Semiclassical description of resonant tunneling

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.Comment: LaTeX, 8 page

Correlations of chaotic eigenfunctions: a semiclassical analysis

We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.Comment: Revtex, 13 pages, 1 postscript figur

Chromosomal Evolution and Evolutionary Relationships of Lebiasina Species (Characiformes, Lebiasinidae)

We present the first cytogenetic data for Lebiasina bimaculata and L. melanoguttata with the aim of (1) investigating evolutionary events within Lebiasina and their relationships with other Lebiasinidae genera and (2) checking the evolutionary relationships between Lebiasinidae and Ctenoluciidae. Both species have a diploid number 2n = 36 with similar karyotypes and microsatellite distribution patterns but present contrasting C-positive heterochromatin and CMA3 + banding patterns. The remarkable interstitial series of C-positive heterochromatin occurring in L. melanoguttata is absent in L. bimaculata. Accordingly, L. bimaculata shows the ribosomal DNA sites as the only GC-rich (CMA3 +) regions, while L. melanoguttata shows evidence of a clear intercalated CMA3 + banding pattern. In addition, the multiple 5S and 18S rDNA sites in L. melanogutatta contrast with single sites present in L. bimaculata. Comparative genomic hybridization (CGH) experiments also revealed a high level of genomic differentiation between both species. A polymorphic state of a conspicuous C-positive, CMA3 +, and (CGG)n band was found only to occur in L. bimaculata females, and its possible relationship with a nascent sex chromosome system is discussed. Whole chromosome painting (WCP) and CGH experiments indicate that the Lebiasina species examined and Boulengerella maculata share similar chromosomal sequences, thus supporting the relatedness between them and the evolutionary relationships between the Lebiasinidae and Ctenoluciidae families

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR