A Proposed Casimir-Like Effect Between Contaminants in Ideal Bose-Einstein Condensates

It is hypothesized that, within Bose-Einstein condensates, contaminants will form a potential that effects the energy state of a condensate. While assuming a system governed by the Gross-Pitaevskii equation, contaminants are modelled as boundary conditions for the wave function of the condensate. It is then found that the energy of the system depends directly upon the distance between contaminants. Energy is minimized as two particles either come together or move apart depending on the nature of the condensate. This is due to the presence of induced standing waves in the condensate between two contaminants, similar to the attractive effect caused by standing electromagnetic waves in a vacuum, the Casimir effect. Quantum calculations are also done to determine the expected strength of the “contaminant in condensate” effect.