Benjamin Doyon, and Aleksandra A. Ziolkowska

Submission summary

As Contributors: Olalla Castro-Alvaredo
Preprint link: scipost_202109_00002v1
Date submitted: 2021-09-02 15:01
Submitted by: Castro-Alvaredo, Olalla
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approaches: Theoretical, Computational


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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Submission & Refereeing History

Reports on this Submission

Anonymous Report 1 on 2021-10-1 (Invited Report)


This paper applies the generalized hydrodynamics formalism in the somewhat unusual setting of integrable field theories with unstable excitations. The specific problem was first studied by some of the authors themselves in Ref. [32], which the present work extends to the problem of “free expansion” into a low-temperature bulk state. I find the authors’ results physically interesting and thoroughly interpreted, and a solid contribution to understanding the consequences of unstable excitations far from equilibrium. However, I request that the authors clarify the following points before the manuscript is published in SciPost:

Fig. 1: this figure gets across the central message of the paper, that particle decay leads to unusual “tails” of the sound modes. While I understand that the initial state is prepared using TBA with parity-breaking phase shifts, I find it a little confusing that the free evolution breaks parity. For example, in a generic non-driven physical system, a thermal state of the form (2) would be parity even. Is there any sense in which parity even/odd observables are more physical or natural in the QFT considered by the authors? (e.g. the sum q_0^+ + q_0^-) Do such observables show the same phenomenology as Fig. 1? And are there parity conserving models with similar physics?

p6: the bath temperature seems to be restricted so that the bath is “free”. Could the authors comment on what changes when the bath is interacting? (i.e. T_a > e^{\sigma/2}). There also seems to be a typo (missing log/exp) in the inequalities for T_a and T_m at the bottom of p6.

p6: “This is akin to having a fluid that is magnetic, and running a magnet pass it. We see a wave that follows the magnet but the fluid itself does not need to move.” The intuition makes sense but the hydrodynamics of magnetic fluids (MHD) is complicated. Could the authors add a specific reference, or a calculation, for the phenomenon they have in mind? This would be helpful because the magnetic analogy is mentioned several more times.

p14: “the decay of matter in closed many-body quantum systems may be experimentally identified”. This sounds very interesting, but which experimental systems do the authors have in mind? As mentioned above, parity violation seems a little unlikely for the initial state (2) in a closed quantum system. Do the authors expect the tail in the sound mode to appear more generally? Or is there an effective experimental Hamiltonian that realizes the specific type of model (parity breaking, relativistic, integrable, unstable excitations) studied in this paper?

A2, Table 2: Since the authors are being thorough with the simulation details, one should also check the conservation of higher conserved charges that sample more of the UV. Is the accuracy similarly good for the charge directly relevant to the initial condition, i.e. energy?

A3: I did not understand how the error benchmarking was done in this appendix – Fig. 9 shows convergence but relative to what? It might clarify matters to add some measure of the error, as in Table 2.

Finally, some minor comments on presentation:

Notation for excitations: using + and – in the main text was a little confusing, as each time I read them as a connective. Could the authors consider writing e.g. (+) or (-), or using some other specialized symbol?

p2: “generalised hydrodynamics (GHD) [26, 27], the hydrodynamic theory which accounts for generalized thermalisation”: GHD is indeed a very successful theory that pins down thermalization to GGEs in certain contexts (when the hydrodynamic assumption holds). But it is not expected to account for all types of approach to GGE (e.g. violent quenches, small systems…).

p2: The GHD necessitates -> GHD requires?

p3: “excitations mostly move at velocities \pm 1”: a qualifier like “relativistic” should be added, since this is not true in all free field theories.

p5: “a spectrum effective velocities” -> spectrum of

p6: “magnet pass” -> magnet past

p14: “an idea which has may lead to a deeper understanding”: has or may?

p19: of of -> of

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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Anonymous on 2021-09-03  [id 1734]