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Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity
by Harukuni Ikeda
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Submission summary
| Authors (as registered SciPost users): | Harukuni Ikeda |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2309.03155v4 (pdf) |
| Date accepted: | 2024-09-24 |
| Date submitted: | 2024-08-27 17:45 |
| Submitted by: | Ikeda, Harukuni |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In one dimension, particles can not bypass each other. As a consequence, the mean-squared displacement (MSD) in equilibrium shows sub-diffusion ${\rm MSD}(t)\sim t^{1/2}$, instead of normal diffusion ${\rm MSD}(t)\sim t$. This phenomenon is the so-called single-file diffusion. Here, we investigate how the above equilibrium behaviors are modified far from equilibrium. In particular, we want to uncover what kind of non-equilibrium driving force can suppress diffusion and achieve the long-range crystalline order in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we investigate the harmonic chain driven by the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the noise spectrum $D(\omega)\sim \omega^{-2\theta}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\theta>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2\theta}$ for large $t$. On the other hand, for the driving forces (i) with $\theta<-1/4$ and (ii)-(iv), MSD remains finite. As a consequence, the harmonic chain exhibits the crystalline order even in one dimension. Furthermore, the density fluctuations of the model are highly suppressed in a large scale in the crystal phase. This phenomenon is known as hyperuniformity. We discuss that hyperuniformity of the noise fluctuations themselves is the relevant mechanism to stabilize the long-range crystalline order in one dimension and yield hyperuniformity of the density fluctuations.
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Author comments upon resubmission
Thank you for your editorial work.
I have carefully studied the referee reports and have revised the paper. I believe that I have fully answered the referees's questions and that they will find the revised version acceptable for publication.
Sincerely yours,
Harukuni Ikeda
List of changes
1. Following Report 2's suggestion, I modified Eq. (8) and the corresponding parts of the main text.
2. Following Report 2's suggestion, I modified a sentence just below Eq. (26) and the corresponding parts of the main text.
3. Following Report 2's suggestion, I removed the sentence in Sec. 4. 1 starting from "Recently Galliano et al...".
Published as SciPost Phys. 17, 103 (2024)