Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

"Gauging" the Fluid

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin \cite{12} quantization formalism is adopted in which the original system is converted to a local gauge theory and is embedded in a {\it canonical} extended phase space. In a different reduced phase space scheme \cite{vy} also the original model is converted to a gauge theory and subsequently the two distinct gauge invariant formulations of the fluid model are related explicitly. This strengthens the equivalence between the relativistic membrane (where a gauge invariance is manifest) and the fluid (where the gauge symmetry is hidden). Relativistic generalizations of the extended model is also touched upon.Comment: Version to appear in J.Phys. A: Mathematical and Genera

Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''

In this reply, we show that when we apply standard distribution theory to the Lippmann-Schwinger equation, the resulting spaces of test functions would comply with the Hardy axiom only if classic results of Paley and Wiener, of Gelfand and Shilov, and of the theory of ultradistributions were wrong. As well, we point out several differences between the ``standard method'' of constructing rigged Hilbert spaces in quantum mechanics and the method used in Time Asymmetric Quantum Theory.Comment: 13 page

The sonic screwdriver

When samples of interest are small enough, even the relatively weak forces and torques associated with light can be sufficient for mechanical manipulation, can offer extraordinary position control, and can measure interactions with three orders of magnitude better resolution than atomic force microscopy. However, as the components of interest grow to slightly larger length scales (which may yet be of interest for microfluidic, lab-on-a-chip technologies and for research involving biomedical imaging), other approaches gain strength. This paper includes discussion of the angular momentum carried by sonic beams that we have implemented both to levitate and controllably rotate disks as large as four inches across. Discussion of such acoustic beams complements the discussion of the angular momentum carried by light and, by further analogy, how we view stationary states discussed in quantum mechanics. Hence, a primary use of the sonic screwdriver is as a model system, although these beams are useful for a variety of other reasons as well (not least for aberration correction for ultrasonic array systems). Methods, including the use of holographically structured fields, are discussed

The Nanoporation Project: a Potential New Application of Magnetic Resonance Guided Focused Ultrasound (MRgFUS)

No abstract available