Harmonic oscillator chains as Wigner Quantum Systems: periodic and fixed wall boundary conditions in gl(1|n) solutions

We describe a quantum system consisting of a one-dimensional linear chain of n identical harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions are taken into account: periodic boundary conditions (where the nth oscillator is coupled back to the first oscillator) and fixed wall boundary conditions (where the first oscillator and the $n$th oscillator are coupled to a fixed wall). The two systems are characterized by their Hamiltonian. For their quantization, we treat these systems as Wigner Quantum Systems (WQS), allowing more solutions than just the canonical quantization solution. In this WQS approach, one is led to certain algebraic relations for operators (which are linear combinations of position and momentum operators) that should satisfy triple relations involving commutators and anti-commutators. These triple relations have a solution in terms of the Lie superalgebra gl(1|n). We study a particular class of gl(1|n) representations V(p), the so-called ladder representations. For these representations, we determine the spectrum of the Hamiltonian and of the position operators (for both types of boundary conditions). Furthermore, we compute the eigenvectors of the position operators in terms of stationary states. This leads to explicit expressions for position probabilities of the n oscillators in the chain. An analysis of the plots of such position probability distributions gives rise to some interesting observations. In particular, the physical behavior of the system as a WQS is very much in agreement with what one would expect from the classical case, except that all physical quantities (energy, position and momentum of each oscillator) have a finite spectrum

On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications

In a Wigner quantum mechanical model, with a solution in terms of the Lie superalgebra gl(1|n), one is faced with determining the eigenvalues and eigenvectors for an arbitrary self-adjoint odd element of gl(1|n) in any unitary irreducible representation W. We show that the eigenvalue problem can be solved by the decomposition of W with respect to the branching gl(1|n) --> gl(1|1) + gl(n-1). The eigenvector problem is much harder, since the Gel'fand-Zetlin basis of W is involved, and the explicit actions of gl(1|n) generators on this basis are fairly complicated. Using properties of the Gel'fand-Zetlin basis, we manage to present a solution for this problem as well. Our solution is illustrated for two special classes of unitary gl(1|n) representations: the so-called Fock representations and the ladder representations

The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)

It is known that the defining relations of the orthosymplectic Lie superalgebra osp(1|2n) are equivalent to the defining (triple) relations of n pairs of paraboson operators $b^\pm_i$. In particular, with the usual star conditions, this implies that the ``parabosons of order p'' correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of osp(1|2n). Apart from the simple cases p=1 or n=1, these representations had never been constructed due to computational difficulties, despite their importance. In the present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the osp(1|2n) generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra u(n) of osp(1|2n) plays a crucial role. Our results also lead to character formulas for these infinite-dimensional osp(1|2n) representations. Furthermore, by considering the branching $osp(1|2n) \supset sp(2n) \supset u(n)$, we find explicit infinite-dimensional unitary irreducible lowest weight representations of sp(2n) and their characters.Comment: typos correcte

The Wigner function of a q-deformed harmonic oscillator model

The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the $q$-oscillator model under consideration. The Wigner function is expressed as a basic hypergeometric series, related to the Al-Salam-Chihara polynomials. It is shown that, in the limit case $h \to 0$ ($q \to 1$), both the Wigner and Husimi distribution functions reduce correctly to their well-known non-relativistic analogues. Surprisingly, examination of both distribution functions in the q-deformed model shows that, when $q \ll 1$, their behaviour in the phase space is similar to the ground state of the ordinary quantum oscillator, but with a displacement towards negative values of the momentum. We have also computed the mean values of the position and momentum using the Wigner function. Unlike the ordinary case, the mean value of the momentum is not zero and it depends on $q$ and $n$. The ground-state like behaviour of the distribution functions for excited states in the q-deformed model opens quite new perspectives for further experimental measurements of quantum systems in the phase space.Comment: 16 pages, 24 EPS figures, uses IOP style LaTeX, some misprints are correctd and journal-reference is adde

My Private Cloud Overview: A Trust, Privacy and Security Infrastructure for the Cloud

Based on the assumption that cloud providers can be trusted (to a certain extent) we define a trust, security and privacy preserving infrastructure that relies on trusted cloud providers to operate properly. Working in tandem with legal agreements, our open source software supports: trust and reputation management, sticky policies with fine grained access controls, privacy preserving delegation of authority, federated identity management, different levels of assurance and configurable audit trails. Armed with these tools, cloud service providers are then able to offer a reliable privacy preserving infrastructure-as-a-service to their clients

Harmonic oscillators coupled by springs: discrete solutions as a Wigner Quantum System

We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In this paper, we approach the system as a Wigner Quantum System, not imposing the canonical commutation relations, but using instead weaker relations following from the compatibility of Hamilton's equations and the Heisenberg equations. In such a setting, the quantum system allows solutions in a finite-dimensional Hilbert space, with a discrete spectrum for all physical operators. We show that a class of solutions can be obtained using generators of the Lie superalgebra gl(1|M). Then we study the properties and spectra of the physical operators in a class of unitary representations of gl(1|M). These properties are both interesting and intriguing. In particular, we can give a complete analysis of the eigenvalues of the Hamiltonian and of the position and momentum operators (including multiplicities). We also study probability distributions of position operators when the quantum system is in a stationary state, and the effect of the position of one oscillator on the positions of the remaining oscillators in the chain

The child's right to protection against economic exploitation in the digital world

Abstract Children face significant consumer risks when surfing online, related to, inter alia, embedded advertisements and privacy-invasive practices, as well as the exploitation of their incredulity and inexperience resulting in overspending or online fraudulent transactions. Behind the fun and playful activities available for children online lie complex revenue models, creating value for companies by feeding children's data into algorithms and self-learning models to profile them and offer personalised advertising or by nudging children to buy or try to win in-app items to advance in the games they play. In this article we argue that specific measures against these forms of economic exploitation of children in the digital world are urgently needed. We focus on three types of exploitative practices that may have a significant impact on the well-being and rights of children - profiling and automated decision-making, commercialisation of play, and digital child labour. For each type, we explain what the practice entails, situate the practice within the existing legislative and children's rights framework and identify concerns in relation to those rights. Keyword

Sentinel-1 detects firn aquifers in the Greenland ice sheet

Firn aquifers in Greenland store liquid water within the upper ice sheet and impact the hydrological system. Their location and area have been estimated with airborne radar sounder surveys (Operation IceBridge, OIB). However, the OIB coverage is limited to narrow flight lines, offering an incomplete view. Here, we show the ability of satellite radar measurements from Sentinel-1 to map firn aquifers across all of Greenland at 1 km(2) resolution. The detection of aquifers relies on a delay in the freezing of meltwater within the firn above the water table, causing a distinctive pattern in the radar backscatter. The Sentinel-1 aquifer locations are in very good agreement with those detected along the OIB flight lines (Cohen's kappa = 0.84). The total aquifer area is estimated at 54,800 km(2). With continuity of Sentinel-1 ensured until 2030, our study lays a foundation for monitoring the future response of firn aquifers to climate change

Easing the inferential leap in competency modeling: The effects of task-related information and subject matter expertise

Despite the rising popularity of the practice of competency modeling, research on competency modeling has lagged behind. This study begins to close this practice–science gap through 3 studies (1 lab study and 2 field studies), which employ generalizability analysis to shed light on (a) the quality of inferences made in competency modeling and (b) the effects of incorporating elements of traditional job analysis into compe-tency modeling to raise the quality of competency inferences. Study 1 showed that competency modeling resulted in poor interrater reliabil-ity and poor between-job discriminant validity amongst inexperienced raters. In contrast, Study 2 suggested that the quality of competency inferences was higher among a variety of job experts in a real organiza-tion. Finally, Study 3 showed that blending competency modeling efforts and task-related information increased both interrater reliability among SMEs and their ability to discriminate among jobs. In general, this set of results highlights that the inferences made in competency modelin