On the Complexity of Quantum ACC

For any $q > 1$, let \MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by $q$. We show that for any $q,t > 1$, \MOD_q is equivalent to \MOD_t (up to constant depth). Based on the case $q=2$, Moore \cite{moore99} has shown that quantum analogs of AC$^{(0)}$, ACC$[q]$, and ACC, denoted QAC$^{(0)}_{wf}$, QACC$[2]$, QACC respectively, define the same class of operators, leaving $q > 2$ as an open question. Our result resolves this question, proving that QAC$^{(0)}_{wf} =$ QACC$[q] =$ QACC for all $q$. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC and BQACC_{\rats}. We define a notion $\log$-planar QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in P/poly. We also define a notion of $\log$-gate restricted QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in TC$^{(0)}$. To do this last proof, we show that TC$^{(0)}$ can perform iterated addition and multiplication in certain field extensions. We also introduce the notion of a polynomial-size tensor graph and show that families of such graphs can encode the amplitudes resulting from apply an arbitrary QACC operator to an initial state.Comment: 22 pages, 4 figures This version will appear in the July 2000 Computational Complexity conference. Section 4 has been significantly revised and many typos correcte

Cosmic microwave background constraints on coupled dark matter

We study CMB constraints on a model with a cosmological constant and a fraction of dark matter non-minimally coupled to a massless scalar field. In this scenario, there is an extra gravity-like fifth force which can affect the evolution of the Universe enough to have a discernible effect on measurements of cosmological parameters. Using Planck and WMAP polarisation data, we find that up to half of the dark matter can be coupled. The coupling can also be several times larger than in models with a single species of cold dark matter coupled to a quintessence scalar field, as the scalar field does not play the role of dark energy and is therefore less constrained by the data.Comment: 5 pages, 4 figure

Stardust microcrater residue compositional groups

Compositional groups are defined in residue from Stardust craters (1-9 Dc) by qualitative EDS. These compositional groups are being further studied by a FIB-SEM technique to determine representative residue compositions

Coulomb screening in mesoscopic noise: a kinetic approach

Coulomb screening, together with degeneracy, is characteristic of the metallic electron gas. While there is little trace of its effects in transport and noise in the bulk, at mesoscopic scales the electronic fluctuations start to show appreciable Coulomb correlations. Within a strictly standard Boltzmann and Fermi-liquid framework, we analyze these phenomena and their relation to the mesoscopic fluctuation-dissipation theorem, which we prove. We identify two distinct screening mechanisms for mesoscopic fluctuations. One is the self-consistent response of the contact potential in a non-uniform system. The other couples to scattering, and is an exclusively non-equilibrium process. Contact-potential effects renormalize all thermal fluctuations, at all scales. Collisional effects are relatively short-ranged and modify non-equilibrium noise. We discuss ways to detect these differences experimentally.Comment: Source: REVTEX. 16 pp.; 7 Postscript figs. Accepted for publication in J. Phys.: Cond. Ma

Electronic spin-triplet nematic with a twist

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards $d$-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial rotational symmetries. This order results in spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a nematic state that is intertwined with a helical modulation in spin space. Such a state is closely related to $d$-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, $p$-wave superconducting state.Comment: 15 pages, 9 figure

High-field noise in metallic diffusive conductors

We analyze high-field current fluctuations in degenerate conductors by mapping the electronic Fermi-liquid correlations at equilibrium to their semiclassical non-equilibrium form. Our resulting Boltzmann description is applicable to diffusive mesoscopic wires. We derive a non-equilibrium connection between thermal fluctuations of the current and resistive dissipation. In the weak-field limit this is the canonical fluctuation- dissipation theorem. Away from equilibrium, the connection enables explicit calculation of the excess ``hot-electron'' contribution to the thermal spectrum. We show that excess thermal noise is strongly inhibited by Pauli exclusion. This behaviour is generic to the semiclassical metallic regime.Comment: 13 pp, one fig. Companion paper to cond-mat/9911251. Final version, to appear in J. Phys.: Cond. Ma

A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf two} degenerate partitions (e.g.\ squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with $\beta=2.4$ on a $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.Comment: Original Raw PS file replace by a tarred, compressed and uuencoded PS fil

Regenerable adsorbent study

Thin film solid regenerable adsorbent for use with sorber plate to determine gase

A possible explanation for the inconsistency between the Giotto grain mass distribution and ground-based observations

Giotto measured the in situ Halley dust grain mass distribution with 2 instruments, Particle Impact Analyzer and Dust Impact Detection System (DIDSY), as well as the total intercepted mass from the deceleration of the spacecraft (Giotto Radio-Science Experiment, GRE). Ground based observations made shortly before encounter have fluxes much higher than would be predicted from Giotto data. It is concluded that Giotto DIDSY and GRE data represent observations of dust originating from a narrow track along the nucleus. They are consistent with ground based data, if assumptions are made about the level of activity along this track. The actual size distribution that should be used for modeling of the whole coma should not include the large mass excess actually observed by Giotto. Extrapolation of the small grain data should be used, since for these grains the velocity dispersion is low and temporal changes at the nucleus would not affect the shape of the mass distribution

Duality between quantum symmetric algebras

Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.Comment: 15 pages. Letters in Math. Phy., to appear soo