Maintenance of order in a moving strong condensate

Abstract

We investigate the conditions under which a moving condensate may exist in a driven mass transport system. Our paradigm is a minimal mass transport model in which n − 1 particles move simultaneously from a site containing n > 1 particles to the neighbouring site in a preferred direction. In the spirit of a Zero-Range process the rate u(n) of this move depends only on the occupation of the departure site. We study a hopping rate u(n) = 1+b/n α numerically and find a moving strong condensate phase for b > b c (α) for all α > 0. This phase is characterised by a condensate that moves through the system and comprises a fraction of the system's mass that tends to unity. The mass lost by the condensate as it moves is constantly replenished from the trailing tail of low occupancy sites that collectively comprise a vanishing fraction of the mass. We formulate an approximate analytical treatment of the model that allows a reasonable estimate of b c (α) to be obtained. We show numerically (for α = 1) that the transition is of mixed order, exhibiting exhibiting a discontinuity in the order parameter as well as a diverging length scale as b b c .

Conditioned random walks and interaction-driven condensation

“…where a c = E f [x] is the mean with respect to f (x i ) and the factor N indicates that any of the random variables can take the role of the condensate. In physics, condensation phenomena have been extensively studied in masstransport models such as the zero-range process (ZRP) and several related models [6,[14][15][16][17][18][19][20][21][22]. These models comprise masses m i (discrete or continuous) that are exchanged locally between neighbouring sites, typically on a one-dimensional lattice.…”

Participation Ratio for Constraint-Driven Condensation with Superextensive Mass

“…In summary, one has in the case δ = δ c a non-standard, weak condensation effect, which does not correspond to the genuine condensation effect reported in the literature [4][5][6][7][8][9][10][11][12][13]. Here, the weak condensation effect simply means that the participation ratio takes a nonzero value in the infinite size limit, indicating that a few random variables carry a finite fraction of the sum.…”

“…Such a phenomenon has been put forward for instance in the context of the glass transition [2,3]. In the framework of particle or mass transport models [4][5][6][7][8][9][10][11][12][13], where the sum of the random variables is fixed to a constant value due to a conservation law of the underlying dynamics, this phenomenon has been called "condensation". This condensation phenomenon has since then been reported in different contexts like in extreme value statistics [14], and in the sample variance of exponentially distributed random variables as well as for conditioned random-walks [1,15,16].…”

Condensation transition and drifting condensates in the accelerated exclusion process

“…[29] it was shown, using the aforementioned modified MF method, that spatial correlations in the steady state often modify this condensate dynamics: they may lead the condensate to drift along the system with a non-zero velocity in any finite system size. The dynamics of condensates is currently an active line of study, as condensing systems provide one of the simplest settings in which collective and emergent motion can be studied [30][31][32][33][34][35][36][37][38] In the present paper, we demonstrate the use of the MF method of Ref. [29] by applying it to the study of condensation in a recently introduced accelerated exclusion process (AEP) [39].…”