The shape of the emerging condensate in effective models of condensation

TL;DR

This paper analyzes effective models of condensation, showing that the condensate forms on a 1/t spatial scale with a universal Gamma density shape, influenced by initial conditions and total mass.

Contribution

It establishes natural conditions for condensate formation, characterizes its universal Gamma density shape, and relates parameters to the model's equation and initial decay properties.

Findings

Condensate forms on a 1/t spatial scale.

The condensate density follows a universal Gamma distribution.

Parameters depend on the equation, total mass, and initial decay.

Abstract

We consider effective models of condensation where the condensation occurs as time t goes to infinity. We provide natural conditions under which the build-up of the condensate occurs on a spatial scale of 1/t and has the universal form of a Gamma density. The exponential parameter of this density is determined only by the equation and the total mass of the condensate, while the power law parameter may in addition depend on the decay properties of the initial condition near the condensation point. We apply our results to some examples, including simple models of Bose-Einstein condensation.