Uniform approximation for the overlap caustic of a quantum state with its translations

The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the semiclassical chord function, also has a caustic along the conjugate curve defined as the locus of diameters, i.e. the maximal chords of the original curve. If the latter is convex, so is its conjugate, resulting in a simple fold caustic. The uniform approximation through this caustic, that is here derived, describes the transition undergone by the overlap of the state with its translation, from an oscillatory regime for small chords, to evanescent overlaps, rising to a maximum near the caustic. The diameter-caustic for the Wigner function is also treated.Comment: 14 pages, 9 figure

Factors controlling spatio-temporal variation in carbon dioxide efflux from surface litter, roots, and soil organic matter at four rain forest sites in the eastern Amazon

[1] This study explored biotic and abiotic causes for spatio-temporal variation in soil respiration from surface litter, roots, and soil organic matter over one year at four rain forest sites with different vegetation structures and soil types in the eastern Amazon, Brazil. Estimated mean annual soil respiration varied between 13-17 t C ha(-1) yr(-1), which was partitioned into 0-2 t C ha(-1) yr(-1) from litter, 6-9 t C ha(-1) yr(-1) from roots, and 5-6 t C ha(-1) yr(-1) from soil organic matter. Litter contribution showed no clear seasonal change, though experimental precipitation exclusion over a one-hectare area was associated with a ten-fold reduction in litter respiration relative to unmodified sites. The estimated mean contribution of soil organic matter respiration fell from 49% during the wet season to 32% in the dry season, while root respiration contribution increased from 42% in the wet season to 61% during the dry season. Spatial variation in respiration from soil, litter, roots, and soil organic matter was not explained by volumetric soil moisture or temperature. Instead, spatial heterogeneity in litter and root mass accounted for 44% of observed spatial variation in soil respiration (p < 0.001). In particular, variation in litter respiration per unit mass and root mass accounted for much of the observed variation in respiration from litter and roots, respectively, and hence total soil respiration. This information about patterns of, and underlying controls on, respiration from different soil components should assist attempts to accurately model soil carbon dioxide fluxes over space and time

Universal quantum signature of mixed dynamics in antidot lattices

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.Comment: 7 page

Decoherence of Semiclassical Wigner Functions

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.Comment: 23 pg, 2 fi