[en] We analytically evaluate the moments of the spectral density of the $q$-body Sachdev-Ye-Kitaev (SYK) model, and obtain order $1/N^2$ corrections for all moments, where $N$ is the total number of Majorana fermions. To order $1/N$, moments are given by those of the weight function of the Q-Hermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the $1/N^2$ correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when $q$ is odd. Therefore the problem of finding $1/N^2$ corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graph-theoretic property, we can compute them for the $q=1$ and $q=2$ SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any $q$ to $1/N^2$ accuracy. The moments are then used to obtain the spectral density of the SYK model to order $1/N^2$. We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated up to eighth order. This shows that the Q-Hermite approximation is accurate even for small values of $N$.

[en] We analyze the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a theoretical tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. We feed the values of the experimental parameters in our formulas in order to make contact with experiments. Although it remains an open question how the geometric phase of neutrinos could be detected, our theoretical results may open new scenarios in the investigation of the neutrino nature.

[en] According to the “Black Box” theorem the experimental confirmation of neutrinoless double beta decay ($0\nu 2\beta$) would imply that at least one of the neutrinos is a Majorana particle. However, a null $0\nu 2\beta$ signal cannot decide the nature of neutrinos, as it can be suppressed even for Majorana neutrinos. In this letter we argue that if the null $0\nu 2\beta$ decay signal is accompanied by a $0\nu 4\beta$ quadruple beta decay signal, then at least one neutrino should be a Dirac particle. This argument holds irrespective of the underlying processes leading to such decays.

[en] A necessary condition for a particle to be its own Majorana particle is to have no charge. Quasi-particles are a concept that allows an easier description of the collective behaviour of electrons in a metal. The behaviour of independent quasi-particles is representative of the sum of a multitude of individual behaviours of electrons interacting with one another and with the surrounding ions. In the conditions of superconductivity quasi-particles have no longer charges and some Majorana quasi-particles have been recently discovered in superconducting nano-structures. (A.C.)

[en] This paper gives a review of the double beta experimental techniques and projects, in the search for the Majorana neutrino. The purpose of this review is to detail, for each technique, the different origins of background, how they can be identified, and how they can be reduced. Advantages and limitations of the different techniques are discussed

No abstract available

[en] We study the magnetic structures and their connections with topological superconductivity due to the proximity effect for coupled magnetic atomic chains deposited on a superconductor. Several magnetic phases are self-consistently determined, including both the coplanar and noncoplanar ones. For an N-chain triangular atomic ladder, topologically nontrivial superconducting states can always be realized, but strongly depend on its magnetic structure and the number of atomic chains. When N is even, the topologically nontrivial states with noncoplanar structures are characterized by ${\mathbb{Z}}_2$ invariants, while the topologically nontrivial noncoplanar states with an odd N are characterized by integer $\mathbb{Z}$ invariants, due to the presence of a new chiral symmetry. The new chiral symmetry for the noncoplanar states is found to be robust against the on-site disorder, as long as the crystal reflection symmetry is respected. (paper)

[en] This paper is an introduction to relationships between topology, quantum computing, and the properties of Fermions. In particular, we study the remarkable unitary braid group representations associated with Majorana fermions.

[en] One of the goals of modern spectroscopy is to invent techniques which detect neutral excitations that have been theoretically proposed. For superconductors, two-point transport measurements detect the Andreev crossed reflection which confirms the existence of Majorana fermions. We suggest that similar information can also be obtained from a measurement using two piezoelectric transducers. One transducer measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipative response. We propose and show theoretically that the dissipative stress response can be used for studying excitations in a topological superconductor. We investigate a topological superconductor for the case when an Abrikosov vortex lattice is formed. In this case the Majorana fermions are dispersive, a fact that is used to compute the dissipative stress response. - Highlights: • We show that the dissipative stress response can be used to study excitations in a topological superconductor. • We have proposed a sound analogue of the Andreev cross reflection. • We have demonstrated that in the presence of an Abrikosov vortex lattice in a topological superconductor, the Majorana fermions are dispersive.

No abstract available