Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

The effects of discontinuously time-varying perturbations on the dynamics of a particle moving in harmonic, symmetric double well and symmetric triple well potentials, are investigated both classically and quantum mechanically. The quantum dynamics is followed using the time-dependent Fourier grid Hamiltonian (TDFGH) method while the classical dynamics is analyzed within the framework of classical Hamiltonian mechanics. Depending on the spatial symmetry of the perturbation and the characteristic features of the reversal time , different types of ‘phase space’ structures are observed in each of the potentials. For symmetric double and triple well potentials, quantum dynamics reveals that complete destruction of tunnelling (CDT) can be achieved in the presence of a time-dependent spatially asymmetric perturbing field that is continuous in time. Any discontinuity in time-variation of the perturbation may induce over the barrier transition. The relevance of these results in the context of (i) tunnelling control and (ii) quantum computing with 3-state or 2-state quantum registers is briefly discussed.     

Regularity for convex viscosity solutions of special Lagrangian equation

We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.     

Raman spectroscopic investigation of frozen and deparaffinized tissue sections of pediatric tumors: neuroblastoma and ganglioneuroma

Raman spectroscopy is a nondestructive technique that can provide information at the molecular level about the biochemicals in tissues. We have investigated the cellular regions in neuroblastoma and ganglioneuroma using Raman spectroscopy and compared their spectral characteristics with those of the corresponding normal adrenal gland. Thin sections from both the frozen and the corresponding formalin‐fixed paraffin‐processed (FFPP) tissues were studied in conjunction with the pathological examination of the tissues. Investigation of the spectral data shows that the normal adrenal gland tissues have higher levels of carotenoids, lipids, and cholesterol compared with the neuroblastoma and ganglioneuroma frozen tissues. However, in comparison with the frozen tissues, the FFPP tissues show a significant alteration of several biochemicals, including the complete removal of carotenoids, lipids, and cholesterol in the adrenal tissues. A quantitative analysis using chemometric methods of principal component analysis and discriminant function analysis of the Raman spectral data obtained from the frozen tissues show a clear‐cut classification among pathological groups with high sensitivity and specificity. We have validated the classification results of the FFPP tissues against a training set data obtained from the archived FFPP tissues of nine other patients. The validation process correctly identified and grouped the data with the training set of normal adrenal gland (>97% of the time) and neuroblastoma (100% of the time) tissues, whereas the validation was not so strong for ganglioneuroma. This study shows that Raman spectroscopy combined with chemometric methods can be successfully used to distinguish neuroblastoma and ganglioneuroma at cellular level in frozen tissue sections. This study also shows that formalin fixation and paraffinization/deparaffinization of tissues can alter their biochemical composition. Copyright © 2012 John Wiley & Sons, Ltd.