SciPost Submission Page
Equations of state in generalized hydrodynamics
by Dinh-Long Vu, Takato Yoshimura
This is not the latest submitted version.
This Submission thread is now published as SciPost Phys. 6, 023 (2019)
|As Contributors:||Dinh-Long VU · Takato Yoshimura|
|Arxiv Link:||https://arxiv.org/abs/1809.03197v2 (pdf)|
|Date submitted:||2018-09-27 02:00|
|Submitted by:||VU, Dinh-Long|
|Submitted to:||SciPost Physics|
We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to TBA that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.
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Submission & Refereeing History
Published as SciPost Phys. 6, 023 (2019)
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Reports on this Submission
Anonymous Report 2 on 2018-12-18 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1809.03197v2, delivered 2018-12-18, doi: 10.21468/SciPost.Report.752
1- Elegant proof for that expectation value of a current in a class of quantum integrable systems
1- A proof already existed
2- The paper is not self contained
3- The paper is not written for a general audience
This paper reports an elegant proof for that expectation value of the currents in a stationary state of a(n integrable) relativistic field theory with diagonal scattering. The work is set in the context of nonequilibrium dynamics of inhomogeneous integrable systems, in the framework of the so-called "generalized hydrodynamics". The proof sounds correct, but the authors did not really point out the novelty with respect to the existing proof, which, incidentally, was exhibited about two years ago by one of the authors himself (together with his collaborators).
I recommend this paper for publication, but, in order to avoid this to be considered a marginal paper, I request the authors to stress the importance of their proof even more.
1- TBA is not defined in the abstract.
2- Since Eq. (10) is the starting point of the proof, I recommend the authors to comment on why that is the relevant form factor.
3- The authors should not assume that the readers have their background. For example, the model considered in section 3.4 is not introduced in a satisfactory way.
Anonymous Report 1 on 2018-11-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1809.03197v2, delivered 2018-11-09, doi: 10.21468/SciPost.Report.651
1- First principle proof of the `equation of states' of the recently introduced generalized hydrodynamics theory of quantum integrable systems
2- Elegant approach based on combinatorics
3- The proof is relatively concise
1- Calculation restricted to relativistic integrable field theories with diagonal scattering (excluding spin chains etc.)
This paper provides a proof of the `equation of states' of the generalized hydrodynamic (GHD) theory of quantum integrable systems. GHD was introduced to capture the time evolution of locally-equibrated states in quantum integrable systems, while taking into account all conservation laws. A key equation in GHD gives the effective velocity of quasi-particle excitations over an equilibrium state given by the thermodynamic Bethe ansatz. This velocity appears in the expectation value of the currents in a given generalized equilibrium state. The proof relies on form factors and on the LeClair-Mussardo formula, and recent results on tree expansion approaches to TBA. The proof is limited to relativistic integrable field theories with diagonal scattering, but this is not unexpected given the approach. This is a very nice result, stated in a clear and elegant way. I recommend publication in SciPost as is, up to a minor comment that the authors might choose to address.
1- As the authors note after equation (4), the hydrodynamics of classical hard rod gases and of classical soliton gases has the same form as the GHD of quantum integrable systems. It would be good to mention that the formula for the velocity eq (3) is exactly what one would naturally write down using a semi-classical soliton gas picture. While this is not a proof, this provides a clear physical interpretation of eq 3 which is currently missing in the manuscript.