Nuclear pairing at finite temperature and angular momentum

An approach is proposed to nuclear pairing at finite temperature and angular momentum, which includes the effects of the quasiparticle-number fluctuation and dynamic coupling to pair vibrations within the self-consistent quasiparticle random-phase approximation. The numerical calculations of pairing gaps, total energies, and heat capacities are carried out within a doubly folded multilevel model as well as several realistic nuclei. The results obtained show that, in the region of moderate and strong couplings, the sharp transition between the superconducting and normal phases is smoothed out, causing a thermal pairing gap, which does not collapse at a critical temperature predicted by the conventional Bardeen-Cooper-Schrieffer's (BCS) theory, but has a tail extended to high temperatures. The theory also predicts the appearance of a thermally assisted pairing in hot rotating nuclei.Comment: 4 pages, 1 figure, To appear in the Proceedings of the First Workshop on State of the Art in Nuclear Cluster Physics, Strasbourg 13 - 16 May, 200

Canonical and microcanonical ensemble descriptions of thermal pairing within BCS and quasiparticle RPA

We propose a description of pairing properties in finite systems within the canonical and microcanonical ensembles. The approach is derived by solving the BCS and self-consistent quasiparticle random-phase approximation with the Lipkin-Nogami particle-number projection at zero temperature. The obtained eigenvalues are embedded into the canonical and microcanonical ensembles. The results obtained are found in quite good agreement with the exact solutions of the doubly-folded equidistant multilevel pairing model as well as the experimental data for $^{56}$Fe nucleus. The merit of the present approach resides in its simplicity and its application to a wider range of particle number, where the exact solution is impracticable.Comment: 10 pages, 2 figures, accepted for publication in Phys. Rev.

Pairing effect on the giant dipole resonance width at low temperature

The width of the giant dipole resonance (GDR) at finite temperature T in Sn-120 is calculated within the Phonon Damping Model including the neutron thermal pairing gap determined from the modified BCS theory. It is shown that the effect of thermal pairing causes a smaller GDR width at T below 2 MeV as compared to the one obtained neglecting pairing. This improves significantly the agreement between theory and experiment including the most recent data point at T = 1 MeV.Comment: 8 pages, 5 figures to be published in Physical Review

Dynamical Behavior of a stochastic SIRS epidemic model

In this paper we study the Kernack - MacKendrick model under telegraph noise. The telegraph noise switches at random between two SIRS models. We give out conditions for the persistence of the disease and the stability of a disease free equilibrium. We show that the asymptotic behavior highly depends on the value of a threshold $\lambda$ which is calculated from the intensities of switching between environmental states, the total size of the population as well as the parameters of both SIRS systems. According to the value of $\lambda$, the system can globally tend towards an endemic case or a disease free case. The aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. Moreover, the attraction of the omega-limit set and the stationary distribution of solutions will be pointed out.Comment: 16 page

Optimal control under uncertainty and Bayesian parameters adjustments

We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayesian rule after each impulse. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. The derivation of the dynamic programming equation seems to be new in this context. The main difficulty lies in the nature of the set of controls which depends in a non trivial way on the initial data through the filtration itself

Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics

The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of $^{28}$Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other topics included are a nuclear Born-Oppenheimer approximation for an {\em ab initio} quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included.Comment: 203 pages, many figure