Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a wave guide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic wave guide.Comment: Published versio

Hunting for the alpha: B→ρρB\to \rho\rho, B→ππB \to \pi\pi, B→πρB \to\pi\rho

The hypothesis of the smallness of penguin contribution to charmless strangeless $B_d (\bar B_d)$ decays allows to determine with high accuracy the value of angle $\alpha$ from the currently available $B \to \rho\rho$, $B \to \pi\pi$ and $B\to \rho\pi$ decay data.Comment: 9 page

Possible large direct CP asymmetry in hadronic B+- -> \pi+- \eta' decays

We calculate the branching ratio and direct CP asymmetry in nonleptonic two body B decays B^+- ->\pi^+- \eta'. It is shown that the tree diagram and gluon fusion mechanism via penguin diagram have comparable contributions to these decays which, as a result, could provide an interesting venue for investigating CP violation. Our estimate shows that the direct CP asymmetry in the above decays could be as large as 75% which along with a branching ratio B(B^- ->\pi^- \eta')=3.4 X 10^{-6} should be accessible to experiment in the near future.Comment: 13 pages, Revtex, 4 figures (included

Tight lower bound to the geometric measure of quantum discord

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.Comment: 10 pages,2 figures. In the previous versions, a constraint was ignored while optimizing the second term in Eq.(5), in which case, only a lower bound on the geometric discord can be obtained. The title is also consequently changed. Accepted in Phys.Rev.