Mapping the Wigner distribution function of the Morse oscillator into a semi-classical distribution function

The mapping of the Wigner distribution function (WDF) for a given bound-state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. Here we give results showing that the SDF gets closer to the corresponding WDF as the number of levels of the Morse oscillator increases. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory.Comment: Revtex, 27 pages including 13 eps figure

Analytic Representation of The Dirac Equation

In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. We interpret the zitterbewegung and the result that a velocity measurement (of a Dirac particle) at any instant in time is, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. From this we infer that, although the form of the Dirac equation serves to make space and time appear on an equal footing mathematically, it is clear that they are still not on an equal footing from a physical point of view. On the other hand, the Foldy-Wouthuysen transformation, which connects the Dirac and square root operator, is unitary. Reflection on these results suggests that a more refined notion (than that of unitary equivalence) may be required for physical systems

A canonical ensemble approach to graded-response perceptrons

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear and quadratic error measure, corresponding to the perceptron respectively the adaline learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated.Comment: 26 pages, 10 ps figure

Agent-based Social Psychology: from Neurocognitive Processes to Social Data

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals as obtained by survey studies of social psychology.Comment: 11 pages, 4 figures, 2 C codes, to appear in Advances in Complex System

Inelastic semiclassical Coulomb scattering

We present a semiclassical S-matrix study of inelastic collinear electron-hydrogen scattering. A simple way to extract all necessary information from the deflection function alone without having to compute the stability matrix is described. This includes the determination of the relevant Maslov indices. Results of singlet and triplet cross sections for excitation and ionization are reported. The different levels of approximation -- classical, semiclassical, and uniform semiclassical -- are compared among each other and to the full quantum result.Comment: 9 figure

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semi-analytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (towards experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure -- which has not been observed experimentally -- shrinks, while that of BP I (O8-) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.Comment: 16 pages, 5 figures. Accepted for publication in Phys. Rev.

Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy

We study the excitation energy for slow changes of the hopping parameter in the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The excitation energy vanishes algebraically for long ramp times with an exponent that depends on whether the ramp takes place within the metallic phase, within the insulating phase, or across the Mott transition line. For ramps within metallic or insulating phase the exponents are in agreement with a perturbative analysis for small ramps. The perturbative expression quite generally shows that the exponent depends explicitly on the spectrum of the system in the initial state and on the smoothness of the ramp protocol. This explains the qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g., Mott insulating) systems. For gapped systems the asymptotic behavior of the excitation energy depends only on the ramp protocol and its decay becomes faster for smoother ramps. For gapless systems and sufficiently smooth ramps the asymptotics are ramp-independent and depend only on the intrinsic spectrum of the system. However, the intrinsic behavior is unobservable if the ramp is not smooth enough. This is relevant for ramps to small interaction in the fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation energy cannot be observed for a linear ramp due to its kinks at the beginning and the end.Comment: 24 pages, 6 figure

Serotonin receptor inhibitor is associated with falls independent of frailty in older adults

Objectives: To evaluate whether fall risk in older adults is associated with the use of selective serotonin receptor inhibitor (SSRI) monotherapy among geriatric outpatients, and whether this association is moderated by the presence of depressive disorder and/or frailty. Methods: Prospective cohort study with a 12-month follow-up and including 811 community-dwelling adults aged 60 or older from a university-based Geriatric Outpatient Unit. Major depressive disorder (MDD) was diagnosed according to DSM-5 criteria; subsyndromal depression as not meeting MDD criteria, but a Geriatric Depression Scale 15-item score ? 6 points. Frailty was evaluated with the FRAIL questionnaire. The association between SSRI use, depression, or both as well as the association between SSRI use, frailty, or both with falls were estimated through a generalized estimating equation (GEE) adjusted for relevant confounders. Results: At baseline, 297 patients (36.6%) used a SSRI (82 without remitted depression) and 306 (37.7%) were classified as physically frail. Frailty was more prevalent among SSRI users (44.8% versus 33.7%, p =.004). After 12 months, 179 participants had at least one fall (22.1%). SSRI use, depression as well as frailty were all independently associated with falls during follow-up. Nonetheless, patients with concurrent of SSRI usage and non-remitted depression had no higher risk compared to either remitted SSRI users or depressed patients without SSRIs. In contrast, concurrence of SSRI use and frailty increases the risk of falling substantially above those by SSRI usage or frailty alone. Conclusion: SSRI usage was independently associated with falls. Especially in frail-depressed patients, treatment strategies for depression other than SSRIs should be considered

Screening for pineal trilateral retinoblastoma revisited: a meta-analysis

Topic To determine until what age children are at risk for pineal trilateral retinoblastoma (TRb), whether its onset is linked to the age at which intraocular retinoblastomas develop, and the lead time from a detectable pineal TRb to symptoms. Clinical relevance About 45% of patients with retinoblastoma – those with a germline RB1 pathogenic variant – are at risk for pineal TRb. Early detection and treatment is essential for survival. Current evidence is unclear on the usefulness of screening for pineal TRb and, if useful, until what age screening should be continued. Methods We conducted a study according to the MOOSE guideline for reporting meta-analyses of observational studies. We searched PubMed and Embase between January 1, 1966, and February 27, 2019, for published literature. We considered articles reporting patients with TRb with survival and follow-up data. Inclusion of articles was performed separately and independently by two authors, and two authors also independently extracted the relevant data. They resolved discrepancies by consensus. Results One hundred thirty-eight patients with pineal TRb were included. Of 22 asymptomatic patients, 21 (95%) were diagnosed before the age of 40 months (median 16, interquartile range 9–29). Age at diagnosis of pineal TRb in patients diagnosed with retinoblastoma at ≤6 months versus >6 months of age were comparable (P=0.44), suggesting independency between the ages at diagnosis of intraocular retinoblastoma and pineal TRb. The laterality of intraocular retinoblastoma and its treatment were unassociated with the age when the pineal TRb was diagnosed. The lead time from an asymptomatic to a symptomatic pineal TRb was approximately 1 year. By performing a screening magnetic resonance imaging scan every 6 months after the diagnosis of heritable retinoblastoma (median age 6 months) until the age of 36 months, at least 311 and 776 scans would be required to detect one asymptomatic pineal TRb and to save one life, respectively. Conclusion Patients with retinoblastoma are at risk for pineal trilateral retinoblastoma for a shorter period than previously assumed and the age at diagnosis of pineal trilateral retinoblastoma is independent of the age at diagnosis of retinoblastoma. The GRADE level of evidence for these conclusions remains low.Peer reviewe