On obtaining classical mechanics from quantum mechanics

Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum mechanical system naturally has the structure of an infinite dimensional symplectic manifold (`quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straight forwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and recovers the linear classical phase space $\mathbb{R}^{\mathrm{2N}}$. We report on how the procedure also allows extraction of non-linear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (Polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality.Comment: revtex4, 24 pages, no figures. In the version 2 certain technical errors in section I-B are corrected, the part on WKB (and section II-B) is removed, discussion of dynamics and semiclassicality is extended and references are added. Accepted for publication on Classical and Quantum Gravit

An overview of NASA intermittent combustion engine research

This paper overviews the current program, whose objective is to establish the generic technology base for advanced aircraft I.C. engines of the early 1990's and beyond. The major emphasis of this paper is on development of the past two years. Past studies and ongoing confirmatory experimental efforts are reviewed, which show unexpectly high potential when modern aerospace technologies are applied to inherently compact and balanced I.C. engine configurations. Currently, the program is focussed on two engine concepts the stratified-charge, multi-fuel rotary, and the lightweight two-stroke diesel. A review is given of contracted and planned high performance one-rotor and one-cylinder test engine work addressing several levels of technology. Also reviewed are basic supporting efforts, e.g., the development and experimental validation of computerized airflow and combustion process models, being performed in-house at Lewis Research Center and by university grants

Benchmarking calculations of excitonic couplings between bacteriochlorophylls

Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum-chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. We also caution against computationally optimizing a crystal structure before calculating couplings, as it can lead to large, uncontrollable errors. Understanding the unavoidable uncertainties can guard against striving for unrealistic precision; at the same time, detailed benchmarks can allow important qualitative questions--which do not depend on the precise values of the simulation parameters--to be addressed with greater confidence about the conclusions

The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects

We study the effect of primordial nongaussianity on large-scale structure, focusing upon the most massive virialized objects. Using analytic arguments and N-body simulations, we calculate the mass function and clustering of dark matter halos across a range of redshifts and levels of nongaussianity. We propose a simple fitting function for the mass function valid across the entire range of our simulations. We find pronounced effects of nongaussianity on the clustering of dark matter halos, leading to strongly scale-dependent bias. This suggests that the large-scale clustering of rare objects may provide a sensitive probe of primordial nongaussianity. We very roughly estimate that upcoming surveys can constrain nongaussianity at the level |fNL| <~ 10, competitive with forecasted constraints from the microwave background.Comment: 16 pages, color figures, revtex4. v2: added references and an equation. submitted to PRD. v3: simplified derivation, additional reference

Semi-classical States in Homogeneous Loop Quantum Cosmology

Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semi-classical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has correct classical limit with respect to the coherent states. In the second approach, the other kind of semi-classical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.Comment: 13 pages, submitted to CQ

Quantum geometry and the Schwarzschild singularity

In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same effects are shown to lead to a resolution of the Schwarzschild singularity. The resulting quantum extension of space-time is likely to have significant implications to the black hole evaporation process. Similarities and differences with the situation in quantum geometrodynamics are pointed out.Comment: 31 pages, 1 figur

Coexistence and competition of magnetism and superconductivity on the nanometer scale in underdoped BaFe1.89Co0.11As2

We report muon spin rotation (muSR) and infrared (IR) spectroscopy experiments on underdoped BaFe1.89Co0.11As2 which show that bulk magnetism and superconductivity (SC) coexist and compete on the nanometer length scale. Our combined data reveal a bulk magnetic order, likely due to an incommensurate spin density wave (SDW), which develops below Tmag \approx 32 K and becomes reduced in magnitude (but not in volume) below Tc = 21.7 K. A slowly fluctuating precursor of the SDW seems to develop alrady below the structural transition at Ts \approx 50 K. The bulk nature of SC is established by the muSR data which show a bulk SC vortex lattice and the IR data which reveal that the majority of low-energy states is gapped and participates in the condensate at T << Tc

Three dimensional loop quantum gravity: coupling to point particles

We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin foam amplitudes. In addition we provide an explicit expression of the (physical) distance operator between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde

Correlated photon pairs generated from a warm atomic ensemble

We present measurements of the cross-correlation function of photon pairs at 780 nm and 1367 nm, generated in a hot rubidium vapor cell. The temporal character of the biphoton is determined by the dispersive properties of the medium where the pair generation takes place. We show that short correlation times occur for optically thick samples, which can be understood in terms of off-resonant pair generation. By modifying the linear response of the sample, we produce near-resonant photon pairs, which could in principle be used for entanglement distribution