52,325 research outputs found

    On the Complexity of Quantum ACC

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    For any q>1q > 1, let \MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by qq. We show that for any q,t>1q,t > 1, \MOD_q is equivalent to \MOD_t (up to constant depth). Based on the case q=2q=2, Moore \cite{moore99} has shown that quantum analogs of AC(0)^{(0)}, ACC[q][q], and ACC, denoted QACwf(0)^{(0)}_{wf}, QACC[2][2], QACC respectively, define the same class of operators, leaving q>2q > 2 as an open question. Our result resolves this question, proving that QACwf(0)=^{(0)}_{wf} = QACC[q]=[q] = QACC for all qq. 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‚Ā°\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‚Ā°\log-gate restricted QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in TC(0)^{(0)}. To do this last proof, we show that TC(0)^{(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

    Radio Images of 3C 58: Expansion and Motion of its Wisp

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    New 1.4 GHz VLA observations of the pulsar-powered supernova remnant 3C 58 have resulted in the highest-quality radio images of this object to date. The images show filamentary structure over the body of the nebula. The present observations were combined with earlier ones from 1984 and 1991 to investigate the variability of the radio emission on a variety of time-scales. No significant changes are seen over a 110 day interval. In particular, the upper limit on the apparent projected velocity of the wisp is 0.05c. The expansion rate of the radio nebula was determined between 1984 and 2004, and is 0.014+/-0.003%/year, corresponding to a velocity of 630+/-70 km/s along the major axis. If 3C 58 is the remnant of SN 1181, it must have been strongly decelerated, which is unlikely given the absence of emission from the supernova shell. Alternatively, the low expansion speed and a number of other arguments suggest that 3C 58 may be several thousand years old and not be the remnant of SN 1181.Comment: 12 pages; accepted for publication in the Astrophysical Journa

    Coulomb screening in mesoscopic noise: a kinetic approach

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    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

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

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    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 ő≤=2.4\beta=2.4 on a 163√ó3216^3\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

    What is novel in quantum transport for mesoscopics?

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    The understanding of mesoscopic transport has now attained an ultimate simplicity. Indeed, orthodox quantum kinetics would seem to say little about mesoscopics that has not been revealed - nearly effortlessly - by more popular means. Such is far from the case, however. The fact that kinetic theory remains very much in charge is best appreciated through the physics of a quantum point contact. While discretization of its conductance is viewed as the exclusive result of coherent, single-electron-wave transmission, this does not begin to address the paramount feature of all metallic conduction: dissipation. A perfect quantum point contact still has finite resistance, so its ballistic carriers must dissipate the energy gained from the applied field. How do they manage that? The key is in standard many-body quantum theory, and its conservation principles.Comment: 10 pp, 3 figs. Invited talk at 50th Golden Jubilee DAE Symposium, BARC, Mumbai, 200

    Ballistic transport is dissipative: the why and how

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    In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central issue of conduction: a quantum wire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly HOW does the quantum wire shed its excess electrical energy? We show that the answer is provided, uniquely, by many-body quantum kinetics. Not only does this inevitably lead to universal quantization of the conductance, in spite of dissipation; it fully resolves a baffling experimental result in quantum-point-contact noise. The underlying physics rests crucially upon the action of the conservation laws in these open metallic systems.Comment: Invited Viewpoint articl

    High-field noise in metallic diffusive conductors

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    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
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