Pub Date : 2020-11-06DOI: 10.1103/PhysRevResearch.3.023224
Victor Buend'ia, Pablo Villegas, R. Burioni, M. A. Muñoz
The human cortex is never at rest but in a state of sparse and noisy neural activity. It has been conjectured that such a state is best described as a critical dynamical process -- whose nature is still not fully understood -- where scale-free avalanches of activity emerge at the edge of a synchronization phase transition. Using a simple model of coupled excitable oscillators, we rule out standard phase transitions to explain the emergence of collective oscillations, as they do not suffice to explain current experimental evidence. Conversely, we uncover a novel hybrid-type of synchronization transition displaying a very-rich dynamical repertoire supporting all key empirical observations, including scale-free avalanches, marginal coherence, and bistability.
{"title":"Hybrid-type synchronization transitions: Where incipient oscillations, scale-free avalanches, and bistability live together","authors":"Victor Buend'ia, Pablo Villegas, R. Burioni, M. A. Muñoz","doi":"10.1103/PhysRevResearch.3.023224","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023224","url":null,"abstract":"The human cortex is never at rest but in a state of sparse and noisy neural activity. It has been conjectured that such a state is best described as a critical dynamical process -- whose nature is still not fully understood -- where scale-free avalanches of activity emerge at the edge of a synchronization phase transition. Using a simple model of coupled excitable oscillators, we rule out standard phase transitions to explain the emergence of collective oscillations, as they do not suffice to explain current experimental evidence. Conversely, we uncover a novel hybrid-type of synchronization transition displaying a very-rich dynamical repertoire supporting all key empirical observations, including scale-free avalanches, marginal coherence, and bistability.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88873940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-02DOI: 10.21468/SCIPOSTPHYS.10.5.099
Lenart Zadnik, Kemal Bidzhiev, M. Fagotti
We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.
{"title":"The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges","authors":"Lenart Zadnik, Kemal Bidzhiev, M. Fagotti","doi":"10.21468/SCIPOSTPHYS.10.5.099","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.10.5.099","url":null,"abstract":"We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72824997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-30DOI: 10.1103/PHYSREVA.103.033309
Philipp S. Weiss, Dennis Hardt, A. Rosch
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_text{r} to infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $Delta S$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $Delta S sim 1/sqrt{t_text{r}}$ in $d=1$ and $Delta S sim ln(t_text{r})/t_text{r}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $Delta S sim 1/t_text{r}$. In order to verify the analytic prediction, we simulate the non-equilibrium dynamics of a classical two-component gas with point-like particles in one spatial dimension and examine the total entropy production as a function of $t_text{r}$.
实现多粒子系统绝热变化的一个典型策略是在一个比内在平衡时间尺度大得多的时间尺度$t_text{r}$上非常缓慢地改变参数。在绝热状态制备的理想情况下，$t_text{r} to infty$，熵产消失。在具有守恒定律的系统中，接近绝热极限受到水动力长尾的阻碍，这是由水动力波动在代数上的缓慢松弛引起的。我们认为，在一维或二维有限温度下，扩散系统的熵产$Delta S$受水动力模式的支配，从而导致$d=1$中的$Delta S sim 1/sqrt{t_text{r}}$和$d=2$中的$Delta S sim ln(t_text{r})/t_text{r}$。在更高的维度中，熵的产生由其他具有$Delta S sim 1/t_text{r}$的高能模式主导。为了验证分析预测，我们在一个空间维度上模拟了具有点状粒子的经典双组分气体的非平衡动力学，并考察了总熵产作为$t_text{r}$的函数。
{"title":"Entropy production for quasiadiabatic parameter changes dominated by hydrodynamics","authors":"Philipp S. Weiss, Dennis Hardt, A. Rosch","doi":"10.1103/PHYSREVA.103.033309","DOIUrl":"https://doi.org/10.1103/PHYSREVA.103.033309","url":null,"abstract":"A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_text{r} to infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $Delta S$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $Delta S sim 1/sqrt{t_text{r}}$ in $d=1$ and $Delta S sim ln(t_text{r})/t_text{r}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $Delta S sim 1/t_text{r}$. In order to verify the analytic prediction, we simulate the non-equilibrium dynamics of a classical two-component gas with point-like particles in one spatial dimension and examine the total entropy production as a function of $t_text{r}$.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83635934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-26DOI: 10.1142/9789811223433_0009
Doruk Efe Gökmen
You will, anyway, if you spend any time talking with Jesse Berezovsky, an associate professor of physics at Case Western Reserve University. The longtime science researcher and a part-time viola player has become consumed with understanding and explaining the connective tissue between the two disciplines—more specifically, how the ordered structure of music emerges from the general chaos of sound.
{"title":"Phase Transitions","authors":"Doruk Efe Gökmen","doi":"10.1142/9789811223433_0009","DOIUrl":"https://doi.org/10.1142/9789811223433_0009","url":null,"abstract":"You will, anyway, if you spend any time talking with Jesse Berezovsky, an associate professor of physics at Case Western Reserve University. The longtime science researcher and a part-time viola player has become consumed with understanding and explaining the connective tissue between the two disciplines—more specifically, how the ordered structure of music emerges from the general chaos of sound.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85035896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-26DOI: 10.1142/9789811223433_0007
Harleen Kaur, Enrico Fermi, P. A. M. Dirac
{"title":"Fermi-Dirac Statistics","authors":"Harleen Kaur, Enrico Fermi, P. A. M. Dirac","doi":"10.1142/9789811223433_0007","DOIUrl":"https://doi.org/10.1142/9789811223433_0007","url":null,"abstract":"","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"1520 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87819538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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