Quantum microscopic approach to low-energy heavy ion collisions

The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of heavy ion collisions at energies around the Coulomb barrier. The competition between fusion and nucleon transfer mechanisms is investigated. For intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by reducing the Coulomb repulsion. A comparison with sub-barrier transfer experimental data shows that pairing correlations are playing an important role in enhancing proton pair transfer. For heavier and more symmetric systems, a fusion hindrance is observed due to the dominance of the quasi-fission process. Typical quasi-fission time of few zeptoseconds are obtained. Actinide collisions are also investigated both within the TDHF approach and with the Ballian-V\'en\'eroni prescription for fluctuation and correlation of one-body observables. The possible formation of new heavy neutron-rich nuclei in actinide collisions is discussed.Comment: Invited Plenary Talk given at NN201

Comments on a Full Quantization of the Torus

Gotay showed that a representation of the whole Poisson algebra of the torus given by geometric quantization is irreducible with respect to the most natural overcomplete set of observables. We study this representation and argue that it cannot be considered as physically acceptable. In particular, classically bounded observables are quantized by operators with unbounded spectrum. Effectively, the latter amounts to lifting the constraints that compactify both directions in the torus.Comment: 10 pages. New "Discussion" section. References added. To appear in IJMP

Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua

We derive an expression that allows for the unambiguous evaluation of the overlap between two arbitrary quasiparticle vacua, including its sign. Our expression is based on the Pfaffian of a skew-symmetric matrix, extending the formula recently proposed by [L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009)] to the most general case, including the one of the overlap between two different blocked n-quasiparticle states for either even or odd systems. The powerfulness of the method is illustrated for a few typical matrix elements that appear in realistic angular-momentum-restored Generator-Coordinate Method calculations when breaking time-reversal invariance and using the full model space of occupied single-particle states.Comment: 10 pages, 3 figure

Effects of Nuclear Structure on Quasi-fission

The quasi-fission mechanism hinders fusion of heavy systems because of a mass flow between the reactants, leading to a re-separation of more symmetric fragments in the exit channel. A good understanding of the competition between fusion and quasi-fission mechanisms is expected to be of great help to optimize the formation and study of heavy and superheavy nuclei. Quantum microscopic models, such as the time-dependent Hartree-Fock approach, allow for a treatment of all degrees of freedom associated to the dynamics of each nucleon. This provides a description of the complex reaction mechanisms, such as quasi-fission, with no parameter adjusted on reaction mechanisms. In particular, the role of the deformation and orientation of a heavy target, as well as the entrance channel magicity and isospin are investigated with theoretical and experimental approaches.Comment: Invited talk to NSRT12. To be published in Eur. Phys. J. Web of Con

The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte

On the causal properties of warped product spacetimes

It is shown that the warped product spacetime P=M *_f H, where H is a complete Riemannian manifold, and the original spacetime M share necessarily the same causality properties, the only exceptions being the properties of causal continuity and causal simplicity which present some subtleties. For instance, it is shown that if diamH=+\infty, the direct product spacetime P=M*H is causally simple if and only if (M,g) is causally simple, the Lorentzian distance on M is continuous and any two causally related events at finite distance are connected by a maximizing geodesic. Similar conditions are found for the causal continuity property. Some new results concerning the behavior of the Lorentzian distance on distinguishing, causally continuous, and causally simple spacetimes are obtained. Finally, a formula which gives the Lorentzian distance on the direct product in terms of the distances on the two factors (M,g) and (H,h) is obtained.Comment: 22 pages, 2 figures, uses the package psfra

Are Causality Violations Undesirable?

Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causality violations, which Bonnor and Steadman identified even in solutions to the Einstein equation referring to ordinary laboratory situations, are not necessarily undesirable. First, a space-time in which every causal curve can be extended into a closed causal curve is singularity free--a necessary property of a globally applicable physical theory. Second, a causality-violating space-time exhibits a nontrivial topology--no closed timelike curve (CTC) can be homotopic among CTCs to a point, or that point would not be causally well behaved--and nontrivial topology has been explored as a model of particles. Finally, if every causal curve in a given space-time passes through an event horizon, a property which can be called "causal censorship", then that space-time with event horizons excised would still be causally well behaved.Comment: Accepted in October 2008 by Foundations of Physics. Latex2e, 6 pages, no figures. Presented at a seminar at the Universidad Nacional Autonoma de Mexico. Version 2 was co-winner of the QMUL CTC Essay Priz

Obstruction Results in Quantization Theory

We define the quantization structures for Poisson algebras necessary to generalise Groenewold and Van Hove's result that there is no consistent quantization for the Poisson algebra of Euclidean phase space. Recently a similar obstruction was obtained for the sphere, though surprising enough there is no obstruction to the quantization of the torus. In this paper we want to analyze the circumstances under which such obstructions appear. In this context we review the known results for the Poisson algebras of Euclidean space, the sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc

Linear Responses in Time-dependent Hartree-Fock-Bogoliubov Method with Gogny Interaction

A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.Comment: 10 pages, 13 figure

How Discrete Patterns Emerge from Algorithmic Fine-Tuning: A Visual Plea for Kroneckerian Finitism

International audienceThis paper sets out to adduce visual evidence for Kroneckerian finitism by making perspicuous some of the insights that buttress Kronecker's conception of arithmetization as a process aiming at disclosing the arithmetical essence enshrined in analytical formulas, by spotting discrete patterns through algorithmic fine-tuning. In the light of a fairly tractable case study, it is argued that Kronecker's main tenet in philosophy of mathematics is not so much an ontological as a methodological one, inasmuch as highly demanding requirements regarding mathematical understanding prevail over mere preemptive reductionism to whole numbers