Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders

We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use reproduces the one proposed by Kempft, Mangano and Mann. It is emphasized that a minimal length acts as a natural regulator for the theory, thus eliminating the otherwise ever appearing infinities. So, we use our results to calculate the first correction to the Casimir Effect due to the minimal length. We also discuss some of the physical consequences of the existence of a minimal length, culminating in a proposal to reformulate the very concept of "position measurement"

Spatial frequency equalization does not prevent spatial–numerical associations

There is an intense debate surrounding the origin of spatial–numerical associations (SNAs), according to which small numbers are mapped onto the left side of the space and large numbers onto the right. Despite evidence suggesting that SNAs would emerge as an innate predisposition to map numerical information onto a left-to-right spatially oriented mental representation, alternative accounts have challenged these proposals, maintaining that such a mapping would be the result of a mere spatial frequency (SF) coding of any visual image. That is, any smaller or larger array of objects would naturally contain more low or high SF information and, accordingly, each hemisphere would be preferentially tuned only for one SF range (e.g., right hemisphere tuned for low SF and left hemisphere tuned for high SF). This would determine the typical SNA (e.g., faster RTs for small numerical arrays with the left hand and for large numerical arrays with the right hand). To directly probe the role of SF coding in SNAs, we tested participants in a typical dot-arrays comparison task with two numerical sets: one in which SFs were confounded with numerosity (Experiment 1) and one in which the full SF power spectrum was equalized across all stimuli, keeping this cue uninformative about numerosity (Experiment 2). We found that SNAs emerged in both experiments, independently of whether SF was confounded or not with numerosity. Taken together, these findings suggest that SNAs cannot simply originate from SF power spectrum alone, and, thus, they rule out the brain’s asymmetric SF tuning as a primary cause of such an effect

From perceived autonomy support to intentional behaviour: Testing an integrated model in three healthy-eating behaviours

A motivational model integrating self-determination theory, the theory of planned behaviour, and the health action process approach was tested in three samples in three behavioural contexts: fruit and vegetable, breakfast, and snack consumption. Perceived support for autonomous (self-determined) forms of motivation from parents and autonomous motivation from self-determination theory were hypothesised to predict intention and behaviour indirectly via the mediation of attitude and perceived behavioural control from the theory of planned behaviour. It was also expected that planning strategies would mediate the effect of intention on behaviour. Relations in the proposed models were expected to be similar across the behaviours. A two-wave prospective design was adopted. Three samples of high-school students (total N = 1041; 59.60% female; M age = 17.13 years ± 1.57) completed measures of perceived autonomy support, autonomous motivation, theory of planned behaviour constructs, planning strategies and behaviour for each of the three behavioural contexts. Three months later, 816 participants (62,24% female; M age: 17.13 years, SD = 1.58) of the initial sample self-reported their behaviour referred to the previous three months. Structural equation models provided support for the key hypothesised effects of the proposed model for the three health-related behaviours. Two direct effects were significantly different across the three behaviours: the effect of perceived autonomy support on perceived behavioural control and the effect of attitude on intention. In addition, planning strategies mediated the effect of intention on behaviour in fruit and vegetable sample only. Findings extend knowledge of the processes by which psychological antecedents from the theories affect energy-balance related behaviours

Smelling the Space Around Us: Odor Pleasantness Shifts Visuospatial Attention in Humans

The prompt recognition of pleasant and unpleasant odors is a crucial regulatory and adaptive need of humans. Reactive answers to unpleasant odors ensure survival in many threatening situations. Notably, although humans typically react to certain odors by modulating their distance from the olfactory source, the effect of odor pleasantness over the orienting of visuospatial attention is still unknown. To address this issue, we first trained participants to associate visual shapes with pleasant and unpleasant odors, and then we assessed the impact of this association on a visuospatial task. Results showed that the use of trained shapes as flankers modulates performance in a line bisection task. Specifically, it was found that the estimated midpoint was shifted away from the visual shape associated with the unpleasant odor, whereas it was moved toward the shape associated with the pleasant odor. This finding demonstrates that odor pleasantness selectively shifts human attention in the surrounding space

About Lorentz invariance in a discrete quantum setting

A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in the context of quantum gravity, the distance between two points becomes an operator and show through a toy model, inspired by Loop Quantum Gravity, that the notion of a quantum of geometry and of discrete spectra of geometric operators, is not inconsistent with Lorentz invariance. The main feature of the model is that a state of definite length for a given observer turns into a superposition of eigenstates of the length operator when seen by a boosted observer. More generally, we discuss the issue of actually measuring distances taking into account the limitations imposed by quantum gravity considerations and we analyze the notion of distance and the phenomenon of Lorentz contraction in the framework of ``deformed (or doubly) special relativity'' (DSR), which tentatively provides an effective description of quantum gravity around a flat background. In order to do this we study the Hilbert space structure of DSR, and study various quantum geometric operators acting on it and analyze their spectral properties. We also discuss the notion of spacetime point in DSR in terms of coherent states. We show how the way Lorentz invariance is preserved in this context is analogous to that in the toy model.Comment: 25 pages, RevTe

Gravitational dynamics in Bose Einstein condensates

Analogue models for gravity intend to provide a framework where matter and gravity, as well as their intertwined dynamics, emerge from degrees of freedom that have a priori nothing to do with what we call gravity or matter. Bose Einstein condensates (BEC) are a natural example of analogue model since one can identify matter propagating on a (pseudo-Riemannian) metric with collective excitations above the condensate of atoms. However, until now, a description of the "analogue gravitational dynamics" for such model was missing. We show here that in a BEC system with massive quasi-particles, the gravitational dynamics can be encoded in a modified (semi-classical) Poisson equation. In particular, gravity is of extreme short range (characterized by the healing length) and the cosmological constant appears from the non-condensed fraction of atoms in the quasi-particle vacuum. While some of these features make the analogue gravitational dynamics of our BEC system quite different from standard Newtonian gravity, we nonetheless show that it can be used to draw some interesting lessons about "emergent gravity" scenarios.Comment: Replaced with published version. 15 pages, no figures, revtex4. Reference adde

Hyperferritinemia without iron overload in patients with bilateral cataracts: a case series

Hepatologists and internists often encounter patients with unexplained high serum ferritin concentration. After exclusion of hereditary hemochromatosis and hemosiderosis, rare disorders like hereditary hyperferritinemia cataract syndrome should be considered in the differential diagnosis. This autosomal dominant syndrome, that typically presents with juvenile bilateral cataracts, was first described in 1995 and has an increasing number of recognized molecular defects within a regulatory region of the L-ferritin gene (FTL). CASE PRESENTATION: Two patients (32 and 49-year-old Caucasian men) from our ambulatory clinic were suspected as having this syndrome and a genetic analysis was performed. In both patients, sequencing of the FTL 5' region showed previously described mutations within the iron responsive element (FTL c.33 C > A and FTL c.32G > C). CONCLUSION: Hereditary hyperferritinemia cataract syndrome should be considered in all patients with unexplained hyperferritinemia without signs of iron overload, particularly those with juvenile bilateral cataracts. Liver biopsy and phlebotomy should be avoided in this disorder

N=2 supersymmetric spin foams in three dimensions

We construct the spin foam model for N=2 supergravity in three dimensions. Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has representations which are not completely reducible. This complicates the procedure when building a state sum. Fortunately, one can and should excise these representations. We show that the restricted subset of representations form a subcategory closed under tensor product. The resulting state-sum is once again a topological invariant. Furthermore, within this framework one can identify positively and negatively charged fermions propagating on the spin foam. These results on osp(2|2) representations and intertwiners apply more generally to spin network states for N=2 loop quantum supergravity (in 3+1 dimensions) where it allows to define a notion of BPS states.Comment: 12 page

Noncommutative fluid dynamics in the Snyder space-time

In this paper, we construct for the first time the non-commutative fluid with the deformed Poincare invariance. To this end, the realization formalism of the noncommutative spaces is employed and the results are particularized to the Snyder space. The non-commutative fluid generalizes the fluid model in the action functional formulation to the noncommutative space. The fluid equations of motion and the conserved energy-momentum tensor are obtained.Comment: 12 pages. Version published by Phys. Rev.