Angular Momentum Distribution Function of the Laughlin Droplet

We have evaluated the angular-momentum distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte-Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the MC calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.Comment: 11 pages of RevTeX, 2 figures available on request. IUCM93-00

The Apm Galaxy Survey IV: Redshifts of Rich Clusters of Galaxies

We present redshifts for a sample of 229 clusters selected from the APM Galaxy Survey, 189 of which are new redshift determinations. Non-cluster galaxy redshifts have been rejected from this sample using a likelihood ratio test based on the projected and apparent magnitude distributions of the cluster fields. We test this technique using cluster fields in which redshifts have been measured for more than 10 galaxies. Our redshift sample is nearly complete and has been used in previous papers to study the three dimensional distribution of rich clusters of galaxies. 157 of the clusters in our sample are listed in the Abell catalogue or supplement, and the remainder are new cluster identifications.Comment: 15 pages UUencoded compressed postscript. Submitted to Monthly Notices of the R.A.

Universal Level dynamics of Complex Systems

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in the case (i), a redefinition of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invariant measure). This equivalence can therefore help us to obtain the correlations for various physically-significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large $N$-values, our results for both cases (i) and (ii) are similar to those obtained for Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore universality of dynamics of the eigenvalues of complex systems.Comment: 11 Pages, Latex Fil

Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.Comment: 10pp, REVTE

Self-similarity and novel sample-length-dependence of conductance in quasiperiodic lateral magnetic superlattices

We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self-similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detected as an abrupt change in the conductance as the Fermi energy is varied, much as a metal-insulator transition. This is a unique feature of transport in this new kind of structure, arising from its inherent two-dimensional nature.Comment: 9 pages, 5 figures, revtex, important revisions made. to be published in Phys. Rev.

Some Properties of the Calogero-Sutherland Model with Reflections

We prove that the Calogero-Sutherland Model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wave-functions for certain particular cases (associated to the root systems of the classical Lie groups B_N, C_N and D_N) is also discussed.Comment: 16 pages, harvmac.te

The Out‐of‐Plane Deformation Frequency of the NH Group in the Peptide Link

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70613/2/JCPSA6-21-3-570-2.pd

The Effect of Hydrogen Bonding on the Hindered Rotation of the Hydroxyl Group in Alcohols

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69594/2/JCPSA6-20-12-1977-1.pd

Effect of Intermolecular Interactions between CH Frequencies on the Infrared Spectra of N‐Paraffins and Polythene

A systematic study has been made of the infrared absorption band near 725 cm—1 which arises from the rocking vibration of methylene groups in n‐paraffins and in polyethylene. In unoriented crystals of n‐paraffins, this band exhibits two components of equal intensity below the transition point; above the transition temperature and in the liquid state only the higher frequency component is found. In solid cold‐drawn polyethylene the two components are of unequal intensity, the low frequency component being the stronger; in liquid polyethylene only the lower frequency component is found. Studies were made of polyethylene in various states of crystallinity and orientation, using both polarized and unpolarized radiation. The results obtained can be consistently interpreted, if the higher frequency component is attributed to crystallites in the polyethylene and the lower frequency component is assumed to be due partly to the crystalline and partly to the amorphous form of the polyethylene. It is concluded that the doubling of this frequency arises from some interaction between methylene groups which is peculiar to the crystalline state of long chain n‐paraffins below their transition points.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69988/2/JCPSA6-22-12-1993-1.pd