Non-universal Casimir forces at approach to Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions. (English) Zbl 1460.81096
Summary: We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance \(D\). The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is \(\sim 1/D^2\) with a non-universal amplitude. The next order correction is \(\sim \ln D/D^3\). These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is \(\sim 1/D^3\) with a universal amplitude. We associate this discrepancy with the D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.
MSC:
| 81T55 | Casimir effect in quantum field theory |
| 81V73 | Bosonic systems in quantum theory |
| 82D05 | Statistical mechanics of gases |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 35G15 | Boundary value problems for linear higher-order PDEs |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
References:
| [1] | Krech, M., Casimir Effect in Critical Systems (1994), Singapore: World Scientific, Singapore |
| [2] | Mostepanienko, VM; Trunov, NN, The Casimir Effect and Its Applications (1997), Oxford: Clarendon Press, Oxford |
| [3] | Kardar, M.; Golestanian, R., The “friction” of vacuum, and other fluctuation-induced forces, Rev. Mod. Phys., 71, 1233 (1999) · doi:10.1103/RevModPhys.71.1233 |
| [4] | Bordag, M., Mohideen, U., Mostepanienko, V.M.: New developments in the Casimir effect. Phys. Rep. 353, (2001) · Zbl 0972.81212 |
| [5] | Brankov, JG; Dantchev, DM; Tonchev, NS, The Theory of Critical Phenomena in Finite-Size Systems—Scaling and Quantum Effects (2000), Singapore: World Scientific, Singapore · Zbl 0967.82002 |
| [6] | Hertlein, C.; Helden, L.; Gambassi, A.; Dietrich, S.; Bechinger, C., Direct measurement of critical Casimir forces, Nature, 451, 172 (2008) · doi:10.1038/nature06443 |
| [7] | Gambassi, A., The Casimir effect: from quantum to critical fluctuations, J. Phys. Conf. Ser., 161, 012037 (2009) · doi:10.1088/1742-6596/161/1/012037 |
| [8] | Landau, LD; Lifshitz, EM, Statistical Physics (2013), Oxford: Pergamon Press, Oxford |
| [9] | Ziff, RM; Uhlenbeck, GE; Kac, M., The ideal Bose-Einstein gas, revisited, Phys. Rep., 32, 169 (1977) · doi:10.1016/0370-1573(77)90052-7 |
| [10] | Landau, LJ; Wilde, IF, On the Bose-Einstein condensation of an ideal gas, Commun. Math. Phys., 70, 43 (1979) · doi:10.1007/BF01220501 |
| [11] | Robinson, D., Bose-Einstein condensation with attractive boundary conditions, Commun. Math. Phys., 50, 53 (1976) · doi:10.1007/BF01608554 |
| [12] | Bratelli, O.; Robinson, DW, Operator Algebras and Quantum Statistical Mechanics (1981), Berlin: Springer, Berlin · Zbl 0463.46052 |
| [13] | Martin, PA; Zagrebnov, VA, The Casimir effect for the Bose-gas in slabs, Europhys. Lett., 73, 15 (2006) · doi:10.1209/epl/i2005-10357-x |
| [14] | We thank the Referee for pointing to us this perspective |
| [15] | Beau, M.; Zagrebnov, VA, The second critical density and anisotropic generalised condensation, Cond. Matter Phys., 13, 23003 (2010) · doi:10.5488/CMP.13.23003 |
| [16] | Zagrebnov, V.A.: Bose-Einstein condensation: geometry and external potentials. In: Cichocki, B., Napiórkowski, M., Piasecki, J. (eds.), 3rd Warsaw School of Statistical Physics, Kazimierz Dolny, Poland, June 27th-July 4th, 2009. pp. 164-194. Warsaw University Press, Warsaw (2010) |
| [17] | Napiórkowski, M.; Piasecki, J., On the relation between Casimir forces and bulk correlations, J. Stat. Phys., 156, 1136 (2014) · Zbl 1302.82107 · doi:10.1007/s10955-014-1050-7 |
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