Scattering through a straight quantum waveguide with combined boundary conditions

Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered using stationary scattering theory. The existence of a matching conditions solution at x=0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.Comment: 26 pages, 3 figure

On the stability of periodically time-dependent quantum systems

The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} | (psi(t),H(t) psi(t)) |<\infty where psi(t) denotes a trajectory at time t of the quantum system under consideration. We start from an analysis of the domain of the quasi-energy operator. Next we show, under certain assumptions, that if the spectrum of the monodromy operator U(T,0) is pure point then there exists a dense subspace of initial conditions for which the mean value of energy is uniformly bounded in the course of time. Further we show that if the propagator admits a differentiable Floquet decomposition then || H(t) psi(t) || is bounded in time for any initial condition psi(0), and one employs the quantum KAM algorithm to prove the existence of this type of decomposition for a fairly large class of H(t). In addition, we derive bounds uniform in time on transition probabilities between different energy levels, and we also propose an extension of this approach to the case of a higher order of differentiability of the Floquet decomposition. The procedure is demonstrated on a solvable example of the periodically time-dependent harmonic oscillator.Comment: 39 page

Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map

Исследуется вопрос устойчивости решения обратной задачи определения скалярного потенциала, возникающего в стационарном уравнении Шредингера в ограниченной области по частичной эллиптической карте Дирихле - Неймана. А именно, условия Дирихле ставятся на затененной части границы области и условия Неймана - на ее освещенной части. Установлена оценка устойчивости типа log log для L^2-нормы (соотв. H^{-1} нормы) для H^t, при t>0 и ограниченых (соотв. L^2) потенциалов

On Time-Fractional Diffusion Equations with Space-Dependent Variable Order

This paper deals with mathematical problems related to space-dependent anomalous diffusion processes. Namely, we investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We establish that variable-order time-fractional Cauchy problems admit a unique weak solution and prove that the space-dependent variable-order coefficient is uniquely determined by the knowledge of a suitable time sequence of partial initial-boundary maps. © 2018, Springer Nature Switzerland AG

HIV-related pulmonary hypertension. From pathogenesis to clinical aspects

HIV-related pulmonary hypertension (HIV-PH) is a cardiovascular complication of HIV infection that has been recognized in the last years with increasing frequency. HIV-related pulmonary hypertension is a clinical disorder which carries a bad prognosis. While a direct HIV infection of the pulmonary vessels in the pathogenesis of this disorder was not demonstrated, currently a multi-factorial pathogenesis of this disease could be hypothesized. Echocardiography has been found to be the most useful screening imaging modality for the diagnosis of HIV-PH, with a high predictive negative value and a low positive predictive value. For this reason Doppler echocardiography is not the gold standard in the diagnosis of HIV-PH. The treatment of HIV-PH is complex and controversial. To date, no study determining the agent of choice for the treatment of this disease exists. Different studies have shown variable results in patiens with HIV-PH treated with highly active antiretroviral therapy (HAART) but only HAART seems not to be effective in lowering pulmonary hypertension in these patients, and in some patients, HIV-PH develops in spite of a previous HAART. It seems reasonable in HIV-PH patients that a treatment with oral vasodilator drugs can improve the adherence of a long-lasting and complex antiretroviral therapy