Understanding the Fano Resonance : through Toy Models

The Fano Resonance, involving the mixing between a quasi-bound `discrete' state of an inelastic channel lying in the continuum of scattering states belonging to the elastic channel, has several subtle features. The underlying ideas have recently attracted attention in connection with interference effects in quantum wires and mesoscopic transport phenomena. Simple toy models are provided in the present study to illustrate the basics of the Fano resonance in a simple and tractable setting.Comment: 17 pages, 1 figur

Remarks on the Noncommutative Gravitational Quantum Well

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either commutative space or noncommutative space descriptions. Comparison with recent experimental data with cold neutrons at Grenoble imposes an upper bound on the noncommutative parameter. Also, our results are compared with a recent numerical analysis of a similar problem.Comment: Latex, 17 pages, Title changed, minor modifications, 3 new references added, To appear in Phys. Rev.

Applicability of Heavy Quark Effective Theory to the Radiative Decay B→K∗+γB\to K^* + \gamma

In the context of the observed decay $B \rightarrow K^* \gamma$ the applicability of the Heavy Quark Effective Theory (HQET), treating both b and s as heavy quarks, is examined. We show that the heavy s-quark approximation, as can be found in the literature, is not reliable.Comment: Plain LaTeX fil

Geometry Of Quantum Evolution And The Coherent State

The geometric approach to quantum mechanics initiated by Berry\u27s remarkable discovery [Proc. R. Soc. London Ser. A 392, 45 (1984)] of the anholonomy of the phase of the wave function and subsequent developments leading to a recent reformulation of the geometry of quantum evolution by Anandan and Aharonov [Phys. Rev. Lett. 65, 1697 (1990)] is shown to find an explicit and suggestive realization through the coherent-state representation

The Harmonic Lattice, Recoilless Transitions, And The Coherent State

The probability for recoilless transitions, relevant for the understanding of x-ray scattering from atoms bound in a crystal (applicable also to elastic scattering of neutrons from solids and to the Mossbauer effect), given by the Debye-Waller factor, is derived in a novel manner using the coherent state basis for the normal mode oscillators describing the harmonic lattice, a method which, while being simple and elegant, also reveals the relationship to a heuristic classical discussion of the problem