Effect of dressing on high-order harmonic generation in vibrating H2 molecules

Wir entwickeln die Starkfeldnäherung für die Erzeugung hoher Harmonischer in Wasserstoffmolekülen, wobei die Vibrationsbewegung berücksichtigt wird, sowie die laserinduzierte Kopplung zwischen den beiden untersten Born-Oppenheimer-Zuständen im Molekülion, das durch die anfängliche Ionisation des Moleküls erzeugt wird. Wir zeigen, dass die Kopplung bei längeren Laserwellenlängen (≈ 2 μm) wichtig wird und zu einer Reduzierung der Erzeugung von Harmonischen führt, sowie zu einer Änderung des Verhältnisses von Harmonischen in verschiedenen Isotopen. ----------------------------------------------------------------------- We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths (≈ 2 μm), leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.

Electron-Nuclear Correlation in Laser-Driven Diatomic Molecules

The interaction of short intense laser pulses with atoms/molecules produces a multitude of highly nonlinear processes requiring a non-perturbative treatment. Detailed study of these highly nonlinear processes by numerically solving the time-dependent Schrodinger equation becomes a daunting task when the number of degrees of freedom is large. Also the coupling between the electronic and nuclear degrees of freedom further aggravates the computational problems. In the present work we show that the time-dependent Hartree (TDH) approximation, which neglects the correlation effects, gives unreliable description of the system dynamics both in the absence and presence of an external field. A theoretical framework is required that treats the electrons and nuclei on equal footing and fully quantum mechanically. To address this issue we discuss two approaches, namely the multicomponent density functional theory (MCDFT) and the multiconfiguration time-dependent Hartree (MCTDH) method, that go beyond the TDH approximation and describe the correlated electron-nuclear dynamics accurately. In the MCDFT framework, where the time-dependent electronic and nuclear densities are the basic variables, we discuss an algorithm to calculate the exact Kohn-Sham (KS) potentials for small model systems. By simulating the photodissociation process in a model hydrogen molecular ion, we show that the exact KS potentials contain all the many-body effects and give an insight into the system dynamics. In the MCTDH approach, the wave function is expanded as a sum of products of single-particle functions (SPFs). The MCTDH method is able to describe the electron-nuclear correlation effects as the SPFs and the expansion coefficients evolve in time and give an accurate description of the system dynamics. We show that the MCTDH method is suitable to study a variety of processes such as the fragmentation of molecules, high-order harmonic generation, the two-center interference effect, and the lochfrass effect. We discuss these phenomena in a model hydrogen molecular ion and a model hydrogen molecule. Inclusion of absorbing boundaries in the mean-field approximation and its consequences are discussed using the model hydrogen molecular ion. To this end, two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full many-particle Hamiltonian and (ii) an approach in the spirit of time-dependent density functional theory (TDDFT), including complex absorbing potentials in the single-particle equations. It is elucidated that for small grids the TDDFT approach is superior to the variational approach.

Factorial Hidden Markov Models

We present a framework for learning in hidden Markov models with distributed state representations. Within this framework, we derive a learning algorithm based on the Expectation--Maximization (EM) procedure for maximum likelihood estimation. Analogous to the standard Baum-Welch update rules, the M-step of our algorithm is exact and can be solved analytically. However, due to the combinatorial nature of the hidden state representation, the exact E-step is intractable. A simple and tractable mean field approximation is derived. Empirical results on a set of problems suggest that both the mean field approximation and Gibbs sampling are viable alternatives to the computationally expensive exact algorithm.

Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B(0) + lambda M and (ii) B = B(0) + lambda M + lambda`M(3), where B(0) is the external magnetic field, and lambda, lambda` are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modi. cation of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort. (C) 2008 Published by Elsevier B.V.

Magnetoresistance and transistor-like behavior of a double quantum-dot via crossed Andreev reflections

The electric current and the magnetoresistance effect are studied in a double quantum-dot system, where one of the dots QD(a) is coupled to two ferromagnetic electrodes (F-1; F-2), while the second QD(b) is connected to a superconductor S. For energy scales within the superconductor gap, electric conduction is allowed by Andreev reflection processes. Due to the presence of two ferromagnetic leads, non-local crossed Andreev reflections are possible. We found that the magnetoresistance sign can be changed by tuning the external potential applied to the ferromagnets. In addition, it is possible to control the current of the first ferromagnet (F-1) through the potential applied to the second one (F-2). We have also included intradot interaction and gate voltages at each quantum dot and analyzed their influence through a mean field approximation. The interaction reduces the current amplitudes with respect to the non-interacting case, but the switching effect still remains as a manifestation of quantum coherence, in scales of the order of the superconductor coherence length. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4723000]

Axial-vector torsion and the teleparallel Kerr spacetime

In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect.

Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund couphng J(H) is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-held approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and (3x(2) - r(2))/(3y(2) - r(2))-type orbital ordering are successfully reproduced based on the JT-phononic model with large JH for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized t(2g) spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic (large JH) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

Deviation from the sech2 superradiant emission law in a two-level atomic system

The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the sech2 law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results. © 1990 The American Physical Society.

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

Droplet formation in cold asymmetric nuclear matter in the quark-meson-coupling model

The quark-meson-coupling model is used to study droplet formation from the liquid-gas phase transition in cold asymmetric nuclear matter. The critical density and proton fraction for the phase transition are determined in the mean field approximation. Droplet properties are calculated in the Thomas-Fermi approximation. The electromagnetic field is explicitly included and its effects on droplet properties are studied. The results are compared with the ones obtained with the NL1 parametrization of the non-linear Walecka model. © 2000 Elsevier Science B.V.

Dinâmica das transições quiral e de desconfinamento da cromodinâmica quântica com o modelo Polyakov-Nambu-Jona-Lasinio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Determinação do gradiente de pH na região interna a duas membranas em equilíbrio com eletrólito

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Amphiphilic planar membranes in ionic equilibrium: a study of pH position-dependent values

The pH values near a planar dissociating membrane are studied under a mean field approximation using the Poisson-Boltzmann equation and its linear form. The equations are solved in planar symmetry with the consideration that the charge density on the dissociating membrane surface results from an equilibrium process with the neighboring electrolyte. Results for the membrane dissociation degree are presented as a function of the electrolyte ionic strength and membrane surface charge density. Our calculations indicate that pH values have an appreciable variation within 2 nm from the membrane. It is shown that the dissociation process is enhanced due to the presence of bivalent ions and that pH values acquire better stability than in an electrolyte containing univalent ions.