How fat is a fat bundle?

Let P M be a principal G-bundle with connection 1-form and curvature . For a subset S of g^* the given connection is S-fat (Weinstein, [5]) if for every in S the form ° is nondegenerate on each horizontal subspace in TP.Let K be a compact group and K/H be its coadjoint orbit. The orthogonal projection t h defines a connection on the principal H-bundle K K/H. We show that this connection is fat off certain walls of Weyl chambers in h^*. We then apply the result to the construction of symplectic fiber bundles over K/H. As an example, we show how higher-dimensional coadjoint orbits fiber symplectically over lower-dimensional orbits.     

How bosonic is a pair of fermions?

Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indicator for bosonic quality is the composite boson normalisation ratio \(\chi _{N+1}/\chi _{N}\) of a state of \(N\) composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large composite numbers \(N\) . Here, we provide an efficient characterisation in terms of the purity \(P\) and the largest eigenvalue \(\lambda _1\) of the reduced single-fermion state. We find the states that extremise \(\chi _N\) for given \(P\) and \(\lambda _1\) , and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic quality of a composite particle and the entanglement of its constituents.     

Why is random close packing reproducible?

We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi{rcp} approximately 0.64 arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.     

How interdisciplinary is nanotechnology?

Facilitating cross-disciplinary research has attracted much attention in recent years, with special concerns in nanoscience and nanotechnology. Although policy discourse has emphasized that nanotechnology is substantively integrative, some analysts have countered that it is really a loose amalgam of relatively traditional pockets of physics, chemistry, and other disciplines that interrelate only weakly. We are developing empirical measures to gauge and visualize the extent and nature of interdisciplinary interchange. Such results speak to research organization, funding, and mechanisms to bolster knowledge transfer. In this study, we address the nature of cross-disciplinary linkages using “science overlay maps” of articles, and their references, that have been categorized into subject categories. We find signs that the rate of increase in nano research is slowing, and that its composition is changing (for one, increasing chemistry-related activity). Our results suggest that nanotechnology research encompasses multiple disciplines that draw knowledge from disciplinarily diverse knowledge sources. Nano research is highly, and increasingly, integrative—but so is much of science these days. Tabulating and mapping nano research activity show a dominant core in materials sciences, broadly defined. Additional analyses and maps show that nano research draws extensively upon knowledge presented in other areas; it is not constricted within narrow silos.

How probable is inflation?

The Henneaux-Gibbons-Hawking-Stewart canonical measure on the set of classical universes is applied to a Friedmann-Robertson-Walker model containing a massive scalar field. Although a uniform probability distribution in this measure would solve the flatness problem, it gives an ambiguous probability for inflation, since both the set of inflationary solutions and the set of noninflationary solutions have infinite measure.     

How adiabatic is quantum tunneling?

We consider the coupling between collective and intrinsic degrees of freedom of a many-dimensional quantum system. We give a criterion for the validity of the adiabatic approximation in tunneling processes and derive an equation for the “lag” of the intrinsic wave function with respect to the adiabatic groundstate. Solutions for several simple cases are presented.     

How old is surface science?

Philosophical and literary testimonies from the Classical World (5th century b.c. to 3rd century a.d.) involving solid surfaces are reviewed. Plato thought the surface to be a real entity, whereas Aristotle considered it to possess an unqualified existence, i.e. not to be a substance, but just an accidental entity. The Old Stoics asserted that surfaces do not possess any physical existence, although the Stoic philosopher Posidonius—apparently the only exception in his school—held them to exist both in thought and reality. While both the Atomists and the Epicureans were very little interested in them, the Sceptic philosopher Sextus Empiricus considered surfaces to be the limits of a body, although he maintained that both the view that they are corporeal or the view that they are incorporeal present unsurmountable difficulties.Among Roman authors, the testimony from Pliny the Elder is mostly concerned with metallic surfaces, chemical change occurring there, and surface treatments used in antiquity.Besides the philosophical motivations, the implications of the testimonies are discussed in the light of surface science. The purely geometrical surface of Plato is found to compare favorably to single-crystal surface, Posidonius’ “corporeal” surface is best likened to an air-oxidized, or otherwise ambient-modified surface, and ancient accounts on mixture are compared to XPS results obtained in adhesion studies of enameled steels. I argue that the long-standing dominance of Aristotle’s view from antiquity onwards may have had a part in delaying theoretical speculation into solid surfaces.     

How Magnetic is the Dirac Neutrino?

We derive model-independent, "naturalness" upper bounds on the magnetic moments munu of Dirac neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, we find that current information on neutrino mass implies that[EQUATION: SEE TEXT] bohr magnetons. This bound is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations.     

How big is the universe today?

If one defines the size of the present universe in terms of a hypersurface of simultaneity generated by the spatial geodesies orthogonal to our world line today, then it is finite in all expanding Big Bang Friedmann models.     

How quantum is the big bang?

When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.     

What is a photon?

Certain properties of photons viewed as quanta (particles of an electromagnetic field) are discussed. Specifically, the nature of localization (size) of photons along and across the direction of wave propagation is examined.     

How random are matrix elements of the nuclear shell model Hamiltonian?

In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonian.We find that nonzero off-diagonal elements exhibit a regular pattern,if one sorts the diagonal matrix elements from smaller to larger values.The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small.     

How effective is the weak mixing angle?

The usefulness of an effective weak mixing angle to parameterise the electroweak couplings of quarks and leptons measured at LEP is discussed. After a review of the theoretical formalism used to handle the electroweak radiative corrections to LEP processes, some suggestions for procedures to be used to extract the mixing angle are given and the various definitions of the effective weak mixing angle used by the experiments are examined. This is followed by an attempt to extract a coherent set of mixing angle values from the four experiments with the published 1989/90 (and some 1991) measurements of the Z⁰ line-shapes, asymmetries and polarisation. These results are updated with preliminary results from the 1991 data presented at the XXVI International Conference on High Energy Physics, in Dallas, USA, in August 1992, including the preliminary measurement ofA _LR at the SLC. The average value found for the effective weak mixing angle, defined for leptons, is sin² _eff ^lept =02322±0.0010. The error on sin² _eff ^lept can be further reduced by imposing the constraints between the parameters implicit in the MSM. With the additional constraint _s=0.123±0.006 imposed in the fit, the result is sin² _eff ^lept , where the central value is form _H =300 GeV, and the second error is the variation ifm _H is changed to 50 GeV (lower error) and 1000 GeV (upper error). Within the MSM, sin² _lept ^eff is directly related to the top-quark mass, and the corresponding value ism _t =153 _–25–23 ⁺²²⁺¹⁹ GeV, where the errors have the same meaning as those for sin² _eff ^lept . Finally, the prospects for improved precision are discussed.     

How different is a hard-sphere fluid from a suspension of hard-sphere colloids near the glass transition?

This paper compares simulation and experiment to verify how a hard-sphere fluid is different from a suspension of hard-sphere colloids near the glass transition at 6% polydispersity. This is done by performing extensive molecular-dynamic simulations and by analyzing the resultant mean-square displacement from a unified viewpoint based on the mean-field theory proposed recently by Tokuyama [Physica A 364 (2006) 23–62]. The remarkable similarities are found in various physical quantities between two systems, except their phase diagrams, in which the experiment shows the glass transition, while the simulation shows the temporal re-entrant melting (transition from crystal to supercooled liquid) followed by the glass transition within a limited waiting time of order 8.4×10⁴$8.4\times {10}^4$ in a dimensionless unit.     

How accurate is the attosecond streak camera?

An attosecond streak camera holds the promise of time resolving the dynamics of photoionization with a few-attosecond accuracy. But can the attosecond measurement be disentangled from the process it measures? We address this question by deriving simple closed-form analytical expressions for the measurement-related apparent time delays in photoionization, associated with the application of the attosecond streak camera and/or resolution of attosecond beating by interference of two-photon transitions techniques. Our analytical results are accurate on about the 1 asec level and show that both intrinsic and measurement-induced delays depend on the same scattering phase and are, therefore, not independent. We also suggest a procedure for extracting intrinsic time delays from the measurement and a possible resolution of the controversy caused by the experiments of Schultze et al. [Science 328, 1658 (2010)].