Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity
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| Format: | Preprint |
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2023
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| _version_ | 1866910627125002240 |
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| author | Ikeda, Harukuni |
| author_facet | Ikeda, Harukuni |
| contents | 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 $D(ω)\sim ω^{-2θ}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $θ>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2θ}$ for large $t$. On the other hand, for the driving forces (i) with $θ<-1/4$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_03155 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity Ikeda, Harukuni Statistical Mechanics Soft Condensed Matter 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 $D(ω)\sim ω^{-2θ}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $θ>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2θ}$ for large $t$. On the other hand, for the driving forces (i) with $θ<-1/4$ 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. |
| title | Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2309.03155 |