Majorana Flat Bands in s-Wave Gapless Topological Superconductors

We demonstrate how the non-trivial interplay between spin-orbit coupling and nodeless $s$-wave superconductivity can drive a fully gapped two-band topological insulator into a time-reversal invariant gapless topological superconductor supporting symmetry-protected Majorana flat bands. We characterize topological phase diagrams by a ${\mathbb Z}_2 \times{\mathbb Z}_2$ partial Berry-phase invariant, and show that, despite the trivial crystal geometry, no unique bulk-boundary correspondence exists. We trace this behavior to the anisotropic quasiparticle bulk gap closing, linear vs. quadratic, and argue that this provides a unifying principle for gapless topological superconductivity. Experimental implications for tunneling conductance measurements are addressed, relevant for lead chalcogenide materials.Comment: 5 pages, 4 figures, Phys. Rev. B, Rapid Comm. published versio

Minimal model of point contact Andreev reflection spectroscopy of multiband superconductors

We formulate a minimal model of point contact Andreev reflection spectroscopy of a normal- metal/multiband superconductor interface. The theory generalizes the Blonder-Tinkham-Klapwijk (BTK) formulation to a multiband superconductor and it is based on the quantum waveguides theory. The proposed approach allows an analytic evaluation of the Andreev and normal reflection coefficients and thus is suitable for a data fitting of point contact experiments. The obtained differential conductance curves present distinctive features similar to the ones measured in the experiments on multiband systems, like the iron-based pnictides and the MgB2.Comment: 5 pages, 4 figure

Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.

ESPRIT for multidimensional general grids

We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-standard domains (i.e going beyond multi-rectangles)

Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

Evolutionary Multiplayer Games

Evolutionary game theory has become one of the most diverse and far reaching theories in biology. Applications of this theory range from cell dynamics to social evolution. However, many applications make it clear that inherent non-linearities of natural systems need to be taken into account. One way of introducing such non-linearities into evolutionary games is by the inclusion of multiple players. An example is of social dilemmas, where group benefits could e.g.\ increase less than linear with the number of cooperators. Such multiplayer games can be introduced in all the fields where evolutionary game theory is already well established. However, the inclusion of non-linearities can help to advance the analysis of systems which are known to be complex, e.g. in the case of non-Mendelian inheritance. We review the diachronic theory and applications of multiplayer evolutionary games and present the current state of the field. Our aim is a summary of the theoretical results from well-mixed populations in infinite as well as finite populations. We also discuss examples from three fields where the theory has been successfully applied, ecology, social sciences and population genetics. In closing, we probe certain future directions which can be explored using the complexity of multiplayer games while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape

A supersymmetric matrix model: II. Exploring higher-fermion-number sectors

Continuing our previous analysis of a supersymmetric quantum-mechanical matrix model, we study in detail the properties of its sectors with fermion number F=2 and 3. We confirm all previous expectations, modulo the appearance, at strong coupling, of {\it two} new bosonic ground states causing a further jump in Witten's index across a previously identified critical 't Hooft coupling $\lambda_c$. We are able to elucidate the origin of these new SUSY vacua by considering the $\lambda \to \infty$ limit and a strong coupling expansion around it.Comment: 14 pages, 4 figure