Efficient Quantum Tensor Product Expanders and k-designs

Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient construction of constant-degree, constant-gap quantum k-tensor product expanders. The key ingredients are an efficient classical tensor product expander and the quantum Fourier transform. Our construction works whenever k=O(n/log n), where n is the number of qubits. An immediate corollary of this result is an efficient construction of an approximate unitary k-design, which is a quantum analogue of an approximate k-wise independent function, on n qubits for any k=O(n/log n). Previously, no efficient constructions were known for k>2, while state designs, of which unitary designs are a generalisation, were constructed efficiently in [Ambainis, Emerson 2007].Comment: 16 pages, typo in references fixe

Neutron/Proton Structure Function Ratio at Large x

We re-examine the large-x neutron/proton structure function ratio extracted from the latest deuteron data, taking into account the most recent developments in the treatment of Fermi motion, binding and nucleon off-shell effects in the deuteron. Our findings suggest that as x->1 the ratio of the neutron to proton structure functions (F_2^n/F_2^p) is consistent with the perturbative QCD expectation of 3/7, but larger than the value of 1/4 obtained in earlier analyses.Comment: 18 pages RevTeX, 4 postscript figures, accepted for publication in Phys. Lett.

Disorder Induced Phase Transition in a Random Quantum Antiferromagnet

A two-dimensional Heisenberg model with random antiferromagnetic nearest-neighbor exchange is studied using quantum Monte Carlo techniques. As the strength of the randomness is increased, the system undergoes a transition from an antiferromagnetically ordered ground state to a gapless disordered state. The finite-size scaling of the staggered structure factor and susceptibility is consistent with a dynamic exponent $z = 2$.Comment: Revtex 3.0, 10 pages + 5 postscript figures available upon request, UCSBTH-94-1

Revised Phase Diagram of the Gross-Neveu Model

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.Comment: Revtex, 12 pages, 15 figures; v2: Axis labelling in Fig. 9 correcte

Structural glass on a lattice in the limit of infinite dimensions

We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing stability of this solution we conclude that the metastable states remain uncorrelated in a finite temperature range below the transition, but become correlated at sufficiently low temperature. We find dynamic and thermodynamic transition temperatures as functions of the density and construct a full thermodynamic description of a typical physical process in which the system gets trapped in one metastable state when cooled below vitrification temperature. We find that for such physical process the entropy and pressure at the glass transition are continuous across the transition while their temperature derivatives have jumps.Comment: 4 pages, 2 figure

Deep Inelastic Scattering from off-Shell Nucleons

We derive the general structure of the hadronic tensor required to describe deep-inelastic scattering from an off-shell nucleon within a covariant formalism. Of the large number of possible off-shell structure functions we find that only three contribute in the Bjorken limit. In our approach the usual ambiguities encountered when discussing problems related to off-shellness in deep-inelastic scattering are not present. The formulation therefore provides a clear framework within which one can discuss the various approximations and assumptions which have been used in earlier work. As examples, we investigate scattering from the deuteron, nuclear matter and dressed nucleons. The results of the full calculation are compared with those where various aspects of the off-shell structure are neglected, as well as with those of the convolution model.Comment: 36 pages RevTeX, 9 figures (available upon request), ADP-93-210/T128, PSI-PR-93-13, accepted for publication in Physical Review

Granularity-induced gapless superconductivity in NbN films: evidence of thermal phase fluctuations

Using a single coil mutual inductance technique, we measure the low temperature dependence of the magnetic penetration depth in superconducting NbN films prepared with similar critical temperatures around 16 K but with different microstructures. Only (100) epitaxial and weakly granular (100) textured films display the characteristic exponential dependence of conventional BCS s-wave superconductors. More granular (111) textured films exhibit a linear dependence, indicating a gapless state in spite of the s-wave gap. This result is quantitatively explained by a model of thermal phase fluctuations favored by the granular structure.Comment: 10 pages, 4 figures, to appear in Phys. Rev.

Curvature Dependence of Running Gauge Coupling and Confinement in AdS/CFT Correspondence

We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.Comment: LaTeX file, 24 pages, presentation is improve

Effect of gluon-exchange pair-currents on the ratio G(E(P))/G(M(P))

The effect of one-gluon-exchange (OGE) pair-currents on the ratio $\mu_p G_E^p/G_M^p$ for the proton is investigated within a nonrelativistic constituent quark model (CQM) starting from $SU(6) \times O(3)$ nucleon wave functions, but with relativistic corrections. We found that the OGE pair-currents are important to reproduce well the ratio $\mu_p G_E^p/G_M^p$. With the assumption that the OGE pair-currents are the driving mechanism for the violation of the scaling law we give a prediction for the ratio $\mu_n G_E^n/G_M^n$ of the neutron.Comment: 5 pages, 4 figure

Neutron Structure Function and A=3 Mirror Nuclei

We investigate deep inelastic scattering from He-3 and H-3 within a conventional convolution treatment of binding and Fermi motion effects. Using realistic Faddeev wave functions together with a nucleon spectral function, we demonstrate that the free neutron structure function can be extracted in deep-inelastic scattering from A=3 mirror nuclei, with nuclear effects canceling to within 2% for x < 0.85.Comment: 13 pages, 4 figures, version to appear in Phys. Lett.