Napiórkowski Marek, Piasecki Jarosław
Faculty of Physics, Institute of Theoretical Physics, University of Warsaw, Hoża 69, PL-00-681 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061105. doi: 10.1103/PhysRevE.84.061105. Epub 2011 Dec 5.
We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand-canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region, the force decays exponentially fast when distance D between the walls tends to infinity. When the Bose-Einstein condensation point is approached, the decay length in the exponential law diverges with critical exponent ν(IMP) = 1, which differs from the perfect gas case where ν(P) = 1/2. In the two-phase region, the Casimir force is long range and decays following the power law D(-3), with the same amplitude as in the perfect gas.
我们展示了对包含在两个无限平行平面壁之间的非理想（平均场）玻色气体中卡西米尔效应的研究。卡西米尔力的推导源于在周期性、狄利克雷和诺伊曼边界条件下，使用最速下降法计算过量巨正则自由能密度。在单相区域，当壁之间的距离(D)趋于无穷大时，力以指数形式快速衰减。当接近玻色 - 爱因斯坦凝聚点时，指数定律中的衰减长度以临界指数(\nu(IMP)=1)发散，这与理想气体情况不同，在理想气体中(\nu(P)=1/2)。在两相区域，卡西米尔力是长程的，并遵循幂律(D^{-3})衰减，其幅度与理想气体中的相同。
