Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

We study the algebra Sp(n,R) of the symplectic model, in particular for the cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.

Distributed photovoltaic systems: Utility interface issues and their present status. Intermediate/three-phase systems

The interface issues between the intermediate-size Power Conditioning Subsystem (PCS) and the utility are considered. A literature review yielded facts about the status of identified issues

Single Boson Images Via an Extended Holstein Primakoff Mapping

The Holstein-Primakoff mapping for pairs of bosons is extended in order to accommodate single boson mapping. The proposed extension allows a variety of applications and especially puts the formalism at finite temperature on firm grounds. The new mapping is applied to the O(N+1) anharmonic oscillator with global symmetry broken down to O(N). It is explicitly demonstrated that N-Goldstone modes appear. This result generalizes the Holstein-Primakoff mapping for interacting boson as developed in ref.[1].Comment: 9 pages, LaTeX. Physical content unchanged. Unnecessary figure remove

Constraints on the Quasiparticle Density of States in High-TcT_c Superconductors

In this Letter we present new tunneling data on YBa$_2$Cu$_3$O$_7$ thin films by low temperature scanning tunneling spectroscopy. Unusual peak-dip-hump features, previously reported in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, are also found in YBa$_2$Cu$_3$O$_7$. To analyse these common signatures we propose a new heuristic model in which, in addition to the d-wave symmetry, the gap function is energy dependent. A simple expression for the quasiparticle density of states is derived, giving an excellent agreement with the experiment. The dynamics of the quasiparticle states and the energy scales involved in the superconducting transition are discussed.Comment: 4 page Letter with 3 figure

A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6

The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions.Comment: 43 pages and 44 figure

Kaluza-Klein Dark Matter

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard positrons, neutrinos and photons with unsuppressed rates. Direct detection signals are also promising. These conclusions are generic to bosonic dark matter candidates.Comment: 4 pages, 3 figures, discussion of spin-independent cross section clarified, references added, published versio

Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf styl

Interference in Exclusive Vector Meson Production in Heavy Ion Collisions

Photons emitted from the electromagnetic fields of relativistic heavy ions can fluctuate into quark anti-quark pairs and scatter from a target nucleus, emerging as vector mesons. These coherent interactions are identifiable by final states consisting of the two nuclei and a vector meson with a small transverse momentum. The emitters and targets can switch roles, and the two possibilities are indistinguishable, so interference may occur. Vector mesons are negative parity so the amplitudes have opposite signs. When the meson transverse wavelength is larger than the impact parameter, the interference is large and destructive. The short-lived vector mesons decay before amplitudes from the two sources can overlap, and so cannot interfere directly. However, the decay products are emitted in an entangled state, and the interference depends on observing the complete final state. The non-local wave function is an example of the Einstein-Podolsky-Rosen paradox.Comment: 13 pages with 3 figures; submitted to Physical Review Letter

Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties

This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the physical properties of a class of solutions to the Einstein equations for disks with constant angular velocity and constant relative density which was constructed in the first part. The metric for these spacetimes is given in terms of theta functions on a Riemann surface of genus 2. It is parameterized by two physical parameters, the central redshift and the relative density of the two counter-rotating streams in the disk. We discuss the dependence of the metric on these parameters using a combination of analytical and numerical methods. Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the static limit which gives a solution of the Morgan and Morgan class and the limit of a disk without counter-rotation. We study the mass and the angular momentum of the spacetime. At the disk we discuss the energy-momentum tensor, i.e. the angular velocities of the dust streams and the energy density of the disk. The solutions have ergospheres in strongly relativistic situations. The ultrarelativistic limit of the solution in which the central redshift diverges is discussed in detail: In the case of two counter-rotating dust components in the disk, the solutions describe a disk with diverging central density but finite mass. In the case of a disk made up of one component, the exterior of the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.