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Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…
Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial-wave amplitudes do not respect exact unitarity relation. There are different approaches to get…
Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…
Static properties of an anharmonic potential model for planar two-electron quantum dots are investigated using a method which allows for the exact representation of the matrix elements, including the full Coulombic electron - electron…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
A renormalization scheme is developed to study an anisotropic quantum XY spin chain in a quasiperiodic transverse field. The critical phase of the quasi-particle excitations of the model with fractal wave functions exists in a finite…
We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body…
In this paper we present numerical and analytical studies on the complete synchronization phenomena exhibited by unidirectionally coupled two variant of Murali-Lakshmanan-Chua circuits. The transition of the coupled system from an…
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we…
The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…
The R- and K-matrix parametrizations are analyzed and compared for the elastic alpha-alpha scattering at center-of-mass energies below 40 MeV. The two parametrizations differ in their definitions of the resonance energy which can lead to…
We show that a saturable single-frequency elastic T-matrix approach to scattering of light by atoms agrees remarkably well with a master equation description in the regime of unsaturated atoms, or for large separation between the atoms. If…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…