4,938 research outputs found
Note on a Conjecture of Wegner
The optimal packings of n unit discs in the plane are known for those natural
numbers n, which satisfy certain number theoretic conditions. Their geometric
realizations are the extremal Groemer packings (or Wegner packings). But an
extremal Groemer packing of n unit discs does not exist for all natural numbers
n and in this case, the number n is called exceptional. We are interested in
number theoretic characterizations of the exceptional numbers. A counterexample
is given to a conjecture of Wegner concerning such a characterization. We
further give a characterization of the exceptional numbers, whose shape is
closely related to that of Wegner's conjecture.Comment: 5 pages; Contributions to Algebra and Geometry, Vol.52 No1 April 201
Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
We develop a new analytical method for solving real time evolution problems
of quantum many-body systems. Our approach is a direct generalization of the
well-known canonical perturbation theory for classical systems. Similar to
canonical perturbation theory, secular terms are avoided in a systematic
expansion and one obtains stable long-time behavior. These general ideas are
illustrated by applying them to the spin-boson model and studying its
non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3
figures
Non-Perturbative U(1) Gauge Theory at Finite Temperature
For compact U(1) lattice gauge theory (LGT) we have performed a finite size
scaling analysis on lattices for fixed by
extrapolating spatial volumes of size to . Within the
numerical accuracy of the thus obtained fits we find for , 5 and~6
second order critical exponents, which exhibit no obvious
dependence. The exponents are consistent with 3d Gaussian values, but not with
either first order transitions or the universality class of the 3d XY model. As
the 3d Gaussian fixed point is known to be unstable, the scenario of a yet
unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of
the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure
Wither the sliding Luttinger liquid phase in the planar pyrochlore
Using series expansion based on the flow equation method we study the zero
temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the
limit of strong diagonal coupling. Starting from the limit of decoupled crossed
dimers we analyze the evolution of the ground state energy and the elementary
triplet excitations in terms of two coupling constants describing the inter
dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the
fully frustrated inter chain coupling is critical, forcing a dimer phase which
adiabatically connects to the state of isolated dimers. This result is
consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev.
B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding
Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl
Wegner bounds for a two-particle tight binding model
We consider a quantum two-particle system on a d-dimensional lattice with
interaction and in presence of an IID external potential. We establish
Wegner-typer estimates for such a model. The main tool used is Stollmann's
lemma
On the nature of the FBS blue stellar objects and the completeness of the Bright Quasar Survey. II
In Paper I (Mickaelian et al. 1999), we compared the surface density of QSOs
in the Bright Quasar Survey (BQS) and in the First Byurakan Survey (FBS) and
concluded that the completeness of the BQS is of the order of 70% rather than
30-50% as suggested by several authors. A number of new observations recently
became available, allowing a re-evaluation of this completeness. We now obtain
a surface density of QSOs brighter than B = 16.16 in a subarea of the FBS
covering ~2250 deg^2, equal to 0.012 deg^-2 (26 QSOs), implying a completeness
of 53+/-10%.Comment: LaTeX 2e, 11 pages, 3 tables and 3 figures (included in text). To
appear in Astrophysics. Uses a modified aaspp4.sty (my_aaspp4.sty), included
in packag
Stress Analysis of Circular Frames
The stresses in circular frames of constant bending stiffnesses, as encountered in thin-wall shells, are investigated from the point of view of finite depth of sectional area of frame. The solution is carried out for four fundamental load conditions. The method is illustrated on a worked out example
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