/ 06 02 09 7 v 1 1 2 Fe b 20 06 Universal behavior of dispersion forces between two dielectric plates in the low - temperature limit

The universal analytic expressions in the limit of low temperatures (short separations) are obtained for the free energy, entropy and pressure between the two parallel plates made of any dielectric. The analytical proof of the Nernst heat theorem in the case of dispersion forces acting between dielectrics is provided. This permitted us to formulate the stringent thermodynamical requirement that must be satisfied in all models used in the Casimir physics. It is common knowledge that dispersion force is a quantum phenomenon which results from fluctuating (thermal) electromagnetic fields [1]. The most well known examples of dispersion interaction are the van der Waals [1] and the Casimir [2–4] forces. Dispersion forces play a very important role in surface phenomena, layered structures, colloid-substrate interactions, adhesion, foam formation and in stability of microelectromechanical systems [5–8]. Recently they were found to be of considerable significance in experiments on quantum reflection and Bose-Einstein condensation of ultracold atoms near different surfaces [9, 10]. Dispersion forces create a free-energy difference between materials in the normal and the superconducting phase which may influence the value of the critical magnetic field [11]. They are responsible for the interaction of atoms and molecules with nanostructures like carbon nanotubes [12]. The theoretical description of all above-listed phenomena is based on the Lifshitz theory [13]. This theory presents the dispersion force, free energy and entropy between the two plates in terms of their dielectric permittivity ε(iξ) along the entire imaginary frequency axis including zero frequency. ε(iξ) is found by means of the dispersion relation using the experimental optical data for the complex refractive index [14]. As these data are available only within a restricted frequency region, the use of some theoretical models of dielectric response becomes unavoidable. Different extrapolations of data outside the regions where they are measured (e.g., to low frequencies) may lead,