61,039 research outputs found
Acyclic orientations on the Sierpinski gasket
We study the number of acyclic orientations on the generalized
two-dimensional Sierpinski gasket at stage with equal to
two and three, and determine the asymptotic behaviors. We also derive upper
bounds for the asymptotic growth constants for and -dimensional
Sierpinski gasket .Comment: 20 pages, 8 figures and 6 table
Some Exact Results for Spanning Trees on Lattices
For -vertex, -dimensional lattices with , the number
of spanning trees grows asymptotically as
in the thermodynamic limit. We present an exact closed-form result for the
asymptotic growth constant for spanning trees on the
-dimensional body-centered cubic lattice. We also give an exact integral
expression for on the face-centered cubic lattice and an exact
closed-form expression for on the lattice.Comment: 7 pages, 1 tabl
Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders
We construct the states of maximal localization taking into account a
modification of the commutation relation between position and momentum
operators to all orders of the minimum length parameter. To first order, the
algebra we use reproduces the one proposed by Kempft, Mangano and Mann. It is
emphasized that a minimal length acts as a natural regulator for the theory,
thus eliminating the otherwise ever appearing infinities. So, we use our
results to calculate the first correction to the Casimir Effect due to the
minimal length. We also discuss some of the physical consequences of the
existence of a minimal length, culminating in a proposal to reformulate the
very concept of "position measurement"
Conservation of connectivity of model-space effective interactions under a class of similarity transformation
Effective interaction operators usually act on a restricted model space and
give the same energies (for Hamiltonian) and matrix elements (for transition
operators etc.) as those of the original operators between the corresponding
true eigenstates. Various types of effective operators are possible. Those well
defined effective operators have been shown being related to each other by
similarity transformation. Some of the effective operators have been shown to
have connected-diagram expansions. It is shown in this paper that under a class
of very general similarity transformations, the connectivity is conserved. The
similarity transformation between hermitian and non-hermitian
Rayleigh-Schr\"{o}dinger perturbative effective operators is one of such
transformation and hence the connectivity can be deducted from each other.Comment: 12 preprint page
A heavy Higgs boson from flavor and electroweak symmetry breaking unification
We present a unified picture of flavor and electroweak symmetry breaking
based on a nonlinear sigma model spontaneously broken at the TeV scale. Flavor
and Higgs bosons arise as pseudo-Goldstone modes. Explicit collective symmetry
breaking yields stable vacuum expectation values and masses protected at one
loop by the little-Higgs mechanism. The coupling to the fermions generates
well-definite mass textures--according to a U(1) global flavor symmetry--that
correctly reproduce the mass hierarchies and mixings of quarks and leptons. The
model is more constrained than usual little-Higgs models because of bounds on
weak and flavor physics. The main experimental signatures testable at the LHC
are a rather large mass m_{h^0} = 317\pm 80 GeV for the (lightest) Higgs boson
and a characteristic spectrum of new bosons and fermions at the TeV scale.Comment: 5 page
Confined magnetic guiding orbit states
We show how snake-orbit states which run along a magnetic edge can be
confined electrically. We consider a two-dimensional electron gas (2DEG)
confined into a quantum wire, subjected to a strong perpendicular and steplike
magnetic field . Close to this magnetic step new, spatially confined
bound states arise as a result of the lateral confinement and the magnetic
field step. The number of states, with energy below the first Landau level,
increases as becomes stronger or as the wire width becomes larger. These
bound states can be understood as an interference between two
counter-propagating one-dimensional snake-orbit states.Comment: 4 pages, 4 figure
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