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

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

Semiclassical approach to fidelity amplitude

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio

Semiclassical Description of Wavepacket Revival

We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.Comment: 10 pages, 6 figure

Orthogonality Catastrophe in Parametric Random Matrices

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure

Consejo Participativo de Garantía como herramienta en la producción agroecológica del Noroeste de Corrientes – Argentina

Esta presentación plantea una propuesta de formación de un Consejo Participativo de Garantía como herramienta para el productor familiar en el noroeste de Corrientes. El trabajo participativo con referentes de organizaciones de productores e Instituciones locales facilita la conformación de un Consejo de Garantía. En dos años de trabajo en que se llevaron a cabo acciones tendientes a la constitución de un equipo de gestión interinstitucional e interdisciplinario, hoy se halla conformado y capacitado, y accesible a incluir más integrantes de acuerdo a las necesidades. Tiene por delante el desafío de elaborar un protocolo de prácticas agroecológicas adaptado a nuestra realidad local y a la idiosincrasia de sus pobladoresEje: B3 Economía y agroecología (Relatos de experiencias)Facultad de Ciencias Agrarias y Forestale

Consejo Participativo de Garantía como herramienta en la producción agroecológica del Noroeste de Corrientes – Argentina

Esta presentación plantea una propuesta de formación de un Consejo Participativo de Garantía como herramienta para el productor familiar en el noroeste de Corrientes. El trabajo participativo con referentes de organizaciones de productores e Instituciones locales facilita la conformación de un Consejo de Garantía. En dos años de trabajo en que se llevaron a cabo acciones tendientes a la constitución de un equipo de gestión interinstitucional e interdisciplinario, hoy se halla conformado y capacitado, y accesible a incluir más integrantes de acuerdo a las necesidades. Tiene por delante el desafío de elaborar un protocolo de prácticas agroecológicas adaptado a nuestra realidad local y a la idiosincrasia de sus pobladoresEje: B3 Economía y agroecología (Relatos de experiencias)Facultad de Ciencias Agrarias y Forestale

Consejo Participativo de Garantía como herramienta en la producción agroecológica del Noroeste de Corrientes – Argentina

Esta presentación plantea una propuesta de formación de un Consejo Participativo de Garantía como herramienta para el productor familiar en el noroeste de Corrientes. El trabajo participativo con referentes de organizaciones de productores e Instituciones locales facilita la conformación de un Consejo de Garantía. En dos años de trabajo en que se llevaron a cabo acciones tendientes a la constitución de un equipo de gestión interinstitucional e interdisciplinario, hoy se halla conformado y capacitado, y accesible a incluir más integrantes de acuerdo a las necesidades. Tiene por delante el desafío de elaborar un protocolo de prácticas agroecológicas adaptado a nuestra realidad local y a la idiosincrasia de sus pobladoresEje: B3 Economía y agroecología (Relatos de experiencias)Facultad de Ciencias Agrarias y Forestale

Coulomb blockade conductance peak fluctuations in quantum dots and the independent particle model

We study the combined effect of finite temperature, underlying classical dynamics, and deformations on the statistical properties of Coulomb blockade conductance peaks in quantum dots. These effects are considered in the context of the single-particle plus constant-interaction theory of the Coulomb blockade. We present numerical studies of two chaotic models, representative of different mean-field potentials: a parametric random Hamiltonian and the smooth stadium. In addition, we study conductance fluctuations for different integrable confining potentials. For temperatures smaller than the mean level spacing, our results indicate that the peak height distribution is nearly always in good agreement with the available experimental data, irrespective of the confining potential (integrable or chaotic). We find that the peak bunching effect seen in the experiments is reproduced in the theoretical models under certain special conditions. Although the independent particle model fails, in general, to explain quantitatively the short-range part of the peak height correlations observed experimentally, we argue that it allows for an understanding of the long-range part.Comment: RevTex 3.1, 34 pages (including 13 EPS and PS figures), submitted to Phys. Rev.

Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings

We use random matrix models to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions treated in Hartree-Fock. This model is applicable to chaotic quantum dots or nanoparticles--in these systems the single-particle statistics follows random matrix theory at energy scales less than the Thouless energy. We find the distribution of Coulomb blockade peak spacings first for a large dot in which the residual interactions can be taken constant: the spacing fluctuations are of order the mean level separation Delta. Corrections to this limit are studied using the small parameter 1/(kf L): both the residual interactions and the effect of the changing confinement on the single-particle levels produce fluctuations of order Delta/sqrt(kf L). The distributions we find are significantly more like the experimental results than the simple constant interaction model.Comment: 17 pages, 4 figures, submitted to Phys. Rev.