Abstract
We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system’s equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.
Highlights
fluctuations[23,24], correlations and response with non-symmetric couplings[25], velocity alignment in active matter[26], systems with Vicsek-like interactions[27,28], velocity fields in granular materials[29,30,31]
The one multiplied by γbTL has a sign that depends on the parity of l and k and this brings to a subleading contribution if one considers L ≫ 1 and j, m ≪ L
We studied spatial and temporal correlations in the NESS reached by a velocity field with viscous interactions defined on the lattice and coupled with Brownian baths
Summary
fluctuations[23,24], correlations and response with non-symmetric couplings[25], velocity alignment in active matter[26], systems with Vicsek-like interactions[27,28], velocity fields in granular materials[29,30,31]. Looking for the emergence of a collective motion in it is motivated by the recent experimental/numerical evidence of slow collective behavior in vibro-fluidized granular materials[8,9] This phenomenon is not yet fully understood and our study tackles this problem, revealing that non-homogeneous heating and frictional interactions (i.e standard features of vibrated granular matter) are minimal ingredients to develop a slow collective dynamics. We note that the HHP is not strictly spatially homogeneous because viscous coefficients and temperatures depend on the position: we refer to it as homogeneously heated meaning that in this phase all the particles are coupled with a bath
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