How should we measure spatial distances?

The use of time-like geodesics to measure temporal distances is better justified than the use of space-like geodesics for a measurement of spatial distances. We give examples where a spatial distance cannot be appropriately determined by the length of a space-like geodesic.     

How far can one send a photon?

The answer to the question How far can one send a photon? depends heavily on what one means by a photon and on what one intends to do with that photon. For direct quantum communication, the limit is approximately 500 km. For terrestrial quantum communication, near-future technologies based on quantum teleportation and quantum memories will soon enable quantum repeaters that will turn the development of a world-wide-quantum-web (WWQW) into a highly non-trivial engineering problem. For Device-Independent Quantum Information Processing, near-future qubit amplifiers (i.e., probabilistic heralded amplification of the probability amplitude of the presence of photonic qubits) will soon allow demonstrations over a few tens of kilometers.     

How should complexity scale with system size?

We study how statistical complexity depends on the system size and how the complexity of the whole system relates to the complexity of its subsystems. We study this size dependence for two well-known complexity measures, the excess entropy of Grassberger and the neural complexity introduced by Tononi, Sporns and Edelman. We compare these results to properties of complexity measures that one might wish to impose when seeking an axiomatic characterization. It turns out that those two measures do not satisfy all those requirements, but a renormalized version of the TSE-complexity behaves reasonably well.     

How much information can one store in a nonequilibrium medium?

It has recently been emphasized again that the very existence of stationary stable localized structures with short-range interactions might allow one to store information in nonequilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and nonstorable information. This leads us to introduce a measure of the long-term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).     

How much can one break chiral symmetry in the linear sigma model?

We show that the hedgehog soliton solution describing the nucleon in theSU(3) ×SU(3) linear sigma model breaks down when the pion mass becomes too large.On leave of absence from the Laboratoire de Physique Théorique, Université de Nice, parc Valrose, F-06034 Nice Cedex, France     

Discrete quantum breathers: what do we know about them?

The knowledge about discrete quantum breathers, accumulated during the last two decades, is reviewed. "Prehistory" of the problem is described and some important properties differentiating localized and extended vibrational modes are outlined. The state of art of our understanding of the principal features of the quantum discrete breathers is presented.     

Phonon concentrating: How many catastrophes do occur?

New types of catastrophes in phonon concentrating (in so-called “phonon focusing”) are described. The conditions for existence of new caustics in crystals are obtained.     

Pion form factor in QCD: How to calculate?

The calculation of the pion form factor F _π(Q ²) in QCD is discussed. The main points of the nonlocal condensate QDC sum rule approach are considered and its results for the pion form factor are shown compared with the predictions of the perturbative and lattice QCD. The local duality (LD) approach for the pion FF in QCD is studied. It is shown that the main parameter of the approach for Q ² ≥ 2 GeV², namely, s ₀^LD(Q ²) should grow with an increase in Q ², rather than remain constant.     

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 does water boil?

Insight into the boiling of water is obtained from molecular dynamics simulations. The process is initiated by the spontaneous formation of small vacuum cavities in liquid water. By themselves, these defects are very short lived. If, however, several cavities occur at close distances, they are likely to merge into larger vacuum holes. At the liquid-vapor interfaces, single or small groups of water molecules tend to leave the liquid surface. Once the system is propagated beyond the transition state, these evaporation events outnumber the competing reintegration into the hydrogen-bonded network.     

How do quasicrystals grow?

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.     

3D Crystal: How Flat its Flat Facets Are?

We investigate the hypothesis that the (random) crystal of the (–)-phase inside the (+)-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to the possibility of formation of an extra monolayer on a facet. We then prove this weaker hypothesis for the Solid-On-Solid model.     

Can one define a preferred symplectic connection?

We define a variational principle for symplectic connections of the Yang-Mills type. When the symplectic manifold is a compact surface we show that the moduli space of the connections which are extremals of the functional coincides with the Teichmüller space of the surface. We indicate that the noncompact situation is very different.     

Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum?

We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence (successfully applied in the past to plasma, optics, and hydrodynamic waves), this nonlinear wave system evolves at long times with a slow transfer of energy from one mode to another. We derive a kinetic equation for the spectral transfer in terms of the second order moment. We show that such a theory describes the approach to an equilibrium wave spectrum and represents also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations that confirm this scenario.     

Renormalization of pinned elastic systems: how does it work beyond one loop?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.