Macroscopic Car Condensation in a Parking Garage

Details Macroscopic Car Condensation in a Parking Garage Macroscopic Car Condensation in a Parking Garage

2002-05-22

arxiv.org/abs/cond-mat/0205456v2

PRE v66, 036118 (2002)

Physics

Condensed Matter

Statistical Mechanics

12 pages including 15 figures; published version in PRE

Scientific paper

10.1103/PhysRevE.66.036118

An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes macroscopically occupied. The total car density $\rho_o$ and the exit probability $\alpha$ are the two control parameters. At the transition, the number of parked cars $N_p$ diverges in both cases, with the length of the road $N_s$, as $N_p\sim N_s^{y_p}$ with $y_p=1/2$. Towards the transition, the number of parked cars vanishes as $N_p\sim \epsilon^\beta$ with $\beta=1$, $\epsilon=|\alpha -\alpha^*|$ or $\epsilon=|\rho^*_o -\rho_o|$ being the distance from the transition. The transition into the normal phase represents also the onset of transmission of information through the garage. This gives rise to unusual parked car autocorrelations and car density profiles near the garage, which depend strongly on the group velocity of the fluctuations along the road.

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