A convenient coordinatization of Siegel-Jacobi domains

We determine the homogeneous K\"ahler diffeomorphism $FC$ which expresses the K\"ahler two-form on the Siegel-Jacobi ball \mc{D}^J_n=\C^n\times \mc{D}_n as the sum of the K\"ahler two-form on \C^n and the one on the Siegel ball \mc{D}_n. The classical motion and quantum evolution on \mc{D}^J_n determined by a hermitian linear Hamiltonian in the generators of the Jacobi group G^J_n=H_n\rtimes\text{Sp}(n,\R)_{\C} are described by a matrix Riccati equation on \mc{D}_n and a linear first order differential equation in z\in\C^n, with coefficients depending also on W\in\mc{D}_n. $H_n$ denotes the $(2n+1)$-dimensional Heisenberg group. The system of linear differential equations attached to the matrix Riccati equation is a linear Hamiltonian system on \mc{D}_n. When the transform $FC:(\eta,W)\rightarrow (z,W)$ is applied, the first order differential equation in the variable \eta=(\un-W\bar{W})^{-1}(z+W\bar{z})\in\C^n becomes decoupled from the motion on the Siegel ball. Similar considerations are presented for the Siegel-Jacobi upper half plane \mc{X}^J_n=\C^n\times\mc{X}_n, where \mc{X}_n denotes the Siegel upper half plane.Comment: 32 pages, corrected typos, Latex, amsart, AMS font

Identification of Berezin-Toeplitz deformation quantization

We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose classifying form is explicitly calculated. Its characteristic class (which classifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegoe kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjoestrand.Comment: 26 page

The Geometry of Quantum Mechanics

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality and M-theory, and it has been suggested that they should also have a counterpart in quantum mechanics. In view of these developments we propose "dequantisation", a mechanism to render a quantum theory classical. Specifically, we present a geometric procedure to "dequantise" a given quantum mechanics (regardless of its classical origin, if any) to possibly different classical limits, whose quantisation gives back the original quantum theory. The standard classical limit $\hbar\to 0$ arises as a particular case of our approach.Comment: 15 pages, LaTe

Study on the isospin equilibration phenomenon in nuclear reactions 40Ca + 40Ca, 40Ca + 46Ti, 40Ca + 48Ca, 48Ca + 48Ca at 25 MeV/nucleon by using the CHIMERA multidetector

We report on the results obtained by studying nuclear reactions between isotopes of Ca and Ti at 25MeV/nucleon. We used the multidetector CHIMERA to detect charged reaction products. In particular, we studied two main effects: the isospin diffusion and the isospin drift. In order to study these processes we performed a moving-source analysis on kinetic energy spectra of the isobar nuclei 3H and3He. This method allows to isolate the emission from the typical sources produced in reactions at Fermi energy: projectile like fragment (PLF), target like fragment (TLF), and mid-velocity (MV) emission. The obtained results are compared to previous experimental investigations and to simulations obtained with CoMD-II model

Kinematical coincidence method in transfer reactions

A new method to extract high resolution angular distributions from kinematical coincidence measurements in binary reactions is presented. Kinematic is used to extract the center of mass angular distribution from the measured energy spectrum of light particles. Results obtained in the case of 10Be+p-->9Be+d reaction measured with the CHIMERA detector are shown. An angular resolution of few degrees in the center of mass is obtained.Comment: 6 Page 10 Figures submitted to Nuclear Instruments and Methods

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Dipolar degrees of freedom and Isospin equilibration processes in Heavy Ion collisions

Background: In heavy ion collision at the Fermi energies Isospin equilibration processes occur- ring when nuclei with different charge/mass asymmetries interacts have been investigated to get information on the nucleon-nucleon Iso-vectorial effective interaction. Purpose: In this paper, for the system 48Ca +27 Al at 40 MeV/nucleon, we investigate on this process by means of an observable tightly linked to isospin equilibration processes and sensitive in exclusive way to the dynamical stage of the collision. From the comparison with dynamical model calculations we want also to obtain information on the Iso-vectorial effective microscopic interaction. Method: The average time derivative of the total dipole associated to the relative motion of all emitted charged particles and fragments has been determined from the measured charges and velocities by using the 4? multi-detector CHIMERA. The average has been determined for semi- peripheral collisions and for different charges Zb of the biggest produced fragment. Experimental evidences collected for the systems 27Al+48Ca and 27Al+40Ca at 40 MeV/nucleon used to support this novel method of investigation are also discussed.Comment: Submitted for publication on Phys. Rev. C. 0n 24-oct-201

Evidence for a Novel Reaction Mechanism of a Prompt Shock-Induced Fission Following the Fusion of 78Kr and 40Ca Nuclei at E/A =10 MeV

An analysis of experimental data from the inverse-kinematics ISODEC experiment on 78Kr+40Ca reaction at a bombarding energy of 10 AMeV has revealed signatures of a hitherto unknown reaction mechanism, intermediate between the classical damped binary collisions and fusion-fission, but also substantially different from what is being termed in the literature as fast fission or quasi fission. These signatures point to a scenario where the system fuses transiently while virtually equilibrating mass asymmetry and energy and, yet, keeping part of the energy stored in a collective shock-imparted and, possibly, angular momentum bearing form of excitation. Subsequently the system fissions dynamically along the collision or shock axis with the emerging fragments featuring a broad mass spectrum centered around symmetric fission, relative velocities somewhat higher along the fission axis than in transverse direction, and virtually no intrinsic spin. The class of massasymmetric fission events shows a distinct preference for the more massive fragments to proceed along the beam direction, a characteristic reminiscent of that reported earlier for dynamic fragmentation of projectile-like fragments alone and pointing to the memory of the initial mass and velocity distribution.Comment: 5 PAGES, 6 FIGURE

Projected Quasi-particle Perturbation theory

The BCS and/or HFB theories are extended by treating the effect of four quasi-particle states perturbatively. The approach is tested on the pairing hamiltonian, showing that it combines the advantage of standard perturbation theory valid at low pairing strength and of non-perturbative approaches breaking particle number valid at higher pairing strength. Including the restoration of particle number, further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative + projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches

Isotope correlations as a probe for freeze-out characterization: central 124Sn+64Ni, 112Sn+58Ni collisions

124Sn+64Ni and 112Sn+58Ni reactions at 35 AMeV incident energy were studied with the forward part of CHIMERA multi-detector. The most central collisions were selected by means of a multidimensional analysis. The characteristics of the source formed in the central collisions, as size, temperature and volume, were inspected. The measured isotopes of light fragments (3 <= Z <=8) were used to examine isotope yield ratios that provide information on the free neutron to proton densities.Comment: 4 pages, Contribution to 8th International Conference on Nucleus-Nucleus Collisions, Moscow 200