What Does Bose–Einstein Condensation Look Like When the Noise is Nonthermal?

Abstract Bose–Einstein condensation occurs when bosons aggregate to effectively form a single megaparticle. Analyses of Bose–Einstein condensation have generally assumed a bath with a temperature, i.e., a thermal equilibrium where random collisions lead to a Gaussian-noise-term. However, many setups in physics involve conversion or transport of energy, i.e., nonequilibrium. Nonequilibrium noise is commonly characterized by the frequent occurrence of large kicks and, as such, can be effectively modeled by the implementation of $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -stable noise, also called Lévy noise. No temperature exists in that case. We analyze the simple case of bosons in a double-well potential subjected to $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -stable noise. A formula for the distribution over the two wells is derived. It is found that Bose–Einstein condensation can still occur, but is probably much harder to engineer. Our results could be significant for understanding the obviously nonequilibrium quark-gluon plasmas that form after high-energy collisions of heavy nuclei.