Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published versio

Explicit solution for vibrating bar with viscous boundaries and internal damper

We investigate longitudinal vibrations of a bar subjected to viscous boundary conditions at each end, and an internal damper at an arbitrary point along the bar's length. The system is described by four independent parameters and exhibits a variety of behaviors including rigid motion, super stability/instability and zero damping. The solution is obtained by applying the Laplace transform to the equation of motion and computing the Green's function of the transformed problem. This leads to an unconventional eigenvalue-like problem with the spectral variable in the boundary conditions. The eigenmodes of the problem are necessarily complex-valued and are not orthogonal in the usual inner product. Nonetheless, in generic cases we obtain an explicit eigenmode expansion for the response of the bar to initial conditions and external force. For some special values of parameters the system of eigenmodes may become incomplete, or no non-trivial eigenmodes may exist at all. We thoroughly analyze physical and mathematical reasons for this behavior and explicitly identify the corresponding parameter values. In particular, when no eigenmodes exist, we obtain closed form solutions. Theoretical analysis is complemented by numerical simulations, and analytic solutions are compared to computations using finite elements.Comment: 29 pages, 6 figure

Robertson Intelligent States

Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In case of canonical observables this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1,1), su(2), h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k power of a_j = a_{1,j} are positive definite and can be diagonalized by symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.DvComment: 23 pages, LaTex. Minor changes in text and references. Accepted in J. Phys.

Financial Incentives for Transcatheter Aortic Valve Implantation in Ontario, Canada: A Cost-Utility Analysis.

Background Transcatheter aortic valve implantation (TAVI) is a minimally invasive therapy for patients with severe aortic stenosis, which has become standard of care. The objective of this study was to determine the maximum cost-effective investment in TAVI care that should be made at a health system level to meet quality indicator goals. Methods and Results We performed a cost-utility analysis using probabilistic patient-level simulation of TAVI care from the Ontario, Canada, Ministry of Health perspective. Costs and health utilities were accrued over a 2-year time horizon. We created 4 hypothetical strategies that represented TAVI care meeting ≥1 quality indicator targets, (1) reduced wait times, (2) reduced hospital length of stay, (3) reduced pacemaker use, and (4) combined strategy, and compared these with current TAVI care. Per-person costs, quality-adjusted life years, and clinical outcomes were estimated by the model. Using these, incremental net monetary benefits were calculated for each strategy at different cost-effectiveness thresholds between $0 and$100 000 per quality-adjusted life year. Clinical improvements over the current practice were estimated with all comparator strategies. In Ontario, achieving quality indicator benchmarks could avoid ≈26 wait-list deaths and 200 wait-list hospitalizations annually. Compared with current TAVI care, the incremental net monetary benefit for this strategy varied from $10 765 (±$8721) and $17 221 (±$8977). This would translate to an annual investment of between ≈$14 to ≈$22 million by the Ontario Ministry of Health to incentivize these performance measures being cost-effective. Conclusions This study has quantified the modest annual investment required and substantial clinical benefit of meeting improvement goals in TAVI care

On the spectrum of the quadratic pencil of differential operators with periodic coefficients on the semi-axis

In this paper, the spectrum and resolvent of the operator L-lambda generated by the differential expression L-lambda(y) = y '' + q(1)(x)y' + [lambda(2) + lambda q(2)(x) + q(3)(x)] y and the boundary condition y'(0) - hy(0) = 0 are investigated in the space L-2(R+). Here the coefficients q(1)(x), q(2)(x), q(3)(x) are periodic functions whose Fourier series are absolutely convergent and Fourier exponents are positive. It is shown that continuous spectrum of the operator L-lambda consists of the interval (-infinity, +infinity). Moreover, at most a countable set of spectral singularities can exists over the continuous spectrum and at most a countable set of eigenvalues can be located outside of the interval (-infinity, +infinity). Eigenvalues and spectral singularities with sufficiently large modulus are simple and lie near the points lambda = +n/2, n is an element of N

Menunggu detik FFPVM6

Tinggal dua hari lagi Festival Filem dan Video Pelajar Malaysia Ke-6 (FFPVM6) bakal bermula. Sebagai panduan, berikut disenaraikan aktiviti-aktiviti menarik sepanjang festival tersebut

Nonperturbative theory of weak pre- and post-selected measurements

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable, which hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov-Albert-Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region, where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are achieved in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. We show that the amplification in the weak PPS measurements is a product of two qualitatively different quantities: proper amplification and enhancement. The effects of the free system and meter Hamiltonians are discussed. We also identify optimal meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory. Moreover, the theory is extended to allow for a completely general post-selection measurement. We also discuss time-symmetry properties of PPS measurements of any strength.Comment: The final version, corrected and expanded; 107 pages, 13 figure