Particle Creation by a Moving Boundary with Robin Boundary Condition

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position

Topological Properties from Einstein's Equations?

In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to immersion. Through of an algorithm and the implementation into algebraic computing system we calculate normal vectors from the immersion to find out the second fundamental form. We make a application for space-time with spherical symmetry and static. We solve the equations of Einstein to the vacuum and we obtain space-times with different topologies.Comment: 7 pages, accepted for publication in Int. J. Mod. Phys.

Inertial forces in the Casimir effect with two moving plates

We combine linear response theory and dimensional regularization in order to derive the dynamical Casimir force in the low frequency regime. We consider two parallel plates moving along the normal direction in $D-$dimensional space. We assume the free-space values for the mass of each plate to be known, and obtain finite, separation-dependent mass corrections resulting from the combined effect of the two plates. The global mass correction is proportional to the static Casimir energy, in agreement with Einstein's law of equivalence between mass and energy for stressed rigid bodies.Comment: 9 pages, 1 figure; title and abstract changed; to appear in Physical Review

Quantum radiation in a plane cavity with moving mirrors

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values

Radiation Pressure as a Source of Decoherence

We consider the interaction of an harmonic oscillator with the quantum field via radiation pressure. We show that a `Schrodinger cat' state decoheres in a time scale that depends on the degree of `classicality' of the state components, and which may be much shorter than the relaxation time scale associated to the dynamical Casimir effect. We also show that decoherence is a consequence of the entanglement between the quantum states of the oscillator and field two-photon states. With the help of the fluctuation-dissipation theorem, we derive a relation between decoherence and damping rates valid for arbitrary values of the temperature of the field. Coherent states are selected by the interaction as pointer states.Comment: 14 pages, 3 figures, RevTex fil

Dynamical Casimir effect with Dirichlet and Neumann boundary conditions

We derive the radiation pressure force on a non-relativistic moving plate in 1+1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the force for a thermal field state as an example for this case. On the other hand, a coherent state introduces a phase reference, and the two types of BC lead to different results.Comment: 12 page

Shallow extra mixing in solar twins inferred from Be abundances

Lithium and beryllium are destroyed at different temperatures in stellar interiors. As such, their relative abundances offer excellent probes of the nature and extent of mixing processes within and below the convection zone. We determine Be abundances for a sample of eight solar twins for which Li abundances have previously been determined. The analyzed solar twins span a very wide range of age, 0.5-8.2 Gyr, which enables us to study secular evolution of Li and Be depletion. We gathered high-quality UVES/VLT spectra and obtained Be abundances by spectral synthesis of the Be II 313 nm doublet. The derived beryllium abundances exhibit no significant variation with age. The more fragile Li, however, exhibits a monotonically decreasing abundance with increasing age. Therefore, relatively shallow extra mixing below the convection zone is necessary to simultaneously account for the observed Li and Be behavior in the Sun and solar twins