Extended gravitational action and novel consequences

It is found that the inclusion of higher derivative terms in the gravitational action along with concepts of phase transition and spontaneous symmetry breaking leads to some novel consequence. The Ricci scalar plays the dual role, like a physical field as well as a geometrical field. One gets Klein-Gordon equation for the emerging field and the corresponding quanta of geometry are called Riccions. For the early universe the model removes singularity along with inflation. In higher dimensional gravity the Riccions can break into spin half particle and antiparticle along with breaking of left-right symmetry. Most tantalizing consequences is the emergence of the physical universe from the geometry in the extreme past. Riccions can Bose condense and may account for the dark matter.

Search on a fractal lattice using a quantum random walk

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

Low ML Decoding Complexity STBCs via Codes Over the Klein Group

In this paper, we give a new framework for constructing low ML decoding complexity space-time block codes (STBCs) using codes over the Klein group K. Almost all known low ML decoding complexity STBCs can be obtained via this approach. New full- diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over K, for number of transmit antennas N = 2(m), m >= 1, and rates R > 1 complex symbols per channel use. When R = N, the new STBCs are information- lossless as well. The new class of STBCs have the least knownML decoding complexity among all the codes available in the literature for a large set of (N, R) pairs.

A Kaluza-Klein subtractor

We generalize the results of arXiv : 1212.1875 and arXiv : 1212.6919 on attraction basins and their boundaries to the case of a specific class of rotating black holes,namely the ergo-free branch of extremal black holes in Kaluza-Klein theory. We find that exact solutions that span the attraction basin can be found even in the rotating case by appealing to certain symmetries of the equations of motion. They are characterized by two asymptotic parameters that generalize those of the non-rotating case, and the boundaries of the basin are spinning versions of the (generalized) subtractor geometry. We also give examples to illustrate that the shape of the attraction basin can drastically change depending on the theory.