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How generalized hydrodynamics time evolution arises from a form factor expansion
by Axel Cortés Cubero
|As Contributors:||Axel Cortes Cubero|
|Date submitted:||2020-12-31 10:16|
|Submitted by:||Cortes Cubero, Axel|
|Submitted to:||SciPost Physics|
The generalized hydrodynamics (GHD) formalism has become an invaluable tool for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional integrable models. The main paradigm of the GHD is that at late times local observables can be computed as generalized Gibbs ensemble averages with space-time dependent chemical potentials. It is, however, still unclear how this semiclassical GHD picture emerges out of the full quantum dynamics. We evaluate the quantum time evolution of local observables in spatially inhomogeneous quenches, based on the quench action method, where observables can be expressed in terms of a form factor expansion around a finite-entropy state. We show how the GHD formalism arises as the leading term in the form factor expansion, involving one particle-hole pair on top of the finite-entropy state. From this picture it is completely transparent how to compute quantum corrections to GHD, which arise from the higher terms in the form factor expansion. Our calculations are based on relativistic field theory results, though our arguments are likely generalizable to generic integrable models.
Author comments upon resubmission
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Reports on this Submission
Anonymous Report 1 on 2021-4-10 (Invited Report)
1- Interesting and timely topic.
2- Systematic approach.
1- Many assumptions are hard to test.
2- The discussion of corrections is incomplete.
I apologise for the delay in submitting this report. Due to some technical issues with the journal website I learnt only very recently about new versions of this paper being uploaded. This report follows my first one submitted on the 23rd of April 2020.
I think that the author responded satisfactorily to most of my comments. However, before recommending the paper for publication, I strongly encourage the author to address the remaining points below.
1- I find the new paragraph added at the end of Section 5 rather misleading. The fact that one can reduce the form factor expansion to the form in Eq. 51 in the Euler limit is strictly speaking an assumption. Indeed, to get this result one has to assume that form factors corresponding to more particle-hole excitations are well behaved and one can perform the saddle point analysis mentioned by the author. I understand that this assumption was made earlier in the literature (in Ref. ) but I think that it would be better to explain this point also in the current paper. I also suggest the author to mention that the calculation presented in the paper is based on a number of non-trivial assumptions both in the introduction and in the conclusions.
2- The author should read carefully the paper again, removing the typos and spurious sentences introduced during revision. For example I found typos/spurious sentences in the discussion above Eq. 42, in the sentence above Eq. 47, and in the sentence above Eq 72. Finally, I am not sure about the grammar of the last sentence of the new paragraph in Sec. 5.