Conserved Mass Models and Particle Systems in One Dimension
| dc.creator | Rajesh, R. | |
| dc.creator | Majumdar, Satya N. | |
| dc.date | 1999-10-14 | |
| dc.date | 2001-04-03 | |
| dc.date.accessioned | 2026-07-07T03:14:48Z | |
| dc.date.available | 2026-07-07T03:14:48Z | |
| dc.description | In this paper we study analytically a simple one dimensional model of mass transport. We introduce a parameter $p$ that interpolates between continuous time dynamics ($p\to 0$ limit) and discrete parallel update dynamics ($p=1$). For each $p$, we study the model with (i) both continuous and discrete masses and (ii) both symmetric and asymmetric transport of masses. In the asymmetric continuous mass model, the two limits $p=1$ and $p\to 0$ reduce respectively to the $q$-model of force fluctuations in bead packs [S.N. Coppersmith et. al., Phys. Rev. E. {\bf 53}, 4673 (1996)] and the recently studied asymmetric random average process [J. Krug and J. Garcia, cond-mat/9909034]. We calculate the steady state mass distribution function $P(m)$ assuming product measure and show that it has an algebraic tail for small $m$, $P(m)\sim m^{-β}$ where the exponent $β$ depends continuously on $p$. For the asymmetric case we find $β(p)=(1-p)/(2-p)$ for $0\leq p <1$ and $β(1)=-1$ and for the symmetric case, $β(p)=(2-p)^2/(8-5p+p^2)$ for all $0\leq p\leq 1$. We discuss the conditions under which the product measure ansatz is exact. We also calculate exactly the steady state mass-mass correlation function and show that while it decouples in the asymmetric model, in the symmetric case it has a nontrivial spatial oscillation with an amplitude decaying exponentially with distance. | |
| dc.description | 14 pages, 5 figures, 1 table added, corrected typos, journal ref | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9910206 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9910206 | |
| dc.identifier | J. Stat. Phys., 99 (2000) 943 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/29812 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Conserved Mass Models and Particle Systems in One Dimension | |
| dc.type | text |