1,171 research outputs found
Development of optimum clamp combinations for strap-down inertial measuring units with field replaceable sensors
Optimum clamp combinations for strap down inertial measuring units with field replaceable sensor
Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example
We study a perturbed Floquet Hamiltonian depending on a coupling
constant . The spectrum is assumed to be pure point and
dense. We pick up an eigen-value, namely , and show the
existence of a function defined on such that
for all , 0 is a point of
density for the set , and the Rayleigh-Schr\"odinger perturbation series
represents an asymptotic series for the function . All ideas
are developed and demonstrated when treating an explicit example but some of
them are expected to have an essentially wider range of application.Comment: Latex, 24 pages, 51
Superfluid-insulator transition in a periodically driven optical lattice
We demonstrate that the transition from a superfluid to a Mott insulator in
the Bose-Hubbard model can be induced by an oscillating force through an
effective renormalization of the tunneling matrix element. The mechanism
involves adiabatic following of Floquet states, and can be tested
experimentally with Bose-Einstein condensates in periodically driven optical
lattices. Its extension from small to very large systems yields nontrivial
information on the condensate dynamics.Comment: 4 pages, 4 figures, RevTe
Weakly regular Floquet Hamiltonians with pure point spectrum
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on
the parameter omega. We assume that the spectrum of H is discrete, {h_m (m =
1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian
operator, 2pi-periodic in t. Let J > 0 and set Omega_0 = [8J/9,9J/8]. Suppose
that for some sigma > 0: sum_{m,n such that h_m > h_n} mu_{mn}(h_m -
h_n)^(-sigma) < infinity where mu_{mn} = sqrt(min{M_m,M_n)) M_m M_n. We show
that in that case there exist a suitable norm to measure the regularity of V,
denoted epsilon, and positive constants, epsilon_* & delta_*, such that: if
epsilon
|Omega_0| - delta_* epsilon and the Floquet Hamiltonian has a pure point
spectrum for all omega in Omega_infinity.Comment: 35 pages, Latex with AmsAr
Neurophysiology
Contains reports on four research projects.National Institutes of Health (Grant B-1865-(C3), Grant MH-04737-02)United States Air Force, Aeronautical Systems Division (Contract AF33(616)-7783)Teagle Foundation, IncorporatedBell Telephone Laboratories, Incorporate
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
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 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
Comprehensive behavioral testing in the R6/2 mouse model of Huntington's disease shows no benefit from CoQ10 or minocycline
Previous studies of the effects of coenzyme Q10 and minocycline on mouse models of Huntington’s disease have produced conflicting results regarding their efficacy in behavioral tests. Using our recently published best practices for husbandry and testing for mouse models of Huntington’s disease, we report that neither coenzyme Q10 nor minocycline had significant beneficial effects on measures of motor function, general health (open field, rotarod, grip strength, rearing-climbing, body weight and survival) in the R6/2 mouse model. The higher doses of minocycline, on the contrary, reduced survival. We were thus unable to confirm the previously reported benefits for these two drugs, and we discuss potential reasons for these discrepancies, such as the effects of husbandry and nutrition
The SKA Particle Array Prototype: The First Particle Detector at the Murchison Radio-astronomy Observatory
We report on the design, deployment, and first results from a scintillation
detector deployed at the Murchison Radio-astronomy Observatory (MRO). The
detector is a prototype for a larger array -- the Square Kilometre Array
Particle Array (SKAPA) -- planned to allow the radio-detection of cosmic rays
with the Murchison Widefield Array and the low-frequency component of the
Square Kilometre Array. The prototype design has been driven by stringent
limits on radio emissions at the MRO, and to ensure survivability in a desert
environment. Using data taken from Nov.\ 2018 to Feb.\ 2019, we characterize
the detector response while accounting for the effects of temperature
fluctuations, and calibrate the sensitivity of the prototype detector to
through-going muons. This verifies the feasibility of cosmic ray detection at
the MRO. We then estimate the required parameters of a planned array of eight
such detectors to be used to trigger radio observations by the Murchison
Widefield Array.Comment: 17 pages, 14 figures, 3 table
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