Theoretical predictions of experimental observables sensitive to the symmetry energy: Results of the SMF transport model

In the framework of mean-field based transport approaches, we discuss recent results concerning heavy ion reactions between charge asymmetric systems, from low up to intermediate energies. We focus on isospin sensitive observables, aiming at extracting information on the density dependence of the isovector part of the nuclear effective interaction and of the nuclear symmetry energy. For reactions close to the Coulomb barrier, we explore the structure of collective dipole oscillations, rather sensitive to the low-density behavior of the symmetry energy. In the Fermi energy regime, we investigate the interplay between dissipation mechanisms, fragmentation and isospin effects. At intermediate energies, where regions with higher density and momentum are reached, we discuss collective flows and their sensitivity to the momentum dependence of the isovector interaction channel, which determines the splitting of neutron and proton effective masses. Finally, we also discuss the isospin effect on the possible phase transition from nucleonic matter to quark matter. Results are critically reviewed, also trying to establish a link, when possible, with the outcome of other transport models.Comment: A contribution to the upcoming EPJA Special Volume on Nuclear Symmetry Energ

Reduced basis emulation of pairing in finite systems

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing highly accurate results. This work is meant to show that the RBM is an efficient and accurate emulator for the strong correlations induced by the pairing interaction in a variety of finite systems like ultrasmall superconducting grains, interacting topological superfluids and mesoscopic hybrid superconductor-semiconductor devices, all of which require an expensive, beyond-mean-field, particle-number conserving description. These systems are modelled by the number-conserving Richardson pairing Hamiltonian and its appropriate generalizations. Their ground state is solved for exactly using the Density Matrix Renormalization Group. The reduced basis is assembled iteratively from a small number of exact ground state vectors, well-chosen from across the relevant parameter space using a fast estimate of the emulation error and a greedy local optimization algorithm. The reduced basis emulation is found to accurately describe the weak-to-strong pairing cross-over in small grains, the third-order topological phase transition of the interacting Richardson-Kitaev chain, and the complex charge stability diagram of a hybrid quantum dot - superconductor device. RBMs are thus confirmed to be cheap and accurate emulators for the widely encountered superconducting phenomena. Capable of providing orders of magnitude computational speed-up with respect to approaches based only on traditional many-body solvers, they open new possibilities in building and solving models of interacting many-body systems and in better interfacing them with experimental design and data analysis.Comment: 16 pages, 17 figure

Surrogate model solver for impurity-induced superconducting subgap states

A simple impurity solver is shown to capture the impurity-induced superconducting subgap states in quantitative agreement with the numerical renormalization group and quantum Monte-Carlo simulations. The solver is based on the exact diagonalization of a single-impurity Anderson model with discretized superconducting reservoirs including only a small number of effective levels. Their energies and couplings to the impurity $d$-level are chosen so as to best reproduce the Matsubara frequency dependence of the hybridization function. We provide a number of critical benchmarks and demonstrate the solvers efficiency in combination with the reduced basis method [Phys. Rev. B 107, 144503 (2023)] by calculating the phase diagram for an interacting three-terminal junction.Comment: 15 pages, 15 figure

Collective features of nuclear dynamics with exotic nuclei within microscopic transport models

We employ a transport model based on Landau-Vlasov equation to explore the dipolar response of neutron rich systems and its dependence on the symmetry energy. We present evidences for collective features of the Pygmy Dipole Resonance (PDR) and study its dependence with the mass number. We extract a parametrization for the energy centroid position, 41A−1/3, which agrees quite well with the data for Ni, Zr, Sn and Pb. A linear correlation between the Energy Weighted Sum Rule (EWSR) associated to PDR and the neutron skin thickness is evidenced. An increase of 15 MeV fm2 of EWSR to a change of 0.1 fm of neutron skin size is obtained. We conclude that different nuclei having close neutron skin size will exhaust the same EWSR in the pygmy region. Consequently a precise experimental estimate of total EWSR exhausted by PDR allows the determination of the neutron skin size and to constrain the slope parameter of the symmetry energy

Collective features of nuclear dynamics with exotic nuclei within microscopic transport models

We employ a transport model based on Landau-Vlasov equation to explore the dipolar response of neutron rich systems and its dependence on the symmetry energy. We present evidences for collective features of the Pygmy Dipole Resonance (PDR) and study its dependence with the mass number. We extract a parametrization for the energy centroid position, 41A−1/3, which agrees quite well with the data for Ni, Zr, Sn and Pb. A linear correlation between the Energy Weighted Sum Rule (EWSR) associated to PDR and the neutron skin thickness is evidenced. An increase of 15 MeV fm2 of EWSR to a change of 0.1 fm of neutron skin size is obtained. We conclude that different nuclei having close neutron skin size will exhaust the same EWSR in the pygmy region. Consequently a precise experimental estimate of total EWSR exhausted by PDR allows the determination of the neutron skin size and to constrain the slope parameter of the symmetry energy