Conformally invariant wave-equations and massless fields in de Sitter spacetime

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.Comment: 21 pages, LaTeX, some details adde

Monitoring of the content of manganese in soils and agricultural plants of the central Chernozem Region of Russia

The paper deals with the analysis of long-term observations of the manganese distribution in the soils of the south-western part of the Central Chernozem region of Russia in the Belgorod regio

Resonant enhanced diffusion in time dependent flow

Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the absence of molecular diffusion, by anomalous transport. For the time-dependent flow considered here, resonances arise between their oscillations in time and either molecular diffusion or a mean flow. The effective diffusivities are calculated using multiscale techniques.Comment: 18 latex pages, 11 figure

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.Comment: 4 pages, 5 figure

On homothetic cosmological dynamics

We consider the homogeneous and isotropic cosmological fluid dynamics which is compatible with a homothetic, timelike motion, equivalent to an equation of state $\rho + 3P = 0$. By splitting the total pressure $P$ into the sum of an equilibrium part $p$ and a non-equilibrium part $\Pi$, we find that on thermodynamical grounds this split is necessarily given by $p = \rho$ and $\Pi = - (4/3)\rho$, corresponding to a dissipative stiff (Zel'dovich) fluid.Comment: 8 pages, to be published in Class. Quantum Gra

The Scalar Field Kernel in Cosmological Spaces

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.Comment: 13 pages, 1 figur

Manifestation of the Arnol'd Diffusion in Quantum Systems

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled non-linear oscillators one of which is governed by an external periodic force with two frequencies. In the classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance, and leads to an increase of total energy of the system. We show that the quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics, and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.Comment: RevTex, 4 pages including 7 ps-figures, corrected forma

Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics

Trans-Planckian wimpzillas

Two previously proposed conjectures--gravitational trans-Planckian particle creation in the expanding universe, and the existence of ultra-heavy stable particles with masses up to the Planck scale (wimpzillas)--are combined in a proposal for trans-Planckian particle creation of wimpzillas. This new scenario leads to a huge enhancement in their production compared to mechanisms put forward earlier. As a result, it requires the trans-Planckian particle creation parameter to be rather small to avoid overproduction of such particles, much less than that is required for observable effects in the primordial perturbation spectrum. This ensures also that wimpzillas are mainly created at the end of primordial inflation. Conditions under which trans-Planckian wimpzillas can constitute the present dark matter are determined.Comment: Replaced with the version to be published in JCAP. Division into sections introduced, discussion expanded, references added, conclusions unchange

Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions

We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti de Sitter space, and show that this perturbative information is not sufficient to describe the non-perturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent non-alternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full non-perturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion.Comment: 18 page