Thermodynamics of the Casimir effect

A complete thermodynamic treatment of the Casimir effect is presented. Explicit expressions for the free and the internal energy, the entropy and the pressure are discussed. As an example we consider the Casimir effect with different temperatures between the plates (T) resp. outside of them (T'). For T'<T the pressure of heat radiation can eventually compensate the Casimir force and the total pressure can vanish. We consider both an isothermal and an adiabatic treatment of the interior region. The equilibrium point (vanishing pressure) turns out instable in the isothermal case. In the adiabatic situation we have both an instable and a stable equilibrium point, if T'/T is sufficiently small. Quantitative aspects are briefly discussed. Received 24 February 1999 and Received in final form 26 April 1999     

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the (n) vector ϕ⁴ model, with long-range interaction decaying algebraically with the interparticle distance r like r ^{-d - σ}, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T _c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d _< = σ) and the upper ( d _> = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001     

Heat transport through a quantum dot with one-dimensional interacting leads under Coulomb blockade regime

The peculiarities of a low temperature heat transfer through a ballistic quantum dot (a double potential barrier) with interacting leads due to a long-range Coulomb interaction (in the geometrical capacitance approach) are considered. It is found that the thermal conductance K shows periodic peaks as a function of the electrostatic potential of a dot at low temperatures. At the peak maximum it is whereas near the minimum it is . Near the peak maximum the dependence K(T) is essentially nonmonotonic at the temperatures correspondent to the level spacing in the quantum dot. Received 20 October 1999 and Received in final form 20 January 2000     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Finite-temperature Casimir effect in piston geometry and its classical limit

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with perfect electric-conductor and perfect magnetic-conductor boundary conditions. The Casimir energy in a rectangular cavity is derived using the cut-off method. It is shown that the divergent part of the Casimir energy does not contribute to the Casimir force acting on the piston, thus renders an unambiguously defined Casimir force acting on the piston. At any temperature, it is found that the Casimir force acting on the piston increases from −∞ to 0 when the separation a between the piston and the opposite wall increases from 0 to ∞. This implies that the Casimir force is always an attractive force pulling the piston towards the closer wall, and the magnitude of the force gets larger as the separation a gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan–Boltzmann (or black-body radiation) term which is of order T ^d+1, it is found that the contributions of this term from the two regions separating the piston cancel with each other in the case of piston. The high-temperature leading-order term of the Casimir force acting on the piston is of order T, which shows that the Casimir force has a nontrivial classical ℏ→0 limit. Explicit formulas for the classical limit are computed.     

Some metallic properties in the framework of Tsallis generalized statistics

Some metallic quantities are calculated on the grounds of Tsallis generalized statistics: the specific heat at constant volume, c _V (T); the chemical potential, ; the Pauli paramagnetic susceptibility, and the Korringa constant, . First it is found that for a general value of q, the Sommerfeld expansion series will exhibit both, odd and even terms, contrary to what is obtained if we use the Fermi-Dirac (FD) statistics, where only even terms appear. It follows that: (i) the specific heat coefficient, , is q-dependent, but the temperature dependence of c_V remains linear, as in the FD case; (ii) the Fermi energy, , differs from the chemical potential by a linear term in T, and not quadratic, as in FD, the same happening for ; (iii) the Korringa constant is q-dependent, but not T-dependent. In the limit the results of FD statistics are recovered. Metallic thin films and multilayers exhibiting fractal surface structures are possible systems where the present results could be tested. Received 30 June 1999 and Received in final form 7 September 1999     

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature T_c. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy E _F is sufficiently small. We calculate the normal state spin susceptibility χ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate . We find that as soon as is comparable to E _F, χ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB₂ samples can be naturally explained in terms of small E _F values associated with the σ-bands of the boron plane, sustaining therefore the hypothesis that MgB₂ is a nonadiabatic metal. Received 31 July 2002 / Received in final form 21 September 2002 Published online 31 December 2002     

Casimir force between metallic mirrors

We study the influence of finite conductivity of metals on the Casimir effect. We put the emphasis on explicit theoretical evaluations which can help comparing experimental results with theory. The reduction of the Casimir force is evaluated for plane metallic plates. The reduction of the Casimir energy in the same configuration is also calculated. It can be used to infer the reduction of the force in the plane-sphere geometry through the “proximity theorem”. Frequency dependent dielectric response functions of the metals are represented either by the simple plasma model or, more accurately, by using the optical data known for the metals used in recent experiments, that is Al, Au and Cu. In the two latter cases, the results obtained here differ significantly from those published recently. Received 30 July 1999     

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 1999