We analyze the semiclassical evolution of Gaussian wave packets in chaotic systems. We show that after some short time a Gaussian wave packet becomes a primitive WKB state. From then on, the state can be propagated using the standard time-dependent WKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of mixed Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the interaction, which can be calculated as suitable thermal averages. We have verified that there is a satisfactory quantitative agreement between theory and simulations in the disordered phases of the XY models, either with attractive or repulsive interactions. Part of the success of the theory is due to the possibility of predicting the shape of the required correlation functions, because this permits the calculation of correlation times as thermal averages.

http://dx.doi.org/10.5007/2175-7941.2016v33n3p822Investigamos o uso intencional de signos científicos por parte de estudantes universitários no laboratório didático de física analisando a resolução de tarefas simples de tratamento estatístico de dados num experimento hipotético de mecânica por meio de um levantamento discursivo. Interpretamos nossos resultados com base na Teoria Histórico-Cultural de Vigotski, descrevendo a forma com que estímulos externos auxiliares podem alterar o comportamento do indivíduo ao relatar, comparar, e reunir dados experimentais. Nossa abordagem naturalmente permite delinear como os signos associados às medições experimentais são gradualmente incorporados pelos indivíduos ao longo da instrução formal no ensino superior.

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The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.