Locating the minimum: Approach to equilibrium in a disordered, symmetric zero range process

Pramana

Mustansir Barma¹  Kavita Jain¹ 

[1] Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India$$

关键词: Quenched disorder;    approach to steady state;    zero range process;    diffusion;    hydrodynamics.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site 𝑘 hops to its nearest neighbor with a quenched rate 𝑤(𝑘). These rates are chosen randomly from the probability distribution 𝑓(𝑤) ∼ (𝑤 - 𝑐)𝑛, where 𝑐 is the lower cutoff. For 𝑛 > 0, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on the local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, regions with a smooth density profile are described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size 𝐿 as 𝐿𝑧 with 𝑧 = 2+ 1/(𝑛+ 1) for 𝑛 > 1 and suggests a different behavior for 𝑛 < 1.

【 授权许可】

Unknown