Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e. to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e. no classical limit can be defined. Numerical simulations on a one dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included, submitted to PR

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Collinear helium under periodic driving: stabilization of the asymmetric stretch orbit

The collinear eZe configuration of helium, with the electrons on opposite sides of the nucleus, is studied in the presence of an external electromagnetic (laser or microwave) field. We show that the classically unstable "asymmetric stretch" orbit, on which doubly excited intrashell states of helium with maximum interelectronic angle are anchored, can be stabilized by means of a resonant driving where the frequency of the electromagnetic field equals the frequency of Kepler-like oscillations along the orbit. A static magnetic field, oriented parallel to the oscillating electric field of the driving, can be used to enforce the stability of the configuration with respect to deviations from collinearity. Quantum Floquet calculations within a collinear model of the driven two-electron atom reveal the existence of nondispersive wave packets localized on the stabilized asymmetric stretch orbit, for double excitations corresponding to principal quantum numbers of the order of N > 10.Comment: 13 pages, 12 figure

Between tinkering and transformation: a contemporary appraisal of climate change adaptation research on the world's islands

Islands are at the center of discourses on climate change. Yet despite extensive work on diverse island systems in a changing climate, we still lack an understanding of climate change-related responses amongst islands and what shifting from what might be called “tinkering” (perhaps heat warnings) to “transformational” adaptation (perhaps relocation) means for these vastly different landmasses which are often grouped together by default. Through a systematic review of the climate change adaptation scientific literature, this paper critically reflects on how considering islands as a homogenous ensemble and the use of buzzwords such as “transformational adaptation” may be problematic for diverse island realities under climate change. Our findings show that the adaptation evidence base actually provides literature on contrasting island types and cultural and political contexts, including Small Island Developing States as well as other island territories. This study finds research gaps with respect to regions (e.g., South America, Africa, and Mediterranean) and that there is overall both little evidence of and a lack of context-specific definitions of transformational adaptation in island contexts. The adaptation literature does not yet fully reflect the experiences or needs of islands regarding transitions and transformations throughout history

Development of a compact muon veto for the nucleus experiment

The Nucleus experiment aims to measure coherent elastic neutrino nucleus scattering of reactor anti-neutrinos using cryogenic calorimeters. Operating at an overburden of 3 meters of water equivalent, muon-induced backgrounds are expected to be one of the dominant background contributions. Besides a high efficiency to identify muon events passing the experimental setup, the Nucleus muon veto has to fulfill tight spatial requirements to fit the constraints given by the experimental site and to minimize the induced detector dead-time. We developed highly efficient and compact muon veto modules based on plastic scintillators equipped with wavelength shifting fibers and silicon photo multipliers to collect and detect the scintillation light. In this paper, we present the full characterization of a prototype module with different light read-out configurations. We conclude that an efficient and compact muon veto system can be built for the Nucleus experiment from a cube assembly of the developed modules. Simulations show that an efficiency for muon identification of >99 % and an associated rate of 325 Hz is achievable, matching the requirements of the Nucleus experiment

The mechanisms of boronate ester formation and fluorescent turn-on in ortho-aminomethylphenylboronic acids

ortho-Aminomethylphenylboronic acids are used in receptors for carbohydrates and various other compounds containing vicinal diols. The presence of the o-aminomethyl group enhances the affinity towards diols at neutral pH, and the manner in which this group plays this role has been a topic of debate. Further, the aminomethyl group is believed to be involved in the turn-on of the emission properties of appended fluorophores upon diol binding. In this treatise, a uniform picture emerges for the role of this group: it primarily acts as an electron-withdrawing group that lowers the pK(a) of the neighbouring boronic acid thereby facilitating diol binding at neutral pH. The amine appears to play no role in the modulation of the fluorescence of appended fluorophores in the protic-solvent-inserted form of the boronic acid/boronate ester. Instead, fluorescence turn-on can be consistently tied to vibrational-coupled excited-state relaxation (a loose-bolt effect). Overall, this Review unifies and discusses the existing data as of 2019 whilst also highlighting why o-aminomethyl groups are so widely used, and the role they play in carbohydrate sensing using phenylboronic acids