760 research outputs found
Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime
We first derive the relation between the eikonal approximation to the Maxwell
wave equations in an inhomogeneous anisotropic medium and geodesic motion in a
three dimensional Riemannian manifold using a method which identifies the
symplectic structure of the corresponding mechanics. We then apply an analogous
method to the five dimensional generalization of Maxwell theory required by the
gauge invariance of Stueckelberg's covariant classical and quantum dynamics to
demonstrate, in the eikonal approximation, the existence of geodesic motion for
the flow of mass in a four dimensional pseudo-Riemannian manifold. These
results provide a foundation for the geometrical optics of the five dimensional
radiation theory and establish a model in which there is mass flow along
geodesics. Finally we discuss the case of relativistic quantum theory in an
anisotropic medium as well. In this case the eikonal approximation to the
relativistic quantum mechanical current coincides with the geodesic flow
governed by the pseudo-Riemannian metric obtained from the eikonal
approximation to solutions of the Stueckelberg-Schr\"odinger equation. This
construction provides a model for an underlying quantum mechanical structure
for classical dynamical motion along geodesics on a pseudo-Riemannian manifold.
The locally symplectic structure which emerges is that of Stueckelberg's
covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit
Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
The renewed interest in the foundations of quantum statistical mechanics in
recent years has led us to study John von Neumann's 1929 article on the quantum
ergodic theorem. We have found this almost forgotten article, which until now
has been available only in German, to be a treasure chest, and to be much
misunderstood. In it, von Neumann studied the long-time behavior of macroscopic
quantum systems. While one of the two theorems announced in his title, the one
he calls the "quantum H-theorem", is actually a much weaker statement than
Boltzmann's classical H-theorem, the other theorem, which he calls the "quantum
ergodic theorem", is a beautiful and very non-trivial result. It expresses a
fact we call "normal typicality" and can be summarized as follows: For a
"typical" finite family of commuting macroscopic observables, every initial
wave function from a micro-canonical energy shell so evolves that for
most times in the long run, the joint probability distribution of these
observables obtained from is close to their micro-canonical
distribution.Comment: 34 pages LaTeX, no figures; v2: minor improvements and additions. The
English translation of von Neumann's article is available as arXiv:1003.213
Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is
derived. The derivation applies to the bistable, excitable, and the Turing
unstable regimes. In the bistable case stability thresholds are obtained for
the Eckhaus and the zigzag instabilities and for the transition to traveling
waves. Neutral stability curves demonstrate the destabilization of stationary
planar patterns at low wavenumbers to zigzag and traveling modes. Numerical
solutions of the model system support the theoretical findings
Gravitational Wave Spectrum in Inflation with Nonclassical States
The initial quantum state during inflation may evolve to a highly squeezed
quantum state due to the amplification of the time-dependent parameter,
, which may be the modified dispersion relation in
trans-Planckian physics. This squeezed quantum state is a nonclassical state
that has no counterpart in the classical theory. We have considered the
nonclassical states such as squeezed, squeezed coherent, and squeezed thermal
states, and calculated the power spectrum of the gravitational wave
perturbation when the mode leaves the horizon.Comment: 21 page
Probing neutrino masses with future galaxy redshift surveys
We perform a new study of future sensitivities of galaxy redshift surveys to
the free-streaming effect caused by neutrino masses, adding the information on
cosmological parameters from measurements of primary anisotropies of the cosmic
microwave background (CMB). Our reference cosmological scenario has nine
parameters and three different neutrino masses, with a hierarchy imposed by
oscillation experiments. Within the present decade, the combination of the
Sloan Digital Sky Survey (SDSS) and CMB data from the PLANCK experiment will
have a 2-sigma detection threshold on the total neutrino mass close to 0.2 eV.
This estimate is robust against the inclusion of extra free parameters in the
reference cosmological model. On a longer term, the next generation of
experiments may reach values of order sum m_nu = 0.1 eV at 2-sigma, or better
if a galaxy redshift survey significantly larger than SDSS is completed. We
also discuss how the small changes on the free-streaming scales in the normal
and inverted hierarchy schemes are translated into the expected errors from
future cosmological data.Comment: 14 pages, 7 figures. Added results with the KAOS proposal and 1
referenc
Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard
Square billiards are quantum systems complying with the dynamical
quantum-classical correspondence. Hence an initially localized wavefunction
launched along a classical periodic orbit evolves along that orbit, the
spreading of the quantum amplitude being controlled by the spread of the
corresponding classical statistical distribution. We investigate wavepacket
dynamics and compute the corresponding de Broglie-Bohm trajectories in the
quantum square billiard. We also determine the trajectories and statistical
distribution dynamics for the equivalent classical billiard. Individual Bohmian
trajectories follow the streamlines of the probability flow and are generically
non-classical. This can also hold even for short times, when the wavepacket is
still localized along a classical trajectory. This generic feature of Bohmian
trajectories is expected to hold in the classical limit. We further argue that
in this context decoherence cannot constitute a viable solution in order to
recover classicality.Comment: Figures downgraded to low resolution; To be published in Found. Phys.
(2009)
Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators
We study domain growth in a nonlinear optical system useful to explore
different scenarios that might occur in systems which do not relax to
thermodynamic equilibrium. Domains correspond to equivalent states of different
circular polarization of light. We describe three dynamical regimes: a
coarsening regime in which dynamical scaling holds with a growth law dictated
by curvature effects, a regime in which localized structures form, and a regime
in which polarization domain walls are modulationally unstable and the system
freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure
Classical Evolution of Quantum Elliptic States
The hydrogen atom in weak external fields is a very accurate model for the
multiphoton excitation of ultrastable high angular momentum Rydberg states, a
process which classical mechanics describes with astonishing precision. In this
paper we show that the simplest treatment of the intramanifold dynamics of a
hydrogenic electron in external fields is based on the elliptic states of the
hydrogen atom, i.e., the coherent states of SO(4), which is the dynamical
symmetry group of the Kepler problem. Moreover, we also show that classical
perturbation theory yields the {\it exact} evolution in time of these quantum
states, and so we explain the surprising match between purely classical
perturbative calculations and experiments. Finally, as a first application, we
propose a fast method for the excitation of circular states; these are
ultrastable hydrogenic eigenstates which have maximum total angular momentum
and also maximum projection of the angular momentum along a fixed direction. %Comment: 8 Pages, 2 Figures. Accepted for publication in Phys. Rev.
Pink‐ and orange‐pigmented Planctomycetes produce saproxanthin‐type carotenoids including a rare C45 carotenoid
Planctomycetes, are ubiquitous and environmentally important Gram-negative aquatic bacteria with key roles in global carbon and nitrogen cycles. Many planctomycetal species have a pink or orange colour and have been suggested to produce carotenoids. Potential applications as food colorants or anti-oxidants have been proposed. Hitherto, the planctomycetal metabolism is largely unexplored and the strain pigmentation has not been identified. For a holistic view on the complex planctomycetal physiology we analyzed carotenoid profiles of the pink-pigmented strain Rhodopirellula rubra LF2T and of the orange strain Rubinisphaera brasiliensis Gr7. During LC-MS/MS analysis of culture extracts we were able to identify three saproxanthin-type carotenoids including a rare C45 carotenoid. These compounds, saproxanthin, dehydroflexixanthin and 2’-isopentenyldehydrosaproxanthin, derive from the common carotenoid precursor lycopene and are characterized by related end groups, namely a 3-hydroxylated β-carotene-like cyclohexene ring as one end group and simple hydration on the other end of the molecule. Based on the observed molecule structure we present putative pathways for their biosynthesis. Results support Planctomycetes as a promising, yet mostly untapped source of carotenoids
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