Quantum and statistical fluctuations in dynamical symmetry breaking

Dynamical symmetry breaking in an expanding nuclear system is investigated in semi-classical and quantum framework by employing a collective transport model which is constructed to mimic the collective behavior of expanding systems. It is shown that the fluctuations in collective coordinates during the expansion are developed mainly by the enhancement of the initial fluctuations by the driving force, and that statistical and quantum fluctuations have similar consequences. It is pointed out that the quantal fluctuations may play an important role in the development of instabilities by reducing the time needed to break the symmetry, and the possible role of quantal fluctuations in spinodal decomposition of nuclei is discussed.Comment: 19 Latex pages including 6 figure

Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as the pseudo-unitary ensemble. We obtain exact results for the nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing. This shows a level repulsion in marked distinction with an algebraic form in the Wigner surmise. We believe that this paves way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.Comment: 9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters on August 20, 200

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

Convexity and the quantum many-body problem

International audienceWe recall some properties of convex functions and, in particular, of the sum of the largest eigenvalues of a Hermitian matrix. From these properties a new estimate of an arbitrary eigenvalue of a sum of Hermitian matrices is derived, which in turn is used to compute an approximate associated spectral projector. These estimates are applied for the first time to explain the generic spectral features of quantum systems. As an application of the formalism, we explain the preponderance of certain ground-state angular momenta as observed in the vibron model with random interactions. We show that the evolution of eigenstates can be predicted from the knowledge of a limited number of spectra and investigate the effect of a three-body interaction in the vibron model on eigenenergies and eigenvectors

Symétrie et géométrie du problème à N-corps. Application à la physique nucléaire

Jean-François BERGER, Alejandro FRANK, Oriol BOHIGAS, Jacques MEYER, Oscar NAVILIAT-CUNCICOne of the main goals of classical and quantum physics is to solve the many-body problem. In nuclear theory, several methods have been developed and provide accurate results. In this thesis, we remind how symmetry can be used to obtain analytical solutions of the quantum many-body problem. We emphasize that unitary Lie algebras play a crucial role in quantum mechanics and propose and implement a method to build irreducible representations of this algebra from its highest-weight state. Calculations of bosonic and fermionic spectra are performed with realistic and with random interactions. Studies with rotationnal invariant two-body random interactions have unveiled high degree of order (e.g. a marked statistical preference is found for ground states with angular momentum equal to zero). In the second chapter of this thesis, it is argued that the spectral properties of this kind of interaction depend on the choice of the valence space. In particular, we propose a geometrical method to predict the properties of the ground state in certain cases. We also present numerical results when the geometrical approach can not be applied. In the third chapter, we study the link between quantum chaos and nuclear spectra calculated with realistic interactions.La résolution du problème à N-corps constitue aussi bien en mécanique classique qu'en mécanique quantique un des grands enjeux de la physique. En physique nucléaire, diverses méthodes ont été développées pour obtenir des solutions approchées permettant de décrire convenablement les propriétés des noyaux (spectres, transitions électromagnétiques...). Dans cette thèse, nous avons tout d'abord rappelé comment les symétries pouvaient être utilisées pour obtenir des solutions exactes. Nous avons notamment insisté sur le rôle occupé par l'algèbre unitaire en mécanique quantique et nous avons développé et implémenté une façon de construire les représentations irréductibles de cette algèbre à partir d'un état dit de poids maximal et dans lesquelles ont été calculés les spectres de systèmes bosoniques et fermioniques aussi bien avec des interactions réalistes qu'avec des interactions aléatoires. L'utilisation d'interactions aléatoires à 1- et 2-corps conservant le moment angulaire a révélé que certaines caractéristiques des spectres (état fondamental de moment angulaire nul, existence de bandes rotationnelles, vibrationnelles...) étaient robustes. Ainsi dans une seconde partie, nous avons montré que le choix de l'espace de valence conditionne fortement les spectres possibles d'un système quantique : en particulier, nous avons élaboré une méthode géométrique qui, dans certains cas, permet de prévoir les propriétés du fondamental. Nous avons également présenté des résultats numériques dans des situations où la méthode géométrique ne s'applique pas. Dans la dernière partie, nous nous sommes intéressés au lien entre le chaos et les spectres des noyaux obtenus avec des interactions réalistes

Analysis of cross sections and Vector Analysing Powers of (d,p) reactions within the CDCC+DWBA approach.

Transfer reactions like AX(d,p)A+1 X are a powerful tool to investigate nuclear structure properties (see e.g. [1–3]) and the emergence of radioactive beams with high intensity will allow the use of this kind of reactions to study the properties of exotic nuclei. Nevertheless the analysis of reactions involving deuteron remains a difficult task because of its weakly bound and composite features. To overcome these issues, R.C. Johnson et al [4] and G.H. Ratwitcher [5] proposed in the seventies the Continuum Discretized Coupled Channels (CDCC) formalism which explicitly takes into account the composite property of the deuteron and includes the effects on cross sections of the coupling between the breakup and the deuteron ground state channels. Since then the CDCC approach has been widely studied [6–8] and it has been quite successfully applied to analyse elastic [7–9] , inelastic [8,10] and transfer cross sections [11–13]. In this contribution, I will propose to re-analyse transfer reactions by the means of CDCC+adiabatic approach for a set of targets with N = 20 or N ≈ 28. I will show that with this approach, using both the differential cross sections and the vector analysing powers one can determine the orbital angular momentum and the spin of the captured nucleon without any adjustment

Elastic and inelastic cross sections calculated within the CDCC approach for deuteron induced reactions

The Continuum Discretized Coupled Channels (CDCC) equations have been extended to rotational nuclei. Within this approach, the deuteron breakup channels and the target excitations are treated simultaneously and one can calculate both the elastic and the inelastic cross sections. Comparisons of the calculated elastic and inelastic differential cross sections with experimental data have been performed for deuteron incident on 116Sn, 90Zr at 183 MeV and on 70Ge, 72Ge, 24Mg, 16O at 171 MeV. Calculations have also been done for 24Mg and 12C targets for incident energies between 60 and 90 MeV. A satisfactory overall agreement has been obtained