Radial pulsations of neutron stars: computing alternative polytropic models regarding density and adiabatic index

We revisit the problem of radial pulsations of neutron stars by computing four general-relativistic polytropic models, in which "density" and "adiabatic index" are involved with their discrete meanings: (i) "rest-mass density" or (ii) "mass-energy density" regarding the density, and (i) "constant" or (ii) "variable" regarding the adiabatic index. Considering the resulting four discrete combinations, we construct corresponding models and compute for each model the frequencies of the lowest three radial modes. Comparisons with previous results are made. The deviations of respective frequencies of the resolved models seem to exhibit a systematic behavior, an issue discussed here in detail.Comment: 19 page

Topological self-organization of strongly interacting particles

We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological features emerge at different energy bands separated by large gaps. The topology manifests in the way the particles organize in real space to form states with different energy. Each of these states contains topological defects/condensations whose Euler characteristic can be used as a topological number to categorize states belonging to the same energy band. We provide analytical formulas for this topological number and the full energy spectrum of the system for both sparsely and densely filled systems. Furthermore, we analyze the connection with the Gauss-Bonnet theorem of differential geometry, by using the curvature generated in real space by the particle structures. Our result is a demonstration of how states with topological characteristics, emerge in strongly interacting many-body systems following simple underlying rules, without considering the spin, long-range microscopic interactions, or external fields.Comment: 6 pages, 1 figure, some revisions, published in EPJ

Coherent wave transmission in quasi-one-dimensional systems with L\'evy disorder

We study the random fluctuations of the transmission in disordered quasi-one-dimensional systems such as disordered waveguides and/or quantum wires whose random configurations of disorder are characterized by density distributions with a long tail known as L\'evy distributions. The presence of L\'evy disorder leads to large fluctuations of the transmission and anomalous localization, in relation to the standard exponential localization (Anderson localization). We calculate the complete distribution of the transmission fluctuations for different number of transmission channels in the presence and absence of time-reversal symmetry. Significant differences in the transmission statistics between disordered systems with Anderson and anomalous localizations are revealed. The theoretical predictions are independently confirmed by tight binding numerical simulations.Comment: 10 pages, 6 figure

Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models

We study the quantum self-organization of interacting particles in one-dimensional(1D) many-body systems, modeled via Hubbard chains with short-range interactions between the particles. We show the emergence of 1D states with density-wave and clustering order, related to topology, at odd denominator fillings that appear also in the fractional-quantum-Hall-effect (FQHE), which is a 2D electronic system with Coulomb interactions between the electrons and a perpendicular magnetic field. For our analysis we use an effective topological measure applied on the real space wavefunction of the system, the Euler characteristic describing the clustering of the interacting particles. The source of the observed effect is the spatial constraints imposed by the interaction between the particles. In overall, we demonstrate a simple mechanism to reproduce many of the effects appearing in the FQHE, without requiring a Coulomb interaction between the particles or the application of an external magnetic field.Comment: 6 pages, 5 figures, small updates in the text and the references, published in EPJ

Edge states versus diffusion in disordered graphene flakes

We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the Inverse Participation Ratio($IPR$) and it scaling which provides the fractal dimension $D_{2}$. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading to edge states and the diffusive interference mechanism introduced by the short-range disorder. This interplay results in a highly abnormal behavior, wavefunctions are becoming progressively less localized as the disorder is increased, indicated by the decrease of the average $\langle IPR\rangle$ and the increase of $D_{2}$. We verify, that this abnormal behavior is absent for graphene flakes with armchair edges which do not provide edge states.Comment: 9 pages, 14 figures, updated the journal referenc