The Casimir-like Force Between Contaminants In Bose-Einstein Condensates With Different Boundary Conditions

Casimir effect and Bose-Einstein Condensate are both important fields in modern physics.Casimir effect is a microscopically observable quantum fluctuation effect.Bose-Einstein Condensate is a low temperature form.It was chosen as one of the greatest discoveries in physics in the 20 th century.There is also a close relationship between the Casimir effect and Bose-Einstein Condensate.Casimir effect exits in Bose-Einstein Condensate which can help improve the measurement of Casimir effect.However,contaminants will inevitably be doped in the process of preparing Bose-Einstein Condensates.Therefore,the effect of these contaminants in condensate has been paid more attention.Oshmyansky proposed that there is a similar interaction as Casimir force in the impurity of Bose-Einstein Condensate.In the one-dimensional ideal Bose-Einstein Condensate,if the contaminant is regarded as the boundary of the condensate,the energy of the condensate is related to the impurity distance.At the same time,the contaminants will also produce force interaction,which called Casimir-like force.With five different boundaries,the Casimir-like force which act on contaminants in Bose-Einstein condensate have been studied in this paper.This paper changes the usual method of studying different boundary conditions separately.Instead,the paper unifies the expressions of frequency related to each boundary by introducing some parameter.On the basis of Oshmyansky's theoretical model,the expressions of the Casimir-like force correspond to the five boundaries when the Bose-Einstein Condensation system at absolute zero degree and finite temperature are calculated separately.The results show that the force is related to the distance and the mass of boson.When the type of boundary is changed,the attractive or repulsive properties of Casimir-like force will also change.Despite the variation of force is not affected by the type of boundary condition,different type of boundary condition can influence the speed of force varying with the distance.As the mass increases,the variation trend of Casimir-like force is also greatly affected by the boundary conditions.Meanwhile,Casimir-like force is relevant to the temperature.