Confronting quasi-exponential inflation with WMAP seven

We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.Comment: 7 pages, 7 figures, Accepted for publication in JCA

Wright-Fisher diffusion with negative mutation rates

We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the "mutation rates" are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the boundary is not reflecting, and we kill the process once it hits the boundary. We derive the explicit exit distribution from the simplex and probabilistic bounds on the exit time. We also prove that these processes can be viewed as a "stochastic time-reversal" of a Wright-Fisher process of increasing dimensions and conditioned at a random time. A key idea in our proofs is a skew-product construction using certain one-dimensional diffusions called Bessel-square processes of negative dimensions, which have been recently introduced by Going-Jaeschke and Yor.Comment: Published in at http://dx.doi.org/10.1214/11-AOP704 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Absolutely continuous energy bands and extended electronic states in an aperiodic comb-shaped nanostructure

The nature of electronic eigenstates and quantum transport in a comb-shaped Fibonacci nanostructure model is investigated within a tight-binding framework. Periodic linear chains are side-attached to a Fibonacci chain, giving it the shape of an aperiodic comb. The effect of the side-attachments on the usual Cantor set energy spectrum of a Fibonacci chain is analyzed using the Greens function technique. A special correlation between the coupling of the side-attached chain with the Fibonacci chain and the inter-atomic coupling of the Fibonacci chain results in a dramatic triggering of the fragmented Cantor set energy spectrum into multiple sets of continuous sub-bands of extended eigenstates. The result is valid even for a disordered comb and turns out to be a rare exception of the conventional Anderson localization problem. The electronic transport thus can be made selectively ballistic within desired energy regimes. The number and the width of such continuous sub-bands can be easily controlled by tuning the number of atomic sites in the side-coupled periodic linear chains. This gives us a scope of proposing such aperiodic nanostructures as potential candidates for prospective energy selective nanoscale filtering devices.Comment: 7 pages, 7 figures, Revtex versio

Canonical decomposition of a tetrablock contraction and operator model

A triple of commuting operators for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set is called a tetrablock contraction or an $\mathbb E$-contraction. The set $\mathbb E$ is defined as $$\mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\, 1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}.$$ We show that every $\mathbb E$-contraction can be uniquely written as a direct sum of an $\mathbb E$-unitary and a completely non-unitary $\mathbb E$-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.Comment: To appear in Journal of Mathematical Analysis and Application