SciPost Submission Page
Exact largescale correlations in integrable systems out of equilibrium
by Benjamin Doyon
This Submission thread is now published as SciPost Phys. 5, 054 (2018)
Submission summary
As Contributors:  Benjamin Doyon 
Arxiv Link:  https://arxiv.org/abs/1711.04568v4 (pdf) 
Date accepted:  20181114 
Date submitted:  20181105 01:00 
Submitted by:  Doyon, Benjamin 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Using the theory of generalized hydrodynamics (GHD), we derive exact Eulerscale dynamical twopoint correlation functions of conserved densities and currents in inhomogeneous, nonstationary states of manybody integrable systems with weak spacetime variations. This extends previous works to inhomogeneous and nonstationary situations. Using GHD projection operators, we further derive formulae for Eulerscale twopoint functions of arbitrary local fields, purely from the data of their homogeneous onepoint functions. These are new also in homogeneous generalized Gibbs ensembles. The technique is based on combining a fluctuationdissipation principle along with the exact solution by characteristics of GHD, and gives a recursive procedure able to generate $n$point correlation functions. Owing to the universality of GHD, the results are expected to apply to quantum and classical integrable field theory such as the sinhGordon model and the LiebLiniger model, spin chains such as the XXZ and Hubbard models, and solvable classical gases such as the hard rod gas and soliton gases. In particular, we find LeclairMussardotype infinite formfactor series in integrable quantum field theory, and exact Eulerscale twopoint functions of exponential fields in the sinhGordon model and of powers of the density field in the LiebLiniger model. We also analyze correlations in the partitioning protocol, extract largetime asymptotics, and, in free models, derive all Eulerscale $n$point functions.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 5, 054 (2018)
Author comments upon resubmission
Indeed as pointed out the assumption is not necessary for the solution to the partitioning protocol. In fact, I realised that it was not necessary for any result I have presented  it was just simplifying my life in characterising the solutions to certain equations, but is in fact not strictly needed. Thus I have modified the discussion of this assumption on page 13, making it a remark only, and I have make appropriate modifications throughout in order to account for this: all places where the derivative of the effective velocity appeared through Jacobian I have added absolute values; in sections 5.3 and E.2 I have taken away the requirement of the monotonicity assumption, and I have adjusted the sentence between eq 3.24 and 3.25 on p 19.
However, perhaps the most interesting realisation from thinking about this is that in general, the rapidity derivative of the effective velocity may vanish. In this case, some largetime asymptotics, at certain rays for instance in the partitioning protocol (e.g. near the maximal velocity), may be modified. I think this is a potentially very interesting effect, which I keep for future works. I have added a paragraph about this in the conclusion, and also a short comment in the Remark on page 13.
I have also corrected all typos found by referee 2.
List of changes
Absolute value for derivative of effective velocity in eqs. 3.36, 4.19, 4.23, 5.12, 5.17, 5.19, 5.21, E.15, E.17, E.20, E.22, E.23, E.24, E.28 and eq above  E.31, E.33
paragraph added in conclusion
discussion adjusted in section 5.3 (p35) and E.2 (p47)
discussion adjusted and remark added p13
adjusted the sentence between eq 3.24 and 3.25 on p 19