Recent results have revealed that "concave" small-angle scattering (SAS) data, (i.e. a succession of power-law decays with decreasing values of the scattering exponents), can be successfully modeled in the framework of fat fractals. In this paper, the SAS structure factor for deterministic fat fractals is studied in momentum space. We show that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor, and therefore in each of these ranges all the properties of regular fractals can be inferred to fat fractals. In order to illustrate the above findings we introduce deterministic "fattened" versions of two well-known 3D structural models: Cantor and Vicsek regular deterministic fractals. We calculate the mono- and polydisperse structure factor and study its scattering properties.

The morphology of elastomeric membranes based on silicone rubber, at various concentrations of the catalyst (C) is determined by small-angle neutron scattering (SANS) technique. Nearly all membranes display a hierarchical organization of crystallites in which ramified mesoscale mass fractals are composed of either mass or surfacelike nano fractals. We use the Beaucae model in order to extract information about the radius of gyration of the clusters and about their fractal dimensions. We show that the fractal dimension of the mesoscale fractal is fixed at 2.68 and is independent with the addition of C. However, the nanoscale fractals are characterized by a transition from mass to surface-like fractals at high values of C concentrations.

We present general results on small-angle scattering (SAS) from deterministic (i.e., exactly self-similar) mass, surface and multi-phase fractals. We suggest a method of obtaining additional information from SAS data of deterministic mass fractals, such as the fractal iteration number, the scaling factor, and the number of structural units composing the mass and surface fractal. For a multi-phase system, we show that the qualitative question can be answered from SAS data whether one fractal ‘absorbs’ another one or they are both immersed in a surrounding homogeneous medium. Surface fractals are shown to be constructed as combinations of mass fractals.

In the ballistic regime, polygonal quantum rings connected with an external circuit can be used to inject into it charge and/or spin, with no need for an external bias. This is a ‘one-parameter’ form of quantum pumping; it requires a time-dependent magnetic field and a proper selection of the geometry. With the field in the plane of a ring having one electron per site and an even number of sites a pure spin current, driven by the spin-orbit interaction, is excited in both wires. One can prove that the charge current vanishes identically if the whole system is a bipartite lattice. The pure spin current can be called a magnetic current since magnetization propagates while the system behaves like a gapless insulator. One can use storage units to concentrate and save this magnetization, in much the same way as capacitors store the electric charge. The stored magnetization is long lived and can be used later. By connecting up and downpolarized reservoirs one produces spin currents in another circuit. These currents show a dynamics. They oscillate while the storage units exchange their polarizations. The intensity and amplitude of the oscillations can controlled by tuning the conductance of the wire used to connect the units.

The implementation of a three-level Lambda System in artificial atoms would allow to perform advanced control tasks typical of quantum optics in the solid state realm, with photons in the µm/mm range. However hardware constraints put an obstacle since protection from decoherence is often conflicting with efficient coupling to external fields. We address the problem of performing conventional STImulated Raman Adiabatic Passage (STIRAP) in the presence of low-frequency noise. We propose two strategies to defeat decoherence, based on “optimal symmetry breaking” and dynamical decoupling. We suggest how to apply to the different implementations of superconducting artificial atoms, stressing the key role of non-Markovianity.

We study the generation of p-shell excitons in optically active disk-shaped quantum dots subjected to ultrafast optical pulses. The single-particle spectral properties are obtained from the four-band kp theory, whereas the Coulomb interaction is taken into account within the configuration-interaction approach, particular attention being payed to configuration mixing due to electron-hole correlations. The effect of intraband relaxation processes is included in the non-unitary dynamics derived from the von-Neumann Lindblad equation. We find that the fast hole relaxation processes drive the p-shell excitons to intermediate states which eventually evolve to s-shell excitons via slower electron relaxation.

We employ a general method based on fractional exclusion statistics and Monte Carlo simulations to study the low temperature dynamics of systems with quenched disorder. Depending on the degree of disorder and type of the interacting potentials, different dynamical behaviors are observed at low temperatures. In particular, the systems with a random mixture of repulsive and atractive interactions exhibit a slow typical glassy dynamics. Analyzing the spatial and autocorrelation functions we point out aging effects which are enhanced in the presence of interactions.

We calculate the optical properties of atomic-sized core-shell graphene - boron nitride nanoflakes with triangular shaped cross-section using the density functional theory. The optical properties can be tuned by using different sizes and proportions of the core-shell materials. Anisotropic effects manifested in the absorption of unpolarized light with different orientations of the optical vector are pointed out.

Optimizing excitation transport in quantum networks is an important precursor to the development of highly-efficient light-harvesting devices. We investigate the phenomenon of dephasing-assisted leakage from trapped states, which may ensure efficient transport of excitations across a network. We consider three small networks with known trapped states and study the effect of Markovian quantum noise and classical noise sources with different correlation times, from very low frequency non-Markovian noise to white noise. We show that the excitation - otherwise stalled in trapped states is able to diffuse rapidly through the networks from a source to a sink, with efficiency being generally maximized for intermediate correlation times.

The Rabi Hamiltonian is studied in the dispersive regime and ultra-strong coupling. We employ a recent unitary transformation to obtain not only the approximate Hamiltonian and its energy levels but also its eigenfunctions. The relationship of the approximation with other regimes and their approximations are also discussed.

The thermoelectric voltage of a quantum dot connected to leads is calculated using the scattering R-matrix method. Our approach takes into account a temperature gradient between the contacts beyond the linear regime. We obtain sign changes of the thermopower when varying the temperature or the chemical potential around the resonances. The influence of the coupling strength of the contacts and of the thermoelectric field on the thermoelectric voltage is discussed.

We study pairing correlations by analyzing the coherence length in a HF+BCS formalism with various types of pairing potentials. We compare the density dependent delta (DDD) pairing interaction to effective Gaussian interactions with different width parameters. We then generalize the discussion to quartet correlations, and finally we evaluate the importance of proton-neutron correlations.

In this work we discuss different features of the collective dynamics in neutron rich nuclei which can contribute to constrain the dependence with density of the symmetry energy below saturation. As two components systems, they manifest both isoscalar and isovector modes whose stability is changing with density in a different manner. Within a Fermi liquid theory it is predicted that the isovector modes remain stable at densities under saturation while the isoscalar modes become unstable below a certain value of density. In connection to the former modes the electric dipole response of exotic nuclei shows the emergence of a low energy component when the number of neutrons in excess increases, which is associated to the dynamics of the low density neutron skin against a more stable core. Within schematic models which generalize the Brown-Bolsterli approach as well as in mean-field descriptions based on the LandauVlasov equation, we analyze the role of the symmetry energy on the energy centroid position and on the sum rules for this mode. Then, by considering the same parameterizations with density of the symmetry energy we investigate the isospin dynamics in the conditions when the growth of the unstable isoscalar fluctuations determine the nuclear fragmentation at Fermi energies.

Rotational bands have been observed to emerge in ab initio no-core configuration interaction (NCCI) calculations for p-shell nuclei, as evidenced by rotational patterns for excitation energies, electromagnetic moments, and electromagnetic transitions. We investigate the ab initio emergence of nuclear rotation in the Be isotopes, focusing on ⁹Be for illustration, and make use of basis extrapolation methods to obtain ab initio predictions of rotational band parameters for comparison with experiment. We find robust signatures for rotational motion, which reproduce both qualitative and quantitative features of the experimentally observed bands.

We present a model which extends the approach introduced by D. Brink to evidence the collective nature of Giant Dipole Resonance. For neutron-rich nuclei the emergence of an additional low energy mode that can be associated to the Pygmy Dipole Resonance (PDR) is predicted. We explore the role of a separable dipole-dipole interaction where the condition to have a unique coupling constant was relaxed in order to account for the density dependence of the symmetry energy. The values of the coupling constants are not affecting too much the position of energy centroid of the pygmy state but are strongly influencing the Energy Weighted Sum Rule (EWSR) exhausted by it.

The exact solution of the SU(2) pairing Hamiltonian with non-degenerate single particle orbits was introduced by Richardson in the early sixties. The exact solution passed almost unnoticed till was recovered in the last decade in an effort to describe the disappearance of superconductivity in ultra-small superconducting grains. Since then it has been extended to several families integrable models, called the RichardsonGaudin (RG) models. In particular, the rational family of integrable RG models has been widely applied to mesoscopic systems like small grains, quantum dots and nuclear systems where finite size effects play an important role. We will first introduce these families of integrable models and then we will describe the first applications of the hyperbolic family to spinless cold fermionic atoms in two dimensional lattices and to heavy nuclei.

We review the main aspects concerning the calculation of α-decay intensities to excited states in even-even nuclei using a Coherent State Model (CSM) for the description of the daughter nucleus. The analysis of the α-emission process is based on an α-daughter interaction having a monopole component and a quadrupole-quadrupole (QQ) interaction. The decaying states are calculated through the coupled channels method. The decay intensities to 2⁺ states are reproduced by means of the QQ strength. This interaction strength can be fitted with a linear dependence on the deformation parameter, as predicted by the CSM. Predicted decay-intensities to higher excited states are in reasonable agreement with available experimental data.

Whenever a system has a symmetry, Noether’s theorem tells us there is an associated conserved quantity. For quantum systems this means the Hamiltonian takes on a block-diagonal form, labeled by “good” quantum numbers. While Noether’s theorem tells us this structure exists, it doesn’t tell us the ordering of the states, or which quantum numbers tend to be associated with the ground state. Yet in physical systems we know the ground state tends to belong to the most symmetric irrep. Could it be otherwise? To explore this question, I construct random matrices with point-group symmetries and find an order above and beyond Noether’s theorem. The pattern persists in detailed simulations of many-body systems, even when all physics besides symmetry is taken out. For atomic nuclei, for example, this means the ground states of even-even nuclides have J=0 not due to pairing as we are taught, but due to underlying mathematical structures.

In this contribution I would like to review a few issues on the recent developments concerning the truncation schemes for the nuclear configuration interaction shell model approach. The seniority scheme is a way to solve the pairing Hamiltonian exactly and a good starting point for shell model calculations. Physically meaningful states may also be selected based on importance truncations from a perturbation perspective.

Double β⁻-decay with two neutrinos is one of the important decay modes for an unstable nucleus which can spontaneously change into a stable nucleus. It is also a very complex decay process where three kinds of interactions, the strong interaction, the Coulomb interaction, and the weak interaction, are involved. Recently we have made a systematic analysis on the experimental data of nuclear double β⁻-decay and proposed that there is a law between the logarithm of double β⁻-decay half-lives and the reciprocal of the decay energy. This is a simple and accurate law for half-lives of the double β⁻-decay. We use this law to predict the half-lives of the double β⁻-decay candidates where the mass number of parent nuclei ranges from A=70 (⁷⁰Zn) to A = 204 (²⁰⁴Hg). Numerical results of the half-lives show that ¹⁴²Ce is a very interesting candidate for future experiments to search new emitters of the double β⁻-decay. We also compare the half-lives of double β⁻-decay and α-decay for ¹⁴²Ce where its decay energies of two modes are close and find that double β⁻-decay dominates in this case although double β⁻-decay is a second order process of the weak interaction. The branching ratios between double β⁻-decay and α-decay are listed for the candidates of double β⁻-decay.

The proton-neutron pairing in self-conjugate nuclei is discussed in a formalism of quartets. Quartets are four-body correlated structures built from two neutrons and two protons coupled to total isospin T = 0 and total angular momentum J = 0. The pairing ground state is described as a product of quartets. We review both the case in which the Hamiltonian has a pure isovector character and the case in which, in addition, it contains isoscalar components. The approach is tested by making comparisons with exact shell model calculations for N=Z nuclei with valence nucleons outside the ¹⁶O, ⁴⁰Ca and ¹⁰⁰Sn cores. The quartet formalism is seen to reproduce with great accuracy the exact ground states energies.

In this paper we summarize the study we have recently performed on the effect of isovector pairing correlations upon the symmetry and Wigner energies. First, we review the basic assumptions of the quartet condensation model (QCM) and show how this model can be used in Hartree-Fock (HF) mean field calculations in order to take into account the isovector pairing correlations. Then, within the HF+QCM approach we discuss the influence of proton-neutron pairing on symmetry and Wigner energies for the isobaric chains of even-even nuclei with 24 < A < 100.

α clustering and α condensation in lighter nuclei is presently strongly and increasingly discussed in the literature both from the experimental side as from the theoretical one. In proto-neutron stars a macroscopic condensate of α particles may occur. A discussion of the present status of the theory for quartet condensation in general and for α particle condensation in nuclear matter in particular will be presented.

Results from photon-scattering experiments on ⁷⁶Se and ⁷⁶Ge are given and compared to statistical approaches, based on standard Lorentzian parametrizations.

We have established the anti-symmetrized molecular dynamics (AMD) calculation including a computational code. A phenomenological Gogny-type nuclear force including spin-orbit coupling has been used. A zero-range three-body force described by δ function is adopted. In order to reduce the computing time, in the present work we mainly performed variation-before-projection calculations. Again due to the limitation of computer capability, the calculations are limited to light nuclei. In the present work, we have investigated the light nuclei from the lightest ³He to heaviest ¹⁶C nuclei. From calculated density distributions by the AMD model, we can see clustering or molecular structures in the light nuclei. The AMD model can also give reasonable binding energies compared with data. We have calculated the spectra of the investigated nuclei, obtaining quite good results compared with experimental data. As a example, we performed a variation-after-projection calculation for ¹⁰Be, showing the significant improvement in the calculation of binding energy. The calculations give that the 0⁺ and 1⁻ states have different molecular structures.

Supernova-(anti-)neutrino–nucleus scattering is discussed with reference to neutral-current (NC) and charged-current (CC) processes in heavy stable nuclei. The Donnelly-Walecka method with the associated multipole expansion of the nucleonic current has been adopted as the basic framework in deriving the neutrino-nucleus scattering cross sections. The needed nuclear wave functions are computed by using the quasiparticle random-phase approximation (QRPA) for the even-even target nuclei in the NC processes and the proton-neutron QRPA (pnQRPA) has been used to compute the CC processes for the mentioned nuclei. The wave functions of the stable odd-mass target nuclei have been obtained by the use of the QRPA-based microscopic quasiparticle-phonon model (MQPM), applied to both NC and CC processes. The obtained cross sections are folded by the energy distributions of the various (anti-)neutrino flavors in order to access detection rates in Earth-based neutrino telescopes. The stable Molybdenum (Mo) nuclei serve as examples of application of the formalism, with a subsequent analysis of the results.

The mutually unbiased bases are widely used in many applications of quantum information theory. Recently it was proved that there is a correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares. An extraordinary supersquare is obtained starting from its generating extraordinary subgroup, therefore knowing the general expression of these kinds of subgroups is extremely important. We are focus here on finding the extraordinary subgroups for $\mathbb{F}8 \times \mathbb{F}8$. Further we construct the set of mutually orthogonal extraordinary supersquare of order 8 with the help of nine extraordinary subgroups, whose unique intersection element is the element zero. Then, we show how the complete set of mutually unbiased bases for d = 8 can be obtained. The case d = 8 corresponds to systems of three particles of spin-1/2.

We study the evolution of the entanglement of two independent bosonic modes embedded in a thermal environment, in the framework of the theory of open quantum systems. As a measure of entanglement we use the logarithmic negativity. For a nonzero temperature of the thermal reservoir the entangled initial Gaussian states become always separable in a finite time. For initial squeezed thermal states we calculate the survival time of entanglement and analyze its dependence on temperature, squeezing parameter and mean thermal photon numbers. For a zero temperature of the thermal bath an entangled initial state remains entangled for all finite times, but in the limit of asymptotically large times it becomes separable.

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the Gaussian geometric discord in terms of Hilbert-Schmidt distance and the rescaled form. The system consists of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We take as initial state of the system a two-mode squeezed thermal state and describe the time evolution of the Gaussian geometric discord under the influence of the thermal bath. By tracing the distance between the state of the considered subsystem and the closest classical-quantum Gaussian state we evaluate the Gaussian geometric discord for all times and temperatures. The geometric discord has finite values between 0 and 1 and decreases asymptotically to zero at large times and temperatures, with oscillations on the time axis.