Related papers: Two-body matrix elements of Pauli-projected excent…
As part of the ongoing NUCLEI-PACK project, this study presents a semi-classical framework for exploring the microscopic geometry of light and exotic nuclei based on optimized sphere packing of nucleons and clusters. Starting from explicit…
Lately, there has been a renewed interest in fermionic 1-body reduced density matrices and their restrictions beyond the Pauli principle. These restrictions are usually quantified using the polytope of allowed, ordered eigenvalues of such…
Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include…
One of the common methods used to investigate the nuclear structures of atomic nuclei is the nuclear shell model. Similar to the placement of atomic electrons into orbits, in the nuclear shell model, protons and neutrons are thought to fill…
Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli…
The basic principles of self-organization of one-component charged particles, confined in disk and circular parabolic potentials, are proposed. A system of equations is derived, that allows us to determine equilibrium configurations for an…
We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated…
The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…
In a recent paper (Hajdukovic 2020a) quantum vacuum was considered as a source of gravity and, the simplest phenomenon, the gravitational polarization of the quantum vacuum by an immersed point-like body, was studied. In the present paper,…
A highly specialized two-center shell model has been developed accounting for the splitting of a deformed parent nucleus into two ellipsoidaly deformed fragments. The potential is based on deformed oscillator wells in direct correspondance…
We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between $N$ excitons can be treated exactly through a set of dimensionless ``Pauli scatterings'' between two excitons. Many-body…
We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined.…
We present a perturbative treatment of nonlinear galaxy clustering in the context of the cubic Galileon modified gravity model, in terms of 2nd order Lagrangian Perturbation theory and an extension of ellipsoidal collapse that includes…
A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…
Physical problems for which the existence of non-trivial topological Pauli phase (i.e. fractional quantization of angular orbital angular momenta that is possible in 2D case) is essential are discussed within the framework of…
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained…
We present an efficient method for construction of a fully anti-commutative set of Pauli generators (elements of the Pauli group) from a commutative set of operators that are composed exclusively from Pauli $\hat x_i$ operators (purely X…
We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of…