Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Modelization of surface diffusion of a molecular dimer

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation¿s results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

Front propagation in the A+B->2A reaction under subdiffusion

We consider an irreversible autocatalytic conversion reaction A+B->2A under subdiffusion described by continuous-time random walks. The reactants transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Effective Electrodiffusion equation for non uniform nanochannels

We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs di fusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.

Evaluation of data for atmospheric models: master equation/RRKM calculations on the combination reaction, BrO+NO2 -> BrONO2, a conundrum

Experimental data for the title reaction were modeled using master equation (ME)/RRKM methods based on the Multiwell suite of programs. The starting point for the exercise was the empirical fitting provided by the NASA (Sander, S. P.; Finlayson-Pitts, B. J.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Molina, M. J.; Moortgat, G. K.; Orkin, V. L.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 15; Jet Propulsion Laboratory: Pasadena, California, 2006)(1) and IUPAC (Atkinson, R.; Baulch, D. L.; Cox, R. A.: R. F. Hampson, J.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data. 2000, 29, 167) 2 data evaluation panels, which represents the data in the experimental pressure ranges rather well. Despite the availability of quite reliable parameters for these calculations (molecular vibrational frequencies (Parthiban, S.; Lee, T. J. J. Chem. Phys. 2000, 113, 145)3 and a. value (Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. 1996, 100,. 19398)4 of the bond dissociation energy, D-298(BrO-NO2) = 118 kJ mol(-1), corresponding to Delta H-0(circle) = 114.3 kJ mol(-1) at 0 K) and the use of RRKM/ME methods, fitting calculations to the reported data or the empirical equations was anything but straightforward. Using these molecular parameters resulted in a discrepancy between the calculations and the database of rate constants of a factor of ca. 4 at, or close to, the low-pressure limit. Agreement between calculation and experiment could be achieved in two ways, either by increasing Delta H-0(circle) to an unrealistically high value (149.3 kJ mol(-1)) or by increasing , the average energy transferred in a downward collision, to an unusually large value (> 5000 cm(-1)). The discrepancy could also be reduced by making all overall rotations fully active. The system was relatively insensitive to changing the moments of inertia in the transition state to increase the centrifugal effect. The possibility of involvement of BrOONO was tested and cannot account for the difficulties of fitting the data.

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

Theoretical study of omeprazole behavior: Racemization barrier and decomposition reaction

omeprazole is a substituted benzimidazole which suppresses gastric-acid secretion by means of H+, K+-ATPase inhibition. It is an optically active drug with the sulfur of the sulfoxide being the chiral center. This pro-drug can be easily converted into its respective sulfenamide at low pH. In this work, omeprazole has been studied in relation to racemization barrier and decomposition reaction. Quantum chemistry coupled to PCA chemometric method were used to find all minimum energy structures. Conformational analysis and calculation of racemization barriers were carried out by PM3 semiempirical method (Gaussian 98). The average racemization energy barrier for all minimum energy structures (43.56 kcal mol(-1)) can be related to the velocity constant in Eyring's equation. The enormous half-life time at 100 degrees C (9.04 x 10(4) years) indicates that the process cannot be observed in human time scale. on the other hand, the difference of free energy change (Delta(Delta G) = -266.78 kcal mol(-1)) for the decomposition reaction shows that the process is favorable to the sulfenamide formation. The highly negative Delta(Delta G) obtained for the decomposition reaction shows that this process is extremely exothermic. This result explains why omeprazole decomposes and does not racemize. (C) 2008 Wiley Periodicals, Inc.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

Population persistence in weakly-coupled sinks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Combining anisotropic diffusion, transport equation and texture synthesis for inpainting textured images

In this work we propose a new image inpainting technique that combines texture synthesis, anisotropic diffusion, transport equation and a new sampling mechanism designed to alleviate the computational burden of the inpainting process. Given an image to be inpainted, anisotropic diffusion is initially applied to generate a cartoon image. A block-based inpainting approach is then applied so that to combine the cartoon image and a measure based on transport equation that dictates the priority on which pixels are filled. A sampling region is then defined dynamically so as to hold the propagation of the edges towards image structures while avoiding unnecessary searches during the completion process. Finally, a cartoon-based metric is computed to measure likeness between target and candidate blocks. Experimental results and comparisons against existing techniques attest the good performance and flexibility of our technique when dealing with real and synthetic images. © 2013 Elsevier B.V. All rights reserved.