平行板受限下伊辛普适类临界卡西米尔力的一种计算方法
|
摘要
研究统计力学中伊辛普适类的临界卡西米尔力。针对临界点上平行板几何约束下的伊辛普适类,基于欧拉-麦克劳林求和法发展了一套计算临界卡西米尔力的有效方法。结果表明,在平行板几何约束下,伊辛普适类临界卡西米尔力表现为以标度指数为-3的方式随板间距离衰减的长程吸引力。
Due to the constraints introduced by boundaries for the long range fluctuations in a massless field, a long-range fluctuation-induced effective force between boundaries is induced, and it is called the Casimir force. The classical Casimir force refers to the interaction between two conducting plates immersed in a vacuum, and it is originated from the quantum fluctuations of the electromagnetic field. In this work, we study the critical Casimir force for the Ising universality class in statistical mechanics. Specifically, we develop an effective method, namely, the Euler-Maclaurin summation method, to calculate the critical Casimir force between two parallel plates at the critical point of the Ising universality class. Our results demonstrate that, in this geometric set-up, the critical Casimir force behaves as a long-range attractive force with a scaling exponent of-3 with respect to the boundary distance.
Due to the constraints introduced by boundaries for the long range fluctuations in a massless field, a long-range fluctuation-induced effective force between boundaries is induced, and it is called the Casimir force. The classical Casimir force refers to the interaction between two conducting plates immersed in a vacuum, and it is originated from the quantum fluctuations of the electromagnetic field. In this work, we study the critical Casimir force for the Ising universality class in statistical mechanics. Specifically, we develop an effective method, namely, the Euler-Maclaurin summation method, to calculate the critical Casimir force between two parallel plates at the critical point of the Ising universality class. Our results demonstrate that, in this geometric set-up, the critical Casimir force behaves as a long-range attractive force with a scaling exponent of-3 with respect to the boundary distance.
引文
[1] Casimir H B G.On the attraction between two perfectly conducting plates[J].Proc Kon Ned Akad Wet,1948,51:793-795.
[2] Sparnaay M J.Measurements of attractive forces between flat plates[J].Physica,1958,24(6-10):751-764.
[3] Lamoreaux S K.Demonstration of the Casimir force in the 0.6 to 6 μm range[J].Physical Review Letters,1997,78(1):5-8.
[4] Mohideen U,Roy A.Precision measurement of the Casimir force from 0.1 to 0.9 μm[J].Physical Review Letters,1998,81(21):4 549-4 552.
[5] Plunien G,Müller B,Greiner W.The casimir effect[J].Physics Reports,1986,134(2/3):87-193.
[6] Elizalde E,Romeo A.Essentials of the Casimir effect and its computation[J].American Journal of Physics,1991,59:711-719.
[7] Kardar M,Golestanian R.The “friction” of vacuum,and other fluctuation-induced forces[J].Reviews of Modern Physics,1999,71(4):1 233-1 245.
[8] Bordag M,Klimchitskaya G L,Mohideen U,et al.Advances in the Casimir effect[M].Oxford:OUP Oxford,2009.
[9] Lamoreaux S K.The Casimir force:background,experiments,and applications[J].Reports on Progress in Physics,2004,68(1):201-236.
[10] Fisher M E,De Gennes P G.Wall phenomena in a critical binary mixture[J].Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences Serie B,1978,287(8):207-209.
[11] Aminov A,Kafri Y,Kardar M.Fluctuation-induced forces in nonequilibrium diffusive dynamics[J].Physical Review Letters,2015,114(23):230 602.
[12] Uchida N.Casimir effect in fluids above the isotropic-lamellar transition[J].Physical Review Letters,2001,87(21):216 101.
[13] Li H,Kardar M.Fluctuation-induced forces between manifolds immersed in correlated fluids[J].Physical Review A,1992,46(10):6 490-6 500.
[14] Zee A.Quantum field theory in a nutshell[M].Princeton:Princeton university press,2010.
[2] Sparnaay M J.Measurements of attractive forces between flat plates[J].Physica,1958,24(6-10):751-764.
[3] Lamoreaux S K.Demonstration of the Casimir force in the 0.6 to 6 μm range[J].Physical Review Letters,1997,78(1):5-8.
[4] Mohideen U,Roy A.Precision measurement of the Casimir force from 0.1 to 0.9 μm[J].Physical Review Letters,1998,81(21):4 549-4 552.
[5] Plunien G,Müller B,Greiner W.The casimir effect[J].Physics Reports,1986,134(2/3):87-193.
[6] Elizalde E,Romeo A.Essentials of the Casimir effect and its computation[J].American Journal of Physics,1991,59:711-719.
[7] Kardar M,Golestanian R.The “friction” of vacuum,and other fluctuation-induced forces[J].Reviews of Modern Physics,1999,71(4):1 233-1 245.
[8] Bordag M,Klimchitskaya G L,Mohideen U,et al.Advances in the Casimir effect[M].Oxford:OUP Oxford,2009.
[9] Lamoreaux S K.The Casimir force:background,experiments,and applications[J].Reports on Progress in Physics,2004,68(1):201-236.
[10] Fisher M E,De Gennes P G.Wall phenomena in a critical binary mixture[J].Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences Serie B,1978,287(8):207-209.
[11] Aminov A,Kafri Y,Kardar M.Fluctuation-induced forces in nonequilibrium diffusive dynamics[J].Physical Review Letters,2015,114(23):230 602.
[12] Uchida N.Casimir effect in fluids above the isotropic-lamellar transition[J].Physical Review Letters,2001,87(21):216 101.
[13] Li H,Kardar M.Fluctuation-induced forces between manifolds immersed in correlated fluids[J].Physical Review A,1992,46(10):6 490-6 500.
[14] Zee A.Quantum field theory in a nutshell[M].Princeton:Princeton university press,2010.