Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach

Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit $\eta\to1.0$. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of sphere and an exact comparison with the quantum mechanical results is observed upto the second decimal place for $kR_{0}\geq{7}$. The contributions of the equatorial, the planar (in the axis of symmetry plane) and the non-planar(3-Dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with $L_z=0$ except for L=1. The remaining quantum mechanical eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure

Laser heterodyne system for obtaining height profiles of minor species in the atmosphere

An infrared laser heterodyne system for obtaining height profiles of minor constituents of the atmosphere was developed and erected. A brief discription of the system is given. The system consists of a tunable CO2 waveguide laser in the 9 to 11 micrometer band, that is used as a local oscillator and a heliostat that follows the sun and brings in solar radiation, that is mixed with the laser beam in a high speed liquid nitrogen cooled mercury cadmium telluride detector. The detected signal is analysed in a RF spectrum analyser that allows tracing absorption line profiles. Absorption lines of a number of minor constituents in the troposphere and stratosphere, such as O3, NH3, H2O, SO2, ClO, N2O, are in the 9 to 11 micrometer band and overlap with that of CO2 laser range. The experimental system has been made operational and trial observations taken. Current measurements are limited to ozone height profiles. Results are presented

Nonuniversal exponents in sandpiles with stochastic particle number transfer

We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing transition occurs is found exactly. We study the critical behavior numerically and find that the exponents associated with both static and time-dependent quantities vary continuously with $p$.Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let

Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid

It is shown that Wen's effective theory correctly describes the Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite fermions. However, the weak residual interaction between composite fermions appears to be a relevant perturbation. The filling factor dependence of the Tomonaga-Luttinger parameter is estimated for interacting composite fermions in a microscopic approach and satisfactory agreement with experiment is achieved. It is suggested that the electron field operator may not have a simple representation in the effective one dimensional theory.Comment: 5 pages; accepted in Phys. Rev. Let

Evolutionary dynamics on strongly correlated fitness landscapes

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables

Number of adaptive steps to a local fitness peak

We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed