Related papers: How random are random nuclei? Shapes, triangles an…
Given $2n$ unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a topological sphere. As $n$ tends to…
Rotational bands are commonly used in the analysis of the spectra of atomic nuclei. The early version of the interacting boson model of Arima and Iachello has been foundational to the description of rotations in nuclei. The model is based…
The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters beta and gamma is a classical theme in nuclear structure. Here we use the quadrupole invariants (Kumar), calculated within…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Quantum fluctuations concerning the shape of nuclei are treated within the framework of covariant density functional theory. Long range correlations beyond mean field are taken into account by configuration mixing of wave functions with…
The signature splitting of the $\gamma$-vibrational band of several Ru, Pd, Xe, Ba, Os and Pt isotopes is analyzed in the framework of the interacting boson model (IBM). The nuclei studied are close to the $\gamma$-unstable SO(6) limit of…
Shapes and high-spin properties of nuclei from the neutron-rich (N>56) zirconium region are calculated using the Nilsson-Strutinsky method with the cranked Woods-Saxon average potential and monopole pairing residual interaction. The shape…
We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we…
The inherent nodal structures of the wavefunctions of 4-nucleon systems have been investigated. The quantum numbers of the excited states (resonances) have been deduced. It was found that all the T=0 even-parity resonances are dominated by…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
The collective dynamics of a many-body system is described as a special case of low-energy quantum dynamics, occurring when the ground state breaks a continuous symmetry of the Hamiltonian. This approach is applied to the spontaneous…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
Random one plus two-body hamiltonians invariant with respect to $O({\cal N}_1) \oplus O({\cal N}_2)$ symmetry in the group-subgroup chains $U({\cal N}) \supset U({\cal N}_1) \oplus U({\cal N}_2) \supset O({\cal N}_1) \oplus O({\cal N}_2)$…
Variational quantum computing offers a flexible computational paradigm with applications in diverse areas. However, a key obstacle to realizing their potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP, its parameter…
The consequences of the spontaneous breaking of rotational symmetry are investigated in a field theory model for deformed nuclei, based on simple separable interactions. The crucial role of the Ward-Takahashi identities to describe the…
It is shown that the nature of quantum statistics can be clarified by assuming the existence of a background of random gravitational fields and waves, distributed isotropically in the space. This background is responsible for correlating…