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Lecture Notes On Generalised Hydrodynamics
by Benjamin Doyon
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Benjamin Doyon |
| Submission information | |
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| Preprint Link: | scipost_202005_00002v2 (pdf) |
| Date accepted: | 2020-08-06 |
| Date submitted: | 2020-08-04 17:53 |
| Submitted by: | Doyon, Benjamin |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.
Author comments upon resubmission
First point, mention of hydrodynamics flow of electrons: indeed this was missing. I have added references and brief mention in the introduction (top of page 6). I had already ref 18 (formerly [13]) about electrons in graphene, but I added more refs and a mention in the text.
Second point, showcasing the theory: this is indeed a very good point. I opted to add a subsection in the introduction of 3-4 pages, "Invitation: the hydrodynamics of a quantum Newton’s cradle experiment", where I briefly describe a quantum Newton's cradle type of experiment. I have included a discussion of the experiment itself (without, of course, going into any experimental detail, of which I am not an expert and which is beyond the scope of the notes), the microscopic description in terms of Hamiltonians and observables we would want to evaluate, the technical difficulties in naively trying to solve this problem either by the direct methods of quantum mechanics or by using integrability, the physics - that of standard hydrodynamics - one might naively expect, the principles behind what is actually happening with the simplified picture of the Newton's cradle, and finally how generalised hydrodynamics solves the problem, with all necessary equations for the full initial value problem. I believe this gives a good intuition as to why GHD is important, and what it consists of at the most basic level. I think going over how it improves upon the Gross-Pitaevskii equation in any cold-atoms setup would go beyond the scope of these notes, as I would like not to assume the reader is familiar with the particular physics of cold atomic gases; instead I have referred to a book about cold atom methods, and papers where their relation to GHD is discussed, at the beginning of this new section. I think there is still research to do in the direction of comparing GHD to other methods.
List of changes
references added according to the referee's comments and to other comments received by colleagues
typos corrected and some clarifications here and there
subsection 1.1 added, as described above.
Published as SciPost Phys. Lect. Notes 18 (2020)