Quantum Energy Expectation in Periodic Time-Dependent hamiltonians via Green Functions

Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a {\em probe energy}), we derive a formula for the Laplace time average of its expectation value up to time $T$ in terms of its eigenvalues and Green functions at the circle of radius $e^{1/T}$. Some simple applications are provided which support its usefulness.Comment: 31 page

Time-Dependent Failure of Viscoelastic Materials Under Cyclic Loads

The problem of failure in viscoelastic materials under cyclic strain histories is treated theoretically by using a fracture model based on the theory of rate processes. Failure times in constant, uniaxial strain tests are compared with failure times encountered in sinusoidal strain histories. The dependence of the latter on the mean strain, the size of the strain variation and its frequency is illustrated. It is pointed out that for certain conditions a difference in the failure times in constant or cyclic strain histories may be masked entirely by statistical data scatter. Finally the failure of solid propellant fuels under cyclic loading is discussed in the light of the results derived for a continuum rubber

Time-dependent changes in postural control in early Parkinson’s disease: what are we missing?

Impaired postural control (PC) is an important feature of Parkinson’s disease (PD), but optimal testing protocols are yet to be established. Accelerometer-based monitors provide objective measures of PC. We characterised time-dependent changes in PC in people with PD and controls during standing, and identified outcomes most sensitive to pathology. Thirty-one controls and 26 PD patients were recruited: PC was measured with an accelerometer on the lower back for 2 minutes (mins). Preliminary analysis (autocorrelation) that showed 2 seconds (s) was the shortest duration sensitive to changes in the signal; time series analysis of a range of PC outcomes was undertaken using consecutive 2-s windows over the test. Piecewise linear regression was used to fit the time series data during the first 30 s and the subsequent 90 s of the trial. PC outcomes changed over the 2 mins, with the greatest change observed during the first 30 s after which PC stabilised. Changes in PC were reduced in PD compared to controls, and Jerk was found to be discriminative of pathology. Previous studies focusing on average performance over the duration of a test may miss time-dependent differences. Evaluation of time-dependent change may provide useful insights into PC in PD and effectiveness of intervention

Time dependent transport phenomena

The aim of this review is to give a pedagogical introduction to our recently proposed ab initio theory of quantum transport.Comment: 28 pages, 18 figure

Time Dependent Resonance Theory

An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g. the coupling of an atom or molecule to a photon-radiation field, and Auger states of the helium atom, as well as in spectral geometry and number theory. We present a dynamic (time-dependent) theory of such quantum resonances. The key hypotheses are (i) a resonance condition which holds generically (non-vanishing of the {\it Fermi golden rule}) and (ii) local decay estimates for the unperturbed dynamics with initial data consisting of continuum modes associated with an interval containing the embedded eigenvalue of the unperturbed Hamiltonian. No assumption of dilation analyticity of the potential is made. Our method explicitly demonstrates the flow of energy from the resonant discrete mode to continuum modes due to their coupling. The approach is also applicable to nonautonomous linear problems and to nonlinear problems. We derive the time behavior of the resonant states for intermediate and long times. Examples and applications are presented. Among them is a proof of the instability of an embedded eigenvalue at a threshold energy under suitable hypotheses.Comment: to appear in Geometrical and Functional Analysi

Hierarchical Time-Dependent Oracles

We study networks obeying \emph{time-dependent} min-cost path metrics, and present novel oracles for them which \emph{provably} achieve two unique features: % (i) \emph{subquadratic} preprocessing time and space, \emph{independent} of the metric's amount of disconcavity; % (ii) \emph{sublinear} query time, in either the network size or the actual Dijkstra-Rank of the query at hand