arXiv subjects

R. Vilela Mendes

Publications and source records attributed to R. Vilela Mendes.

At least 73 records · Page 4Linked to original sources

arXiv2007

Reduction and approximation in gyrokinetics

The gyrokinetics formulation of plasmas in strong magnetic fields aims at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. In a perturbative treatment or as a time-averaging procedure, gyrokinetics is in general an approximation to the true dynamics. Here we discuss the conditions under which gyrokinetics is either an approximation or an exact operation in the framework of reduction of dynamical systems with symmetry

physics.plasm-ph↗

arXiv2006

Fluctuations and control in the Vlasov-Poisson equation

In this paper we study the fluctuation spectrum of a linearized Vlasov-Poisson equation in the presence of a small external electric field. Conditions for the control of the linear fluctuations by an external electric field are established.

physics.plasm-ph↗

arXiv2006

Random sampling in chirp space

For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.

math.PR↗

arXiv2006

A stochastic representation for the Poisson-Vlasov equation

A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence proof and an intuitive characterization of the solutions, may also be used to obtain an intrinsic definition of the fluctuations.

physics.plasm-ph↗

arXiv2006

A probabilistic operator symbol framework for quantum information

Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic interpretation, a particular class of operator symbols (tomograms) is proposed as a framework for quantum information problems. Qudit states are identified with maps of the unitary group into the simplex. The image of the unitary group on the simplex provides a geometrical characterization of the nature of the quantum states. Generalized measurements, typical quantum channels, entropies and entropy inequalities are discussed in this setting.

quant-ph↗

arXiv2004

Deterministic Bak-Sneppen model. Lyapunov spectrum and avalanches as return times

A deterministic version of the Bak-Sneppen model is studied. The role of the Lyapunov spectrum in the onset of scale-free behavior is established and avalanches are interpreted as return times to a zero-measure set. The problem of accurate determination of the scaling exponents near the critical barrier is addressed using a characteristic function approach. A general equation for return times to a small measure set is established and used to obtain information on the nature of Bak-Sneppen dynamics.

nlin.AO↗

arXiv2004

Dynamics and coding of a biologically-motivated network

A four-node network consisting of a negative loop controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully characterized and coded. The biologically relevant situations are identified and conclusions drawn concerning the effectiveness of the p53 network as a tumour inhibitor mechanism.

q-bio.MN↗

arXiv2004

Tools for network dynamics

Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics, ergodic invariants and estimates of invariant measures by small random perturbations. A few network examples are discussed as an application of some of the dynamical tools.

cond-mat.dis-nn↗

arXiv2003

The nonlinear directional coupler. An analytic solution

Linear and nonlinear directional couplers are currently used in fiber optics communications. They may also play a role in multiphoton approaches to quantum information processing if accurate control is obtained over the phases and polarizations of the signals at the output of the coupler. With this motivation, the constants of motion of the coupler equation are used to obtain an explicit analytical solution for the nonlinear coupler.

physics.optics↗

arXiv2003

Quantum control in infinite dimensions

Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators.

quant-ph↗

arXiv2003

Network dependence of strong reciprocity

Experimental evidence suggests that human decisions involve a mixture of self-interest and internalized social norms which cannot be accounted for by the Nash equilibrium behavior of Homo Oeconomicus. This led to the notion of strong reciprocity (or altruistic punishment) to capture the human trait leading an individual to punish norm violators at a cost to himself. For a population with small autonomous groups with collective monitoring, the interplay of intra- and intergroup dynamics shows this to be an adaptive trait, although not fully invasive of a selfish population. However, the absence of collective monitoring in a larger society changes the evolution dynamics. Clustering seems to be the network parameter that controls maintenance and evolution of the reciprocator trait.

nlin.AO↗

arXiv2002

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.

math-ph↗

arXiv2002

Quantum control and the Strocchi map

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product which provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a Käller manifold. Quantum control is discussed in this setting. Quantum time-evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, non unitarily controllable systems becoming controllable by ``measurement plus evolution''. A picture of quantum evolution as Hamiltonian dynamics in a classical-like phase-space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion of optimal control and sliding mode techniques.

quant-ph↗

arXiv2002

Reconstructing an economic space from a market metric

Using a metric related to the returns correlation, a method is proposed to reconstruct an economic space from the market data. A reduced subspace, associated to the systematic structure of the market, is identified and its dimension related to the number of terms in factor models. Example were worked out involving sets of companies from the DJIA and S&P500 indexes. Having a metric defined in the space of companies, network topology coefficients may be used to extract further information from the data. A notion of "continuous clustering" is defined and empirically related to the occurrence of market shocks.

cond-mat.stat-mech↗

arXiv2002

Quantum games and social norms. The quantum ultimatum game

The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash equilibria. A restricted version of quantum games is proposed to implement, in mathematical games, the interplay of self-interest and internalized social norms that rules human behavior.

quant-ph↗

arXiv2002

Quantum sensitive dependence

Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in quantum control, may have continuous spectrum and the rate of growth of observables is an issue of both theoretical and practical concern. Rates of growth in quantum mechanics are discussed by constructing quantities with the same physical meaning as those involved in the classical Lyapunov exponent. A generalized notion of quantum sensitive dependence is introduced and the mathematical structure of the operator matrix elements that correspond to different types of growth is characterized.

quant-ph↗

arXiv2002

A dynamical characterization of the small world phase

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the $β-$model, a coupled map dynamical system is defined on the network. Entrance to and exit from the SW phase are related to the behavior of the ergodic invariants of the dynamics.

cond-mat.stat-mech↗

arXiv2001

Quantum collision states for positive charges in an octahedral cage

One-electron energy levels are studied for a configuration of two positive charges inside an octahedral cage, the vertices of the cage being occupied by atoms with a partially filled shell. Although ground states correspond to large separations, there are relatively low-lying states with large collision probabilities. Electromagnetic radiation fields used to excite the quantum collisional levels may provide a means to control nuclear reactions. However, given the scale of the excitation energies involved, this mechanism cannot provide an explanation for the unexplained ``cold fusion'' events.

quant-ph↗