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

The Realities of Evaluating Educational Technology in School Settings

\ua9 2024 Copyright held by the owner/author(s).HCI researchers are increasingly interested in the evaluation of educational technologies in context, yet acknowledge that challenges remain regarding the logistical, material and methodological constraints of this approach to research [18, 53].Through the analysis of the authors\u27 contributed thematic research vignettes, the following article exposes the practical realities of evaluating educational technologies in school settings. This includes insights into the planning stages of evaluation, the relationship between the researcher and the school environment, and the impact of the school context on the data collection process.We conclude by providing an orientation for the design of HCI educational technology research undertaken in school contexts, providing guidance such as considering the role of modular research design, clarifying goals and expectations with school partners, and reporting researcher positionality

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

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

Patients’ use of information about medicine side effects in relation to experiences of suspected adverse drug reactions

Background Adverse drug reactions (ADRs) are common, and information about medicines is increasingly widely available to the public. However, relatively little work has explored how people use medicines information to help them assess symptoms that may be suspected ADRs. Objective Our objective was to determine how patients use patient information leaflets (PILs) or other medicines information sources and whether information use differs depending on experiences of suspected ADRs. Method This was a cross-sectional survey conducted in six National Health Service (NHS) hospitals in North West England involving medical in-patients taking at least two regular medicines prior to admission. The survey was administered via a questionnaire and covered use of the PIL and other medicines information sources, perceived knowledge about medicines risks/ADRs, experiences of suspected ADRs, plus demographic information. Results Of the 1,218 respondents to the survey, 18.8 % never read the PIL, whilst 6.5 % only do so if something unexpected happens. Educational level was related to perceived knowledge about medicines risks, but not to reading the PIL or seeking further information about medicines risks. Over half the respondents (56.0 %) never sought more information about possible side effects of medicines. A total of 57.2 % claimed they had experienced a suspected ADR. Of these 85.9 % were either very sure or fairly sure this was a reaction to a medicine. Over half of those experiencing a suspected ADR (53.8 %) had read the PIL, of whom 36.2 % did so before the suspected ADR occurred, the remainder afterwards. Reading the PIL helped 84.8 % of these respondents to decide they had experienced an ADR. Educational level, general knowledge of medicines risks and number of regular medicines used all increased the likelihood of experiencing an ADR. Conclusion More patients should be encouraged to read the PIL supplied with medicines. The results support the view that most patients feel knowledgeable about medicines risks and suspected ADRs and value information about side effects, but that reading about side effects in PILs or other medicines information sources does not lead to experiences of suspected ADRs

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

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Ni-substituted sites and the effect on Cu electron spin dynamics of YBa2Cu{3-x}NixO{7-\delta}

We report Cu nuclear quadrupole resonance experiment on magnetic impurity Ni-substituted YBa$_2$Cu$_{3-x}$Ni$_x$O$_{7-\delta}$. The distribution of Ni-substituted sites and its effect on the Cu electron spin dynamics are investigated. Two samples with the same Ni concentration $x$=0.10 and nearly the same oxygen content but different $T_c$'s were prepared: One is an as-synthesized sample (7-$\delta$=6.93) in air ($T_c$$\approx 80 K$), and the other is a quenched one (7-$\delta$=6.92) in a reduced oxygen atmosphere ($T_c$$\approx 70 K$). The plane-site $^{63}$Cu(2) nuclear spin-lattice relaxation for the quenched sample was faster than that for the as-synthesized sample, in contrast to the $^{63}$Cu(1) relaxation that was faster for the as-synthesized sample. This indicates that the density of plane-site Ni(2) is higher in the quenched sample, contrary to the chain-site Ni(1) density which is lower in the quenched sample. From the analysis in terms of the Ni-induced nuclear spin-lattice relaxation, we suggest that the primary origin of suppression of $T_c$ is associated with nonmagnetic depairing effect of the plane-site Ni(2).Comment: 7 pages, 5 figure