1,053 research outputs found
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
THE BIOMECHANIST AS EXPERT WITNESS
INTRODUCTION
There is a critical need for qualified Biomechanists in the areas of civil and criminal litigation. Currently few "true Biomechanists" work in this area. This has resulted in a vacuum of qualified personnel being filled by people who speak to biomechanical issues with little or no education, training, and experience in anatomy, kinesiology, physiology, research methods, statistics and other areas that constitute the discipline of Biomechanics. The result is that legal decisions are made based upon incorrect or inadequate information.
We suggest that as professional Biomechanists we may have a responsibility to enter this area or in our absence abdicate our role to less qualified individuals. If we as a discipline do engage this role we will upgrade the quality and truthfulness of at least a portion of the litigation process
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
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
Is respiratory activity in the brain mitochondria responsive to thyroid hormone action?: a critical re-evaluation
Excitation of Small Quantum Systems by High-Frequency Fields
The excitation by a high frequency field of multi--level quantum systems with
a slowly varying density of states is investigated. A general approach to study
such systems is presented. The Floquet eigenstates are characterized on several
energy scales. On a small scale, sharp universal quasi--resonances are found,
whose shape is independent of the field parameters and the details of the
system. On a larger scale an effective tight--binding equation is constructed
for the amplitudes of these quasi--resonances. This equation is non--universal;
two classes of examples are discussed in detail.Comment: 4 pages, revtex, no figure
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