Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man`ko states and circular squeezed states. The relation between these states and the ""classical"" trajectories is investigated, and we present numerical explorations of some semiclassical quantities. (C) 2009 Elsevier B.V. All rights reserved.

The intramolecular charge transfer in a donor-pi-acceptor dianion probed by resonance Raman spectroscopy and quantum chemical calculations

The dideprotonation of 4-(4-nitrophenylazo)resorcinol generates an anionic species with substantial electronic pi delocalization. As compared to the parent neutral species, the anionic first excited electronic transition, characterized as an intramolecular charge transfer (ICT) from the CO(-) groups to the NO(2) moiety, shows a drastic red shift of ca. 200 nm in the lambda(max) in the UV-vis spectrum, leading to one of the lowest ICT energies observed (lambda(max) = 630 nm in dimethyl sulfoxide (DMSO)) in this class of push-pull molecular systems. Concomitantly, a threefold increase in the molar absorptivity (epsilon(max)) in comparison to the neutral species is observed. The resonance Raman enhancement profiles reveal that in the neutral species the chromophore involves several modes, as nu(C-N), nu(N=N), nu(C=C) and nu(s)(NO(2)), whereas in the dianion, there is a selective enhancement of the NO(2) vibrational modes. The quantum chemical calculations of the electronic transitions and vibrational wavenumbers led to a consistent analysis of the enhancement patterns observed in the resonance Raman spectra. Copyright (C) 2009 John Wiley & Sons, Ltd.

Azo-hydrazone tautomerism in protonated aminoazobenzenes: Resonance Raman spectroscopy and quantum-chemical calculations

The protonation effect on the vibrational and electronic spectra of 4-aminoazobenzene and 4-(dimethylamino)azobenzene was investigated by resonance Raman spectroscopy, and the results were discussed on the basis of quantum-chemical calculations. Although this class of molecular systems has been investigated in the past concerning the azo-hydrazone tautomerism, the present work is the first to use CASSCF/CASPT2 calculations to unveil the structure of both tautomers as well the nature of the molecular orbitals involved in chromophoric moieties responsible for the resonance Raman enhancement patterns. More specifically both the resonance Raman and theoretical results show clearly that in the neutral species, the charge transfer transition involves mainly the azo moiety, whereas in the protonated forms there is a great difference, depending on the tautomer. In fact, for the azo tautomer the transition is similar to that observed in the corresponding neutral species, whereas in the hydrazone tautomer such a transition is much more delocalized due to the contribution of the quinoid structure. The characterization of protonated species and the understanding of the tautomerization mechanism are crucial for controlling molecular properties depending on the polarity and pH of the medium.

The electronic delocalization in para-substituted beta-nitrostyrenes probed by resonance Raman spectroscopy and quantum-chemical calculations

The electronic (UV-vis) and resonance Raman (RR) spectra of a series of para-substituted trans-beta-nitrostyrenes were investigated to determine the influence of the electron donating properties of the substituent (X = H, NO2, COOH, Cl, OCH3, OH, N(CH3)(2), and O-) on the extent of the charge transfer to the electron-withdrawing NO2 group directly linked to the ethylenic (C=C) unit. The Raman spectra and quantum chemical calculations show clearly the correlation of the electron donating power of the X group with the wavenumbers of the nu(s)(NO2) and nu (C=C)(sty) normal modes. In conditions of resonance with the lowest excited electronic state, one observes for X = OH and N(CH3)2 that the symmetric stretching of the NO2. nu(s)(NO2), is the most substantially enhanced mode, whereas for X = O-, the chromophore is extended over the whole molecule, with substantial enhancement of several carbon backbone modes. Copyright (c) 2008 John Wiley & Sons, Ltd.

STRONG COUPLING LIMITS and QUANTUM ISOMORPHISMS of THE GAUGED THIRRING MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

The NINJA-2 project: detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave (GW) astrophysics communities. The purpose of NINJA is to study the ability to detect GWs emitted from merging binary black holes (BBH) and recover their parameters with next-generation GW observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete BBH hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a 'blind injection challenge' similar to that conducted in recent Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo science runs, we added seven hybrid waveforms to two months of data recoloured to predictions of Advanced LIGO (aLIGO) and Advanced Virgo (AdV) sensitivity curves during their first observing runs. The resulting data was analysed by GW detection algorithms and 6 of the waveforms were recovered with false alarm rates smaller than 1 in a thousand years. Parameter-estimation algorithms were run on each of these waveforms to explore the ability to constrain the masses, component angular momenta and sky position of these waveforms. We find that the strong degeneracy between the mass ratio and the BHs' angular momenta will make it difficult to precisely estimate these parameters with aLIGO and AdV. We also perform a large-scale Monte Carlo study to assess the ability to recover each of the 60 hybrid waveforms with early aLIGO and AdV sensitivity curves. Our results predict that early aLIGO and AdV will have a volume-weighted average sensitive distance of 300 Mpc (1 Gpc) for 10M circle dot + 10M circle dot (50M circle dot + 50M circle dot) BBH coalescences. We demonstrate that neglecting the component angular momenta in the waveform models used in matched-filtering will result in a reduction in sensitivity for systems with large component angular momenta. This reduction is estimated to be up to similar to 15% for 50M circle dot + 50M circle dot BBH coalescences with almost maximal angular momenta aligned with the orbit when using early aLIGO and AdV sensitivity curves.

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Supersymmetric extension of the quantum spherical model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short- and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.

Quantum state tomography and quantum logical operations in a three qubits NMR quadrupolar system

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP) and the various stages of each implementation were verified by quantum state tomography (QST). The results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms are presented here. Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Neural Networks as Cybernetic Systems (3rd and revised edition) - Part I

Neural Networks as Cybernetic Systems is a textbox that combines classical systems theory with artificial neural network technology. This third edition essentially compares with the 2nd one, but has been improved by correction of errors and by a rearrangement and minor expansion of the sections referring to recurrent networks. These changes hopefully allow for an easier comprehension of the essential aspects of this important domain that has received growing attention during the last years.