Neurophysiology

Contains reports on three research projects.National Institutes of Health (Grant 5 RO1 NB-04985-03)Instrumentation Laboratory under the auspices of DSR Project 55-257Bioscience Division of National Aeronautics and Space Administration through Contract NSR 22-009-138Bell Telephone Laboratories, Inc. (Grant)The Teagle Foundation, Inc. (Grant)U. S. Air Force (Aerospace Medical Division) under Contract AF33(615)-388

Neurophysiology

Contains reports on seven research projects.National Institutes of Health (Training Grant 5 TO1 EY00090)Bell Laboratories (Grant

Neurophysiology

Contains reports on two research projects.Teagle Foundation, IncorporatedNational Institutes of HealthBell Telephone Laboratories, Incorporate

Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate |V(t)_{m,n}|0, p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and \epsilon is small enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where \sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was discussed earlier in the literature by Howland

Clinical features of the retinopathy, globe enlarged (rge) chick phenotype

AbstractThe purpose of the study reported here was to characterize the clinical aspects of the autosomal recessive retinopathy, globe enlarged (rge) phenotype in chicks (Gallus gallus). Rge/rge, rge/+ and +/+ chicks were studied from hatch to 336 days of age by general clinical examination, post-mortem examination, vision testing with an optokinetic device, ophthalmoscopy, biomicroscopy, tonometry, central corneal pachymetry, a-mode ultrasonography, infrared photoretinoscopy and photokeratometry. Additionally, preliminary electroretinographic and histopathologic investigations were performed. There is a variable degree of vision loss in rge/rge chicks at 1 day of age with further chicks losing vision over the next few weeks until all chicks become functionally blind by 30 days of age (although some optokinetic responses remain in some of the rge/rge chicks). Over the first few weeks of life rge/rge chicks develop thicker corneas with a larger radius, hyperopia, shallower anterior chambers and enlarged globes both radially and axially, compared to controls. A preliminary ERG study showed that 1 day old rge/rge chicks have an elevated response threshold, a lower amplitude a-wave with a markedly shallow leading slope, a lack of both oscillatory responses and c-waves and, at brighter flashes, an increased b-wave amplitude. Light microscopy revealed no gross retinal abnormalities in young chicks to account for the blindness. A thinning of all retinal layers developed in parallel with globe enlargement. The rge defect is a unique progressive retinal dystrophy that results in a severe visual deficit, abnormal electroretinographic waveforms, and secondary globe enlargement

Neurophysiology

Contains a report on a research project

Pulse-driven quantum dynamics beyond the impulsive regime

We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure

Neurophysiology

Contains reports on five research projects.Bell Telephone Laboratories, IncorporatedNational Institutes of HealthTeagle Foundation, Incorporate