4,412 research outputs found
The A-theoretic FarrellāJones conjecture for virtually solvable groups
We prove the A -theoretic FarrellāJones conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S -arithmetic groups and lattices in almost connected Lie groups
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
Anderson-Mott Transition in a Magnetic Field: Corrections to Scaling
It is shown that the Anderson-Mott metal-insulator transition of
paramagnetic, interacting disordered electrons in an external magnetic field is
in the same universality class as the transition from a ferromagnetic metal to
a ferromagnetic insulator discussed recently. As a consequence, large
corrections to scaling exist in the magnetic-field universality class, which
have been neglected in previous theoretical descriptions. The nature and
consequences of these corrections to scaling are discussed.Comment: 5pp., REVTeX, no figs, 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
Surface-electronic structure of La(0001) and Lu(0001)
Most spectroscopic methods for studying the electronic structure of metal
surfaces have the disadvantage that either only occupied or only unoccupied
states can be probed, and the signal is cut at the Fermi edge. This leads to
significant uncertainties, when states are very close to the Fermi level. By
performing low-temperature scanning tunneling spectroscopy and ab initio
calculations, we study the surface-electronic structure of La(0001) and
Lu(0001), and demonstrate that in this way detailed information on the
surface-electronic structure very close to the Fermi energy can be derived with
high accuracy.Comment: 6 pages, 4 figures, 1 table submitted to PR
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