An analytically solvable model of probabilistic network dynamics

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur

Chaos in one-dimensional lattices under intense laser fields

A model is investigated where a monochromatic, spatially homogeneous laser field interacts with an electron in a one-dimensional periodic lattice. The classical Hamiltonian is presented and the technique of stroboscopic maps is used to study the dynamical behavior of the model. The electron motion is found to be completely regular only for small field amplitudes, developing a larger chaotic region as the amplitude increases. The quantum counterpart of the classical Hamiltonian is derived. Exact numerical diagonalizations show the existence of universal, random-matrix fluctuations in the electronic energy bands dressed by the laser field. A detailed analysis of the classical phase space is compatible with the statistical spectral analysis of the quantum model. The application of this model to describe transport and optical absorption in semiconductor superlattices submitted to intense infrared laser radiation is proposed.Comment: 9 pages, RevTex 3.0, EPSF (6 figures), to appear in Europhys. J.

Energy transfer dynamics and thermalization of two oscillators interacting via chaos

We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment (HE), consisting of N non-interacting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with HE an indirect coupling between them is observed only if the particles are in near resonance. We study the equilibrium properties of the system considering ensemble averages for the case N=1 and single trajectory dynamics for N large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large N a temperature can be assigned to the system.Comment: 8 pages, 6 figure

Semiclassical coherent state propagator for systems with spin

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.Comment: 19 pages, no figure

A conjugate for the Bargmann representation

In the Bargmann representation of quantum mechanics, physical states are mapped into entire functions of a complex variable z*, whereas the creation and annihilation operators $\hat{a}^\dagger$ and $\hat{a}$ play the role of multiplication and differentiation with respect to z*, respectively. In this paper we propose an alternative representation of quantum states, conjugate to the Bargmann representation, where the roles of $\hat{a}^\dagger$ and $\hat{a}$ are reversed, much like the roles of the position and momentum operators in their respective representations. We derive expressions for the inner product that maintain the usual notion of distance between states in the Hilbert space. Applications to simple systems and to the calculation of semiclassical propagators are presented.Comment: 15 page

Spectral Analysis and the Dynamic Response of Complex Networks

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network characteristics: random networks follow Wigner's semicircular law whereas scale-free networks exhibit a triangular distribution. In this paper we show that the spectral density of hierarchical networks follow a very different pattern, which can be used as a fingerprint of modularity. Of particular importance is the value $\rho(0)$, related to the homeostatic response of the network: it is maximum for random and scale free networks but very small for hierarchical modular networks. It is also large for an actual biological protein-protein interaction network, demonstrating that the current leading model for such networks is not adequate.Comment: 4 pages 14 figure

Comparação da taxa de lotação em piquetes de Panicum maximum cv. Tazania irrigado e sequeiro com suplementação.

O presente trabalho teve como objetivo comparar a taxa de lotação em pastagem de Panicum maximum " cv. Tanzânia, irrigada e em sequeiro, de acordo com o consumo de forragem de vacas em lactação, da raça holandesa preta e branca, suplementadas com concentrado de acordo com suas produções, predicto pelo programa de Cornell 3.0

Pasteurização do leite-do-amapá in natura para controle do escurecimento enzimático.

O extrato do amapazeiro (Brosimum parinarioides Ducke), conhecido como leite-do-amapá, é utilizado pelas populações amazônicas como fonte alimentar e medicinal. A rápida alteração de cor do látex após extração representa a presença de enzimas como polifenoloxidase (PPO) e peroxidase (POD), escurecendo o produto in natura e desqualificando-o para comercialização. Desse modo, este trabalho objetivou a avaliação da atividade das enzimas PPO e POD em três amostras de leite-do-amapá resfriadas a 8°C, coletadas em amapazeiros em Moju (PA), e onze amostras de leite-do-amapá após o processo de pasteurização em diversos binômios tempo/temperatura e posteriormente resfriadas a 8°C, visando à otimização da conservação do produto in natura. Após resfriamento a 8°C, as amostras de leite-do-amapá in natura apresentaram diferença significativa entre os valores de atividade da enzima POD e, posteriormente observou-se elevação dessa atividade durante os períodos de tempo analisados. Como também se observou atividade da enzima PPO nas mesmas amostras, constata-se que esse tipo de conservação não foi efi ciente para as enzimas POD e PPO para leite-do-amapá. As amostras pasteurizadas de leitedo-amapá, e posteriormente resfriadas, apresentaram atividades das enzimas POD e PPO significativamente diferenciadas da respectiva amostra controle (sem pasteurização), concluindo que a pasteurização nos binômios estudados, aliada ao resfriamento, foi eficaz na diminuição da atividade das enzimas peroxidase e polifenoloxidase, alcançando-se a inativação destas, podendo ser um processo potencial para conservação desse produto