Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

Temperature correction to the Casimir force in cryogenic range and anomalous skin effect

Temperature correction to the Casimir force is considered for real metals at low temperatures. With the temperature decrease the mean free path for electrons becomes larger than the field penetration depth. In this condition description of metals with the impedance of anomalous skin effect is shown to be more appropriate than with the permittivity. The effect is crucial for the temperature correction. It is demonstrated that in the zero frequency limit the reflection coefficients should coincide with those of ideal metal if we demand the entropy to be zero at T=0. All the other prescriptions discussed in the literature for the $n=0$ term in the Lifshitz formula give negative entropy. It is shown that the temperature correction in the region of anomalous skin effect is not suppressed as it happens in the plasma model. This correction will be important in the future cryogenic measurements of the Casimir force.Comment: 12 pages, 2 figures, to be published in Phys. Rev.

Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals

We give a rigorous analytical derivation of low-temperature behavior of the Casimir entropy in the framework of the Lifshitz formula combined with the Drude dielectric function. An earlier result that the Casimir entropy at zero temperature is not equal to zero and depends on the parameters of the system is confirmed, i.e. the third law of thermodynamics (the Nernst heat theorem) is violated. We illustrate the resolution of this thermodynamical puzzle in the context of the surface impedance approach by several calculations of the thermal Casimir force and entropy for both real metals and dielectrics. Different representations for the impedances, which are equivalent for real photons, are discussed. Finally, we argue in favor of the Leontovich boundary condition which leads to results for the thermal Casimir force that are consistent with thermodynamics.Comment: 24 pages, 3 figures, accepted for publication in Phys. Rev.

X-ray and neutron diffraction studies of coupled structural phase transitions in DyBaCo2_{2}O5.5_{5.5}

A structural transition at $T\approx 322$ K from the $Pmmm$ to $Pmma$ phase is found to coincide with an anomaly of resistivity. Another structural phase transition doubling the lattice parameter $c$, which has been postulated earlier to accompany a low-temperature magnetic transition in TbBaCo$_{2}$O$_{5.5}$, is observed in a single crystal DbBaCo$_{2}$O$_{5.5}$ by means of the X-ray and neutron diffraction. The low temperature phase does not belong to the space group $Pcca$ that has been chosen earlier as the highest subgroup of the $Pmma$. The transition is of the first order with the temperature hysteresis, between $T\approx 100$ and $T\approx 200$ K, which probably explains anomalous magnetic properties in this temperature range.Comment: 6 pages, 4 figure

Epidemic Diseases of Fruit Trees in Illinois 1922-1928

From 1921 through 1928, a survey was made in Illinois of the epidemic diseases of fruit-trees. During these years, methods of measuring the epidemics had to be devised, tested, and perfected; in every year the epidemics were measured with the means at hand, and the measurements were recorded according to definite plans. The full results of this survey are now reported in the text of this paper.published or submitted for publicationis peer reviewe

Surface-impedance approach solves problems with the thermal Casimir force between real metals

The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics which are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates are performed at different separations and temperatures. It is argued that the surface impedance approach lays a reliable framework for the future measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude model attains at zero temperature a positive value which depends on the parameters of a system, i.e., the Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test, whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates. The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer predicted from this impedance is several times less than previous predictions due to different contributions from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula is discussed. It is concluded that new measurements of radiative heat transfer are required to find out the adequate description of a metal in the theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.

Energy Independent Solution to the Solar Neutrino Anomaly including the SNO data

The global data on solar neutrino rates and spectrum, including the SNO charged current rate, can be explained by LMA, LOW or the energy independent solution -- corresponding to near-maximal mixing. All the three favour a mild upward renormalisation of the Cl rate. A mild downward shift of the $B$ neutrino flux is favoured by the energy independent and to a lesser extent the LOW solution, but not by LMA. Comparison with the ratio of SK elastic and SNO charged current scattering rates favours the LMA over the other two solutions, but by no more than $1.5\sigma$.Comment: 18 pages, latex, 3 figure

Higher order conductivity corrections to the Casimir force

The finite conductivity corrections to the Casimir force in two configurations are calculated in the third and fourth orders in relative penetration depth of electromagnetic zero oscillations into the metal. The obtained analytical perturbation results are compared with recent computations. Applications to the modern experiments are discussed.Comment: 15 pages, 4 figure

Analytic approach to the thermal Casimir force between metal and dielectric

The analytic asymptotic expressions for the Casimir free energy, pressure and entropy at low temperature in the configuration of one metal and one dielectric plate are obtained. For this purpose we develop the perturbation theory in a small parameter proportional to the product of the separation between the plates and the temperature. This is done using both the simplified model of an ideal metal and of a dielectric with constant dielectric permittivity and for the realistic case of the metal and dielectric with frequency-dependent dielectric permittivities. The analytic expressions for all related physical quantities at high temperature are also provided. The obtained analytic results are compared with numerical computations and good agreement is found. We demonstrate for the first time that the Lifshitz theory, when applied to the configuration of metal-dielectric, satisfies the requirements of thermodynamics if the static dielectric permittivity of a dielectric plate is finite. If it is infinitely large, the Lifshitz formula is shown to violate the Nernst heat theorem. The implications of these results for the thermal quantum field theory in Matsubara formulation and for the recent measurements of the Casimir force between metal and semiconductor surfaces are discussed.Comment: 34 pages, 3 figures, elsart.cls is used, to appear in Ann. Phys. (N.Y.), 200