3,349 research outputs found
Rigid unit modes in tetrahedral crystals
The 'rigid unit mode' (RUM) model requires unit blocks, in our case
tetrahedra of SiO_4 groups, to be rigid within first order of the displacements
of the O-ions. The wave-vectors of the lattice vibrations, which obey this
rigidity, are determined analytically. Lattices with inversion symmetry yield
generically surfaces of RUMs in reciprocal space, whereas lattices without this
symmetry yield generically lines of RUMs. Only in exceptional cases as in
beta-quartz a surface of RUMs appears, if inversion symmetry is lacking. The
occurence of planes and bending surfaces, straight and bent lines is discussed.
Explicit calculations are performed for five modifications of SiO_2 crystals.Comment: 18 pages, 6 figures, improved notatio
A metal-insulator transition as a quantum glass problem
We discuss a recent mapping of the Anderson-Mott metal-insulator transition
onto a random field magnet problem. The most important new idea introduced is
to describe the metal-insulator transition in terms of an order parameter
expansion rather than in terms of soft modes via a nonlinear sigma model. For
spatial dimensions d>6 a mean field theory gives the exact critical exponents.
In an epsilon expansion about d=6 the critical exponents are identical to those
for a random field Ising model. Dangerous irrelevant quantum fluctuations
modify Wegner's scaling law relating the conductivity exponent to the
correlation or localization length exponent. This invalidates the bound s>2/3
for the conductivity exponent s in d=3. We also argue that activated scaling
might be relevant for describing the AMT in three-dimensional systems.Comment: 10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final
version as publishe
Limit cycles of effective theories
A simple example is used to show that renormalization group limit cycles of
effective quantum theories can be studied in a new way. The method is based on
the similarity renormalization group procedure for Hamiltonians. The example
contains a logarithmic ultraviolet divergence that is generated by both real
and imaginary parts of the Hamiltonian matrix elements. Discussion of the
example includes a connection between asymptotic freedom with one scale of
bound states and the limit cycle with an entire hierarchy of bound states.Comment: 8 pages, 3 figures, revtex
Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach
Recently we have studied the Bloch effective Hamiltonian approach to bound
states in 2+1 dimensional gauge theories. Numerical calculations were carried
out to investigate the vanishing energy denominator problem. In this work we
study similarity renormalization approach to the same problem. By performing
analytical calculations with a step function form for the similarity factor, we
show that in addition to curing the vanishing energy denominator problem,
similarity approach generates linear confining interaction for large transverse
separations. However, for large longitudinal separations, the generated
interaction grows only as the square root of the longitudinal separation and
hence produces violations of rotational symmetry in the spectrum. We carry out
numerical studies in the G{\l}azek-Wilson and Wegner formalisms and present low
lying eigenvalues and wavefunctions. We investigate the sensitivity of the
spectra to various parameterizations of the similarity factor and other
parameters of the effective Hamiltonian, especially the scale . Our
results illustrate the need for higher order calculations of the effective
Hamiltonian in the similarity renormalization scheme.Comment: 31 pages, 4 figures, to be published in Physical Review
Dynamical modelling of luminous and dark matter in 17 Coma early-type galaxies
Dynamical models for 17 Coma early-type galaxies are presented. The galaxy
sample consists of flattened, rotating as well as non-rotating early-types
including cD and S0 galaxies with luminosities between M=-18.79 and M=-22.56.
Kinematical long-slit observations cover at least the major and minor axis and
extend to 1-4 effective radii. Axisymmetric Schwarzschild models are used to
derive stellar mass-to-light ratios and dark halo parameters. In every galaxy
models with a dark matter halo match the data better than models without. The
statistical significance is over 95 percent for 8 galaxies, around 90 percent
for 5 galaxies and for four galaxies it is not significant. For the highly
significant cases systematic deviations between observed and modelled
kinematics are clearly seen; for the remaining galaxies differences are more
statistical in nature. Best-fit models contain 10-50 percent dark matter inside
the half-light radius. The central dark matter density is at least one order of
magnitude lower than the luminous mass density. The central phase-space density
of dark matter is often orders of magnitude lower than in the luminous
component, especially when the halo core radius is large. The orbital system of
the stars along the major-axis is slightly dominated by radial motions. Some
galaxies show tangential anisotropy along the minor-axis, which is correlated
with the minor-axis Gauss-Hermite coefficient H4. Changing the balance between
data-fit and regularisation constraints does not change the reconstructed mass
structure significantly. Model anisotropies tend to strengthen if the weight on
regularisation is reduced, but the general property of a galaxy to be radially
or tangentially anisotropic, respectively, does not change. (abridged)Comment: 31 pages, 34 figures; accepted for publication in MNRA
Mechanisms for Spin-Supersolidity in S=1/2 Spin-Dimer Antiferromagnets
Using perturbative expansions and the contractor renormalization (CORE)
algorithm, we obtain effective hard-core bosonic Hamiltonians describing the
low-energy physics of spin-dimer antiferromagnets known to display
supersolid phases under an applied magnetic field. The resulting effective
models are investigated by means of mean-field analysis and quantum Monte Carlo
simulations. A "leapfrog mechanism", through means of which extra singlets
delocalize in a checkerboard-solid environment via correlated hoppings, is
unveiled that accounts for the supersolid behavior.Comment: 12 pages, 10 figure
Dynamics of weakly localized waves
We develop a transport theory to describe the dynamics of (weakly) localized
waves in a quasi-1D tube geometry both in reflection and in transmission. We
compare our results to recent experiments with microwaves, and to other
theories such as random matrix theory and supersymmetric theory.Comment: RevTeX, 4 pages, 2 figure
Block Diagonalization using SRG Flow Equations
By choosing appropriate generators for the Similarity Renormalization Group
(SRG) flow equations, different patterns of decoupling in a Hamiltonian can be
achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent
nucleon-nucleon potentials in momentum space are generated as examples and
compared to analogous low-momentum interactions ("v_lowk").Comment: 4 pages, 9 figures (pdfLaTeX
Integral Transforms for Conformal Field Theories with a Boundary
A new method is developed for solving the conformally invariant integrals
that arise in conformal field theories with a boundary. The presence of a
boundary makes previous techniques for theories without a boundary less
suitable. The method makes essential use of an invertible integral transform,
related to the radon transform, involving integration over planes parallel to
the boundary. For successful application of this method several nontrivial
hypergeometric function relations are also derived.Comment: 20 pagess, LateX fil
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