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

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

Quantum integrable system with two color components in two dimensions

The Davey-Stewartson 1(DS1) system[9] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimensions. For latters with the $\delta$-function interactions and being solved by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solusions is discussed.Comment: 14 pages, LaTeX fil

Giant electron-electron scattering in the Fermi-liquid state of Na_0.7CoO_2

The in-plane resistivity, rho, and thermal conductivity, kappa, of a single crystal of Na_0.7CoO_2 were measured down to 40 mK. Verification of the Wiedemann-Franz law, kappa/T = L_0/rho as T -> 0, and observation of a T^2 dependence of rho at low temperature, rho = rho_0 + AT^2, establish the existence of a well-defined Fermi-liquid state. The measured value of coefficient A reveals enormous electron-electron scattering, characterized by the largest Kadowaki-Woods ratio, A/gamma^2, encountered in any material. The rapid suppression of A with magnetic field suggests a possible proximity to a magnetic quantum critical point. We also speculate on the possible role of magnetic frustration and proximity to a Mott insulator.Comment: 4 pages, 4 figures; replaced with published version; added references and supporting dat

Spectrum of a spin chain with inverse square exchange

The spectrum of a one-dimensional chain of $SU(n)$ spins positioned at the static equilibrium positions of the particles in a corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane--Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate ``super-multiplets''. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitely. On the basis of this algebra and numerical studies we give the complete spectrum and thermodynamics of the $SU(2)$ system.Comment: 9 pages, late

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.

Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model

We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the authors. Our method is based on the theory of the Jack polynomials with a prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur

Spectra of Homologous Series of Monosubstituted Amides

Infrared spectra of the pure liquid and of dilute solution were observed for N‐methyl, N‐ethyl, N‐propyl, and N‐butyl acetamides and propionamides and of N‐deuterated N‐butylacetamide. Also infrared spectra of N15‐butylacetamide and N‐deuterated N15‐butylacetamide and the Raman spectra of N‐butylacetamide and N‐deuterated N‐butylacetamide were observed. In each series a band in the higher members was related to each band of the N‐methyl compound on the basis of similarity in frequency, intensity, band width, and the influence of dilution. In N‐methylacetamide and N‐butylacetamide bands thus related were found to have also similar Raman activities and similar shifts on replacing the peptide hydrogen by deuterium. The extra bands could be related systematically to the extra CH2 groups. The implications of these results in protein spectroscopy and in the spectroscopic study of homologous series is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70627/2/JCPSA6-29-5-1097-1.pd

The Power Spectrum of the PSC Redshift Survey

We measure the redshift-space power spectrum P(k) for the recently completed IRAS Point Source Catalogue (PSC) redshift survey, which contains 14500 galaxies over 84% of the sky with 60 micron flux >= 0.6 Jansky. Comparison with simulations shows that our estimated errors on P(k) are realistic, and that systematic errors due to the finite survey volume are small for wavenumbers k >~ 0.03 h Mpc^-1. At large scales our power spectrum is intermediate between those of the earlier QDOT and 1.2 Jansky surveys, but with considerably smaller error bars; it falls slightly more steeply to smaller scales. We have fitted families of CDM-like models using the Peacock-Dodds formula for non-linear evolution; the results are somewhat sensitive to the assumed small-scale velocity dispersion \sigma_V. Assuming a realistic \sigma_V \approx 300 km/s yields a shape parameter \Gamma ~ 0.25 and normalisation b \sigma_8 ~ 0.75; if \sigma_V is as high as 600 km/s then \Gamma = 0.5 is only marginally excluded. There is little evidence for any `preferred scale' in the power spectrum or non-Gaussian behaviour in the distribution of large-scale power.Comment: Latex, uses mn.sty, 14 pages including 11 Postscript figures. Accepted by MNRA