Narrow Results

In this research, a general formula for the Casimir force between ideal metal plate and a dissipative dielectric slab has been obtained. The dielectric function of the slab is assumed to be an arbitrary complex function of frequency satisfying Kramers–Kronig relations. A classical expression for the radiation pressure of the vacuum fields on the slab is presented by using the Maxwell stress tensor. With the transition to the quantum domain and using the fluctuation dissipation theorem and Kubo's formula, the resulting expression is written in terms of the imaginary part of the vector potential Green functions components of the system. Finally, by computing the Green function, the Casimir force on the slab is obtained. This formalism enables us to calculate the Casimir force without resorting to the explicit form of the field operators. The general expression is confirmed by limiting and comparing with one of the previous works.

We study the bifurcations of three-dimensional periodic motions from two-dimensional orbits of small particles in the neighborhood of a system that consists of three major bodies being always in syzygy. We assume that two of them have equal masses and are located at equal distances from the third body which has a different mass. All or some of the primaries are radiation sources and therefore apart from gravitational forces, we also consider forces that result from radiation. We apply the method of vertical critical stability in order to find the families of three-dimensional periodic orbits that bifurcate from families of planar periodic motions. Consequently, we study the parametric variations of the bifurcation points.

We study the evolution of the regions where three-dimensional motions of a small body are allowed in the Copenhagen case of the restricted three-body problem where one or both primaries, are radiation sources. We discuss the bifurcations in the topology of the zero-velocity surfaces, as well as in the trapping regions of the particle motion for various cases.

We consider the three-dimensional motion of a massless particle in a regular polygon formation of N primary bodies, one of which is located at the system's center of mass. Assuming that the central primary is a radiation source, we apply the simplified theory suggested by Radzievskii, in order to study the effect of radiation pressure in the three-dimensional dynamics of the system. We particularly study the evolution of the zero-velocity surfaces for various values of the radiation coefficient b₀ and investigate also the cases with b₀ > 1 (that is, radiation surpasses gravity) since for these cases, significant changes in the dynamics occur. We then locate numerically the onset of three-dimensional periodic motion from planar periodic motion by calculating the orbits' vertical critical stability. Many families of three-dimensional periodic motions are presented and the regions of the three-dimensional space where these motions take place, are determined. We subsequently investigate how the bifurcations from planar to three-dimensional periodic orbits are affected by the increase of the primary's radiation coefficient and how the overall dynamics of the system is affected by the value of the primaries' number N.

The Stefan–Boltzmann (SB) law relates the radiant emittance of an ideal black-body cavity at thermal equilibrium to the fourth power of the absolute temperature $T$ as $q=\sigma T^4$, with $\sigma =5.67\times 10^{-8}$Wm${}^{-2}$K${}^{-4}$ the SB constant, first estimated by Stefan to within $11\%$ of the present theoretical value. The law is an important achievement of modern physics since, following Planck [Ueber das Gesetz der Energieverteilung im Normalspectrum [On the law of distribution of energy in the normal spectrum], Ann. Phys. 4 (1901) 553–563], its microscopic derivation implies the quantization of the energy related to the electromagnetic field spectrum. Somewhat astonishing, Boltzmann presented his derivation in 1878 making use only of electrodynamic and thermodynamic classical concepts, apparently without introducing any quantum hypothesis (here called first Boltzmann paradox). By contrast, the Boltzmann derivation implies two assumptions not justified within a classical approach, namely: (i) the zero value of the chemical potential and (ii) the internal energy of the black body with a finite value and dependent from both temperature and volume. By using Planck [Ueber das Gesetz der Energieverteilung im Normalspectrum [On the law of distribution of energy in the normal spectrum], Ann. Phys. 4 (1901) 553–563] quantization of the radiation field in terms of a gas of photons, the SB law received a microscopic interpretation free from the above assumptions that also provides the value of the SB constant on the basis of a set of universal constants including the quantum action constant $h$. However, the successive consideration by Planck [Uber die Begründung des Gesetzes der schwarzen Strahlung [On the grounds of the law of black body radiation], Ann. Phys. 6 (1912) 642–656] concerning the zero-point energy contribution was found to be responsible of another divergence of the internal energy for the single photon mode at high frequencies. This divergence is of pure quantum origin and is responsible for a vacuum-catastrophe, to keep the analogy with the well-known ultraviolet catastrophe of the classical black-body radiation spectrum, given by the Rayleigh–Jeans law in 1900. As a consequence, from a rigorous quantum-mechanical derivation we would expect the divergence of the SB law (here called second Boltzmann paradox). Here, both the Boltzmann paradoxes are revised by accounting for both the quantum-relativistic photon gas properties, and the Casimir force.

We show how collective vibrational modes of two distant mirrors of an optical Fabry–Perot cavity can be entangled by the light bouncing between them. Such an entanglement can be demonstrated even at the macroscopic level of vibrational modes with an effective mass of the order of milligrams.

Optomechanical devices in which a flexible SiN membrane is placed inside an optical cavity allow for very high finesse and mechanical quality factor in a single device. They also provide fundamentally new functionality: the cavity detuning can be a quadratic function of membrane position. This enables a measurement of "position squared" (x²) and in principle a QND phonon number readout of the membrane. However, the readout achieved using a single transverse cavity mode is not sensitive enough to observe quantum jumps between phonon Fock states.

Here we demonstrate an x²-sensitivity that is orders of magnitude stronger using two transverse cavity modes that are nearly degenerate. We derive a first-order perturbation theory to describe the interactions between nearly-degenerate cavity modes and achieve good agreement with our measurements using realistic parameters. We also demonstrate theoretically that the x²-coupling should be easily tunable over a wide range.

The Lagrangian points for the Sun-Earth system are considered due to their special importance for the scientific community for the design of space missions. The location of the Lagrangian points with the trajectories and stability regions are computed numerically for the initial conditions very close to the points. The influence of belt, effect of radiation pressure due to the Sun and oblateness effect of second primary(finite body Earth) is presented for various values of parameters. The collinear points are asymptotically stable within a specific interval of time t correspond to the values of parameters and initial conditions.

Radiation pressure cross-sections for clumps of hollow bacterial grains with thin coatings of graphite are calculated using rigorous Guttler formulae. The carbonized skins are expected to form through exposure to solar ultraviolet radiation, but a limiting thickness of about 0.03 μm is determined by opacity effects. The ratios of radiation pressure to gravity P/G are calculated for varying sizes of the clumps and for varying thickness of the graphite coatings. Bacterial clumps and individual desiccated bacteria without coatings of radii in the range 0.3–8 μm have P/G ratios less than unity, whereas particles with coatings of 0.02 μm thickness have ratios in excess of unity. Such coatings also provide protection from damaging ultraviolet radiation. Putative cometary bacteria, such as have been recently collected in the stratosphere, are thus not gravitationally bound in the solar system provided they possess carbonised exterior coatings. They are rapidly expelled from the solar system reaching nearby protosolar nebulae in timescales of a few million years. Even with the most pessimistic assumptions galactic cosmic rays are unable to diminish viability to an extent that vitiates the continuity of panspermia.