Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example

We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that $\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a point of density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series represents an asymptotic series for the function $\lambda(\beta)$. 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

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

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

An Experimental Approach to a Rapid Propulsion and Aeronautics Concepts Testbed

Modern aircraft design tools have limitations for predicting complex propulsion-airframe interactions. The demand for new tools and methods addressing these limitations is high based on the many recent Distributed Electric Propulsion (DEP) Vertical Take-Off and Landing (VTOL) concepts being developed for Urban Air Mobility (UAM) markets. We propose that low cost electronics and additive manufacturing can support the conceptual design of advanced autonomy-enabled concepts, by facilitating rapid prototyping for experimentally driven design cycles. This approach has the potential to reduce complex aircraft concept development costs, minimize unique risks associated with the conceptual design, and shorten development schedule by enabling the determination of many "unknown unknowns" earlier in the design process and providing verification of the results from aircraft design tools. A modular testbed was designed and built to evaluate this rapid design-build-test approach and to support aeronautics and autonomy research targeting UAM applications utilizing a complex, transitioning-VTOL aircraft configuration. The testbed is a modular wind tunnel and flight model. The testbed airframe is approximately 80% printed, with labor required for assembly. This paper describes the design process, fabrication process, ground testing, and initial wind tunnel structural and thermal loading of a proof-of-concept aircraft, the Langley Aerodrome 8 (LA-8)

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

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

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

The Rat Medial Prefrontal Cortex Exhibits Flexible Neural Activity States during the Performance of an Odor Span Task

Medial prefrontal cortex (mPFC) activity is fundamental for working memory (WM), attention, and behavioral inhibition; however, a comprehensive understanding of the neural computations underlying these processes is still forthcoming. Toward this goal, neural recordings were obtained from the mPFC of awake, behaving rats performing an odor span task of WM capacity. Neural populations were observed to encode distinct task epochs and the transitions between epochs were accompanied by abrupt shifts in neural activity patterns. Putative pyramidal neuron activity increased earlier in the delay for sessions where rats achieved higher spans. Furthermore, increased putative interneuron activity was only observed at the termination of the delay thus indicating that local processing in inhibitory networks was a unique feature to initiate foraging. During foraging, changes in neural activity patterns associated with the approach to a novel odor, but not familiar odors, were robust. Collectively, these data suggest that distinct mPFC activity states underlie the delay, foraging, and reward epochs of the odor span task. Transitions between these states likely enables adaptive behavior in dynamic environments that place strong demands on the substrates of working memory

User-Centered Evaluation of a Discovery Layer System with Google Scholar

Discovery layer systems allow library users to obtain search results from multiple library resources and view results in a consistent format. The implementation of a discovery layer is expected to simplify users’ workflow of searching for scholarly information. Previous studies on discovery layer systems focused on functionality and content, but not quality of search results from the user’s perspective. The objective of this study was to obtain users’ assessment of search results of a discovery layer system (Ex Libris Primo®) and compare that with a widely used scholarly search tool (Google Scholar). Results showed that Primo’s search results relevancy is comparable to Google Scholar, but it received significantly lower usability and preference ratings. A number of usability issues of Primo were also identified from the study. Results of the study are used to improve the interface of Primo and adjust relevancy ranking options. The empirical method of search results assessment and feedback collection used in this study can be extended to similar user-centered system implementation and evaluation efforts