Operators with singular continuous spectrum,VII. Examples with borderline time decay

We construct one-dimensional potentialsV(x) so that if onL ²(), thenH has purely singular spectrum; but for a dense setD, D implies that |,e ^-itH |C |t|^-1/2 ln(|t|) for t>2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of Malozemov-Molchanov, provides counterexamples to the direct extension of the theorem of Simon-Spencer on one-dimensional infinity high barriers.This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.     

Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators

We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.

     

Methods for correlating T1ρ and FID components in wideline H NMR studies of motionally heterogeneous polymer systems

We address the problem of correlating the observed FID and T_1ρ components in wideline ¹H relaxation measurements of motionally heterogeneous polymers, and show that different methods of data treatment can highlight different aspects of the correlations present. For a sample of polypropylene we find that the T_1ρ relaxation behaviour is driven by relaxation associated with the intermediate FID component, which strongly suggests a motionally inhomogeneous amorphous region in the sample.     

Direct-to-video holographic readout in quantum wells for three-dimensional imaging through turbid media

Customized photorefractive quantum-well devices have been developed for real-time video acquisition of coherence-gated, three-dimensional images in turbid media. Large-field-of-view holographic imaging with direct video capture is now possible. We have evaluated the role of intensity-limited device performance in Fourier-plane and image-plane holography in such devices and, using near-infrared light, have imaged through turbid phantoms of 13 mean free paths' scattering depth with 50-microm transverse and 60-microm depth resolution.     

Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators

Journal of Statistical Physics - Let V 0be a real-valued function on [0,∞) and V∈L 1([0,R]) for all R&;gt;0 so that H(V 0)=? $\frac{{d^2 }}{{dx^2 }}$ +V 0in L 2([0,∞))...     

Inconsistency in the application of the adiabatic theorem

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.     

In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography

An ultrahigh-speed spectral domain optical coherence tomography (SD-OCT) system is presented that achieves acquisition rates of 29,300 depth profiles/s. The sensitivity of SD-OCT and time domain OCT (TD-OCT) are experimentally compared, demonstrating a 21.7-dB improvement of SD-OCT over TD-OCT. In vivo images of the human retina are presented, demonstrating the ability to acquire high-quality structural images with an axial resolution of 6 microm at ultrahigh speed and with an ocular exposure level of less than 600 microW.     

Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography

A signal-to-noise ratio (SNR) analysis is presented for optical coherence tomography (OCT) signals in which time-domain performance is compared with that of the spectral domain. A significant SNR gain of several hundredfold is found for acquisition in the spectral domain. The SNR benefit is demonstrated experimentally in a hybrid time-domain-spectral-domain OCT system.     

ALP production through non-linear Compton scattering in intense fields

We derive production yields for massive pseudo-scalar and scalar axion-like-particles (ALPs), through non-linear Compton scattering of an electron in the background of low- and high-intensity electromagnetic fields. In particular, we focus on electromagnetic fields from Gaussian plane wave laser pulses. A detailed study of the angular distributions and effects of the scalar and pseudo-scalar masses is presented. It is shown that ultra-relativistic seed electrons can be used to produce scalars and pseudo-scalars with masses up to the order of the electron mass. We briefly discuss future applications of this work towards lab-based searches for light beyond-the-Standard-Model particles.