Majoranas with and without a 'character': hybridization, braiding and Majorana number

In this paper we demonstrate under what conditions a pseudo-spin degree of freedom or character can be ascribed to the Majorana bound states (MBS) which can be created at the end of one dimensional non-interacting systems, corresponding to D, DIII and BDI in the usual classification scheme. We have found that such a character is directly related to the class of the topological superconductor and its description by a $\mathbb{Z}$, rather than a $\mathbb{Z}_2$, invariant which corresponds to the BDI class. We have also found that the DIII case with mirror symmetry, which supports multiple MBS, is in fact equivalent to the BDI class with an additional time-reversal symmetry. In all cases where a character can be given to the Majorana states we show how to construct the appropriate operator explicitly in various examples. We also examine the consequences of the Majorana character by considering possible hybridization of MBS brought into proximity and find that two MBS with the same character do not hybridize. Finally, we show that having this character or not has no consequence on the braiding properties of MBS.Comment: 10 pages, 1 figur

Dust in Brown Dwarfs IV. Dust formation and driven turbulence on mesoscopic scales

Dust formation in brown dwarf atmospheres is studied by utilising a model for driven turbulence in the mesoscopic scale regime. We apply a pseudo-spectral method where waves are created and superimposed within a limited wavenumber interval. The turbulent kinetic energy distribution follows the Kolmogoroff spectrum which is assumed to be the most likely value. Such superimposed, stochastic waves may occur in a convectively active environment. They cause nucleation fronts and nucleation events and thereby initiate the dust formation process which continues until all condensible material is consumed. Small disturbances are found to have a large impact on the dust forming system. An initially dust-hostile region, which may originally be optically thin, becomes optically thick in a patchy way showing considerable variations in the dust properties during the formation process. The dust appears in lanes and curls as a result of the interaction with waves, i.e. turbulence, which form larger and larger structures with time. Aiming on a physical understanding of the variability of brown dwarfs, related to structure formation in substellar atmospheres, we work out first necessary criteria for small-scale closure models to be applied in macroscopic simulations of dust forming astrophysical systems.Comment: A&A accepted, 20 page

Spin and Charge Correlations in Quantum Dots: An Exact Solution

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an {\it exact} analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials.Comment: JETPL class, 6 pages, 2 figure

Center-to-Limb Variation of Solar Line Profiles as a Test of NLTE Line Formation Calculations

We present new observations of the center-to-limb variation of spectral lines in the quiet Sun. Our long-slit spectra are corrected for scattered light, which amounts to 4-8 % of the continuum intensity, by comparison with a Fourier transform spectrum of the disk center. We examine the effect of inelastic collisions with neutral hydrogen in NLTE line formation calculations of the oxygen infrared triplet, and the Na I 6160.8 A line. Adopting a classical one-dimensional theoretical model atmosphere, we find that the sodium transition, formed in higher layers, is much more effectively thermalized by hydrogen collisions than the high-excitation oxygen lines. This result appears as a simple consequence of the decrease of the ratio NH/Ne with depth in the solar photosphere. The center-to-limb variation of the selected lines is studied both under LTE and NLTE conditions. In the NLTE analysis, inelastic collisions with hydrogen atoms are considered with a simple approximation or neglected, in an attempt to test the validity of such approximation. For the sodium line studied, the best agreement between theory and observation happens when NLTE is considered and inelastic collisions with hydrogen are neglected in the rate equations. The analysis of the oxygen triplet benefits from a very detailed calculation using an LTE three-dimensional model atmosphere and NLTE line formation. The chi**2 statistics favors including hydrogen collisions with the approximation adopted, but the oxygen abundance derived in that case is significantly higher than the value derived from OH infrared transitions.Comment: 10 pages, 8 figures, to appear in A&

rural and urban schools northern greece in the interwar period

Modernism—as cultural and artistic expression of modern core values—is often associated with urban and industrial contexts, in stark contrast to a "backward countryside". Focusing on modernist reinventions of the rural landscape, MODSCAPES (funded under HERA JRP III call "Uses of the Past", Oct. 2016–2019) specifically questions these preconceived ideas. In different political and ideological contexts agricultural development schemes carried out in Europe during the twentieth century were pivotal experiments in nation-building policies. In addition, they provided a common testing ground for the ideas, and tools, of environmental and social scientists, architects and engineers, planners and landscape architects, as well as artists. This contribution presents the case study of Northern Greece, focusing on rural and urban schools as a key architectural theme, called upon to express the founding values of a collective identity. The dialectic between tradition and innovation, eclecticism and modernism, uncovers its meaning case by case