The non-equilibrium behavior of pseudo-Casimir forces. (English) Zbl 1459.82216
Summary: While techniques for computing thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of free classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.
MSC:
| 82C27 | Dynamic critical phenomena in statistical mechanics |
References:
| [1] | Kardar M and Golestanian R 1999 Rev. Mod. Phys.71 1233 · doi:10.1103/RevModPhys.71.1233 |
| [2] | Mostepanenko V M and Trunov N N 1997 The Casimir Effect and its Applications (Oxford: Oxford University Press) |
| [3] | Milton K A 2001 The Casimir Effect: Physical Manifestations of Zero-Point Energy (Singapore: World Scientific) · Zbl 1025.81003 · doi:10.1142/9789812810526 |
| [4] | Fisher M E and de Gennes P G 1978 C. R. Acad. Sci. Paris B 287 207 |
| [5] | Hertlein C, Helden L, Gambassi A, Dietrich S and Bechinger C 2008 Nature451 172 · doi:10.1038/nature06443 |
| [6] | Garcia R and Chan M H W 1999 Phys. Rev. Lett.83 1187 · doi:10.1103/PhysRevLett.83.1187 |
| [7] | Ganshin A, Scheidemantel S, Garcia R and Chan M H W 2006 Phys. Rev. Lett.97 075301 · doi:10.1103/PhysRevLett.97.075301 |
| [8] | Maciolek A, Gambassi A and Dietrich S 2007 Phys. Rev. E 76 031124 · doi:10.1103/PhysRevE.76.031124 |
| [9] | Zandi R, Shackell A, Rudnick J, Kardar M and Chayes L P 2007 Phys. Rev. E 76 030601 · doi:10.1103/PhysRevE.76.030601 |
| [10] | Zandi R, Rudnick J and Kardar M 2004 Phys. Rev. Lett.93 155302 · doi:10.1103/PhysRevLett.93.155302 |
| [11] | Hucht A 2007 Phys. Rev. Lett.99 185301 · doi:10.1103/PhysRevLett.99.185301 |
| [12] | Vasilyev O, Gambassi A, Maciolek A and Dietrich S 2007 Europhys. Lett.80 60009 · doi:10.1209/0295-5075/80/60009 |
| [13] | Ajdari A, Peliti L and Prost J 1991 Phys. Rev. Lett.66 1481 · doi:10.1103/PhysRevLett.66.1481 |
| [14] | Bartolo D, Adjari A and Fournier J B 2003 Phys. Rev. E 67 061112 · doi:10.1103/PhysRevE.67.061112 |
| [15] | Najafi A and Golestanian R 2004 Europhys. Lett.68 776 · doi:10.1209/epl/i2004-10275-5 |
| [16] | Gambassi A and Dietrich S 2006 J. Stat. Phys.123 929 · Zbl 1103.82017 · doi:10.1007/s10955-006-9089-8 |
| [17] | Gambassi A 2008 Eur. Phys. J. B 64 379 · doi:10.1140/epjb/e2008-00043-y |
| [18] | Bartolo D, Adjari A, Fournier J B and Golestanian R 2002 Phys. Rev. Lett.89 230601 · doi:10.1103/PhysRevLett.89.230601 |
| [19] | Brito R, Marini Bettolo Marconi U and Soto R 2007 Phys. Rev. E 76 011113 · doi:10.1103/PhysRevE.76.011113 |
| [20] | Buenzli P R and Soto R 2008 Phys. Rev. E 78 020102(R) · doi:10.1103/PhysRevE.78.020102 |
| [21] | Krech M and Dietrich S 1992 Phys. Rev. A 46 1886 · doi:10.1103/PhysRevA.46.1886 |
| [22] | Gradshteyn I S and Ryzhik I M 2000 Table of Integrals Series and Products (New York: Academic) · Zbl 0981.65001 |
| [23] | Dean D S and Gopinathan A 2009 in preparation |
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