Effect of Frequency and Intensity of Defoliation on Oat- Vetch Mixture

An experiment was conducted to evaluate the effect of different cutting regimes on productivity and complementarity between oat and vetch in a mixture. The treatments were allocated in a factorial design on a split-split-plot disposition: they were 3 cutting frequencies (each 35, 70 and 105 days), 3 cutting heights (2, 8 and 14 cm above ground) and 3 crops (oat, vetch and the 1:1 mixture). Forage production (dry matter per hectare) and complementarity between species Relative Yield Total (RYT) were evaluated. The highest forage production (p- 0.05) was obtained with a cutting height of 2 cm and a frequency of 70 days, both in mixture and pure crops. Mixture production was significantly higher than pure stands (p- 0.01) and RYT was higher than unity (p- 0.01) under all defoliation regimens. Defoliation treatments did not modify RYT. In these experimental conditions, cutting frequency and cutting height affected forage production but did not modify complementarity between species

On the classical-quantum correspondence for the scattering dwell time

Using results from the theory of dynamical systems, we derive a general expression for the classical average scattering dwell time, tau_av. Remarkably, tau_av depends only on a ratio of phase space volumes. We further show that, for a wide class of systems, the average classical dwell time is not in correspondence with the energy average of the quantum Wigner time delay.Comment: 5 pages, 1 figur

Measuring the Lyapunov exponent using quantum mechanics

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the difference between the two Hamiltonians larger, the characteristic exponential decay time becomes the Lyapunov exponent of the classical system. We illustrate our theoretical findings by investigating numerically the overlap decay function of a two-dimensional dynamical system.Comment: 9 pages, 6 figure

How do wave packets spread? Time evolution on Ehrenfest time scales

We derive an extension of the standard time dependent WKB theory which can be applied to propagate coherent states and other strongly localised states for long times. It allows in particular to give a uniform description of the transformation from a localised coherent state to a delocalised Lagrangian state which takes place at the Ehrenfest time. The main new ingredient is a metaplectic operator which is used to modify the initial state in a way that standard time dependent WKB can then be applied for the propagation. We give a detailed analysis of the phase space geometry underlying this construction and use this to determine the range of validity of the new method. Several examples are used to illustrate and test the scheme and two applications are discussed: (i) For scattering of a wave packet on a barrier near the critical energy we can derive uniform approximations for the transition from reflection to transmission. (ii) A wave packet propagated along a hyperbolic trajectory becomes a Lagrangian state associated with the unstable manifold at the Ehrenfest time, this is illustrated with the kicked harmonic oscillator.Comment: 30 pages, 3 figure

WKB Propagation of Gaussian Wavepackets

We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB 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.Comment: 4 pages, 4 figures; significant improvement

Semiclassical expansion of parametric correlation functions of the quantum time delay

We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of open channels $M$, a non-symmetry breaking parameter $x$, and a symmetry breaking parameter $y$. Several terms in the Taylor expansion about $\tau=0$, which depend on all parameters, are shown to be identical to those obtained from Random Matrix Theory.Comment: 21 pages, no figure

Quantum baker maps with controlled-NOT coupling

The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each subsystem has power-of-two Hilbert space dimension. We here study the particular example of two baker maps that interact via a controlled-not interaction. Numerical evidence indicates that the control subspace becomes an ideal Markovian environment for the target map in the limit of large Hilbert space dimension.Comment: 8 page

Lyapunov exponent of many-particle systems: testing the stochastic approach

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.Comment: 11 pages including 6 figure