Optimal temperature in the accumulation of particles in networked traps

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 ki. Specifically, it will become a power law when the potential energy Ei takes the form Ei = lnki. Furthermore, we surprisingly reveal that there is an optimal temperature Tok for the accumulation/condensation of particles at each group of nodes with the same degree k and Tok increases with k until Tohub of the hub, in contrast to the monotonous relationship between temperature and condensation in BEC. The optimal Tok 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.