Eur. Phys. J. B (2012) 85: 113
https://doi.org/10.1140/epjb/e2012-20794-x

Regular Article

Optimal temperature in the accumulation of particles in networked traps

Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200062, P.R. China

^a e-mail: zhliu@phy.ecnu.edu.cn

Received: 24 August 2011
Received in final form: 15 December 2011
Published online: 30 March 2012

Abstract

Previous studies have shown that in the Bose-Einstein condensation (BEC), temperature is a key factor, i.e., the lower the temperature is, the easier to observe particle condensation. While in recent studies of particle condensation on complex networks, temperature is not involved. We here propose a model of networked traps with distributed potential depths to include the temperature into particle diffusion. Through three typical potential forms, we find that the particle distribution in equilibrium satisfies a super-linear relationship with the node degree k_i. Specifically, it will become a power law when the potential energy E_i takes the form E_i = lnk_i. Furthermore, we surprisingly reveal that there is an optimal temperature T_o^k for the accumulation/condensation of particles at each group of nodes with the same degree k and T_o^k increases with k until T_o^hub of the hub, in contrast to the monotonous relationship between temperature and condensation in BEC. The optimal T_o^k comes from the competition between the trapping from attractive interaction among particles and the fluctuation controlled by temperature. Numerical simulations have completely confirmed the theoretical predictions.