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In Coupled-Cluster (CC) theory, unphysical complex energies may arise in the presence of strong magnetic fields, near conical intersections, or in systems exhibiting complex Abelian point group symmetries. This issue originates from the…

When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase…

We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly…

Clustering plays an important role in the structure of nuclei, especially for light nuclei in the $p$-shell. In nuclear cluster models these degrees of freedom are introduced explicitly. In the Resonating Group Method or in the Generator…

We present a phenomenological theory of nuclei which incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy at low densities of nuclear matter and is consistent…

This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the…

We investigate properties and the distribution of light nuclei (A<4) in symmetric nuclear matter of finite temperature within a microscopic framework. For this purpose we have solved few-body Alt-Grassberger-Sandhas type equations for…

The isothermal compression of a dilute nucleonic gas invoking cluster degrees of freedom is studied in an equilibrium statistical model; this clusterized system is found to be more stable than the pure nucleonic system. The equation of…

A theoretical approach was developed to describe secondary particle emission in heavy ion collisions, with special regards to pre-equilibrium {\alpha}-particle production. Griffin's model of non-equilibrium processes is used to account for…

The four-particle system is the simplest few-body system containing the fundamental physics involved in ultracold fermionic gases. We have made recent efforts to solve the quantum four-body problem in the adiabatic hyperspherical…

We investigate nuclear matter at finite temperature and density, including the formation of light clusters up to the alpha particle The novel feature of this work is to include the formation of clusters as well as their dissolution due to…

In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al. introduced a new variational approach to treat strong attractive boson-fermion (BF) correlations in BF atomic mixtures. The proposed theory predicts a first order phase…

The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical…

We prove a new concentration result for non-catalytic decoupling by showing that, for suitably large $t$, applying a unitary chosen uniformly at random from an approximate $t$-design on a quantum system followed by a fixed quantum operation…

We obtain possibly valuable information about the phase diagram of rather dense composite particles at high fermion as well as boson number density but low temperature, which is not accessible to relativistic heavy ion collision…

We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…

We propose a Constraint Molecular Dynamics model for Fermionic system. In this approach the equations of motion of wave packets for the nuclear many-body problem are solved by imposing that the one-body occupation probability…

In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…

We have recently developed a self-consistent theory of Strong-Coupling in the presence of an incoherent pumping [arXiv:0807.3194] and shown how it could reproduce quantitatively the experimental data [PRL 101, 083601 (2008)]. Here, we…

We present a microscopic calculation of alpha-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The alpha-cluster…