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

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

Coherent elastic neutrino-nucleus scattering: Terrestrial and astrophysical applications

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a process in which neutrinos scatter on a nucleus which acts as a single particle. Though the total cross section is large by neutrino standards, CE$\nu$NS has long proven difficult to detect, since the deposited energy into the nucleus is $\sim$ keV. In 2017, the COHERENT collaboration announced the detection of CE$\nu$NS using a stopped-pion source with CsI detectors, followed up the detection of CE$\nu$NS using an Ar target. The detection of CE$\nu$NS has spawned a flurry of activities in high-energy physics, inspiring new constraints on beyond the Standard Model (BSM) physics, and new experimental methods. The CE$\nu$NS process has important implications for not only high-energy physics, but also astrophysics, nuclear physics, and beyond. This whitepaper discusses the scientific importance of CE$\nu$NS, highlighting how present experiments such as COHERENT are informing theory, and also how future experiments will provide a wealth of information across the aforementioned fields of physics

Coherent elastic neutrino-nucleus scattering: Terrestrial and astrophysical applications

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a process inwhich neutrinos scatter on a nucleus which acts as a single particle. Thoughthe total cross section is large by neutrino standards, CE$\nu$NS has longproven difficult to detect, since the deposited energy into the nucleus is$\sim$ keV. In 2017, the COHERENT collaboration announced the detection ofCE$\nu$NS using a stopped-pion source with CsI detectors, followed up thedetection of CE$\nu$NS using an Ar target. The detection of CE$\nu$NS hasspawned a flurry of activities in high-energy physics, inspiring newconstraints on beyond the Standard Model (BSM) physics, and new experimentalmethods. The CE$\nu$NS process has important implications for not onlyhigh-energy physics, but also astrophysics, nuclear physics, and beyond. Thiswhitepaper discusses the scientific importance of CE$\nu$NS, highlighting howpresent experiments such as COHERENT are informing theory, and also how futureexperiments will provide a wealth of information across the aforementionedfields of physics.<br

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

Global and local dynamical invariants and quasienergy states of time-periodic Hamiltonians

A formalism is developed for calculating the quasienergy states and spectrum for time-periodic quantum systems when a time-periodic dynamical invariant operator with a nondegenerate spectrum is known. The method, which circumvents the integration of the Schr-odinger equation, is applied to an integrable class of systems, where the global invariant operator is constructed. Furthermore, a local integrable approximation for more general non-integrable systems is developed. Numerical results are presented for the doubleresonance model