Fourth order real space solver for the time-dependent Schr\"odinger equation with singular Coulomb potential

We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the symmetry axis. Our propagation algorithm is based on merging the method of the split-operator approximation of the exponential operator with the implicit equations of second order cylindrical 2D Crank-Nicolson scheme. We call this method hybrid splitting scheme because it inherits both the speed of the split step finite difference schemes and the robustness of the full Crank-Nicolson scheme. Based on a thorough error analysis, we verified both the fourth order accuracy of the spatial discretization in the optimal spatial step size range, and the fourth order scaling with the time step in the case of proper high order expressions of the split-operator. We demonstrate the performance and high accuracy of our hybrid splitting scheme by simulating optical tunneling from a hydrogen atom due to a few-cycle laser pulse with linear polarization

Carrier-envelope phase controlled isolated attosecond pulses in the nm wavelength range, based on superradiant nonlinear Thomson-backscattering

A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulae, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realistic parameters, single-cycle isolated pulses of ca. 20 as length are predicted in the XUV -- soft X-ray spectral range, including the 2.33-4.37 nm water window. According to our analysis, the generated almost linearly polarized beam is extremely well collimated around the initial velocity of the electron bunch, with considerable intensity and with its CEP locked to that of the fs laser pulse.Comment: 11 pages, 6 figures, reviewed, corrected and extended work, regarding the intensity dependence of the emitted attosecond puls

Quantum entanglement in strong-field ionization

We investigate the time-evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion-core. Since the standard procedure is numerically prohibitive in this case, we propose a novel way to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime

Biokémiai markerek jelentősége a neuroendokrin daganatok felismeresében és a betegek követésében

Circulating markers of neuroendocrine tumours are useful tools in the diagnosis of these tumours. Laboratory tests for general biomarkers have acceptable sensitivity for the recognition of neuroendocrine tumours as these biologically active proteins are typically synthesized by all types of neuroendocrine cells. Measurement of chromogranin A is widely used not only in the diagnosis of neuroendocrine tumours but it may predict the prognosis of the diseases and the effect of the antitumor therapy. It is also a useful tool for the detection of residual tumours. Neurendocrine tumours represent a heterogeneous group of tumours with the ability to secrete several hormones and, therefore, measurement of these hormones can also serve as neuroendocrine cell type-specific markers in routine clinical practice. In this review the authors summarize the significance of tumour markers in the diagnosis of neuroendocrine tumours as well as in the management and follow-up of patients with this disease. Orv. Hetil., 2014, 155(45), 1775-1782