81,414 research outputs found
Basis-conjugating automorphisms of a free group and associated Lie algebras
Let F_n = denote the free group with generators {x_1,...,x_n}.
Nielsen and Magnus described generators for the kernel of the canonical
epimorphism from the automorphism group of F_n to the general linear group over
the integers. In particular among them are the automorphisms chi_{k,i} which
conjugate the generator x_k by the generator x_i leaving the x_j fixed for j
not k. A computation of the cohomology ring as well as the Lie algebra obtained
from the descending central series of the group generated by chi_{k,i} for i<k
is given here. Partial results are obtained for the group generated by all
chi_{k,i}.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Orbital ice: an exact Coulomb phase on the diamond lattice
We demonstrate the existence of orbital Coulomb phase as the exact ground
state of p-orbital exchange Hamiltonian on the diamond lattice. The Coulomb
phase is an emergent state characterized by algebraic dipolar correlations and
a gauge structure resulting from local constraints (ice rules) of the
underlying lattice models. For most ice models on the pyrochlore lattice, these
local constraints are a direct consequence of minimizing the energy of each
individual tetrahedron. On the contrary, the orbital ice rules are emergent
phenomena resulting from the quantum orbital dynamics. We show that the orbital
ice model exhibits an emergent geometrical frustration by mapping the
degenerate quantum orbital ground states to the spin-ice states obeying the
2-in-2-out constraints on the pyrochlore lattice. We also discuss possible
realization of the orbital ice model in optical lattices with p-band fermionic
cold atoms.Comment: 6 pages, 5 figure
Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models
Exact analyses are given for two three-dimensional lattice systems: A system
of close-packed dimers placed in layers of honeycomb lattices and a layered
triangular-lattice interacting domain wall model, both with nontrivial
interlayer interactions. We show that both models are equivalent to a 5-vertex
model on the square lattice with interlayer vertex-vertex interactions. Using
the method of Bethe ansatz, a closed-form expression for the free energy is
obtained and analyzed. We deduce the exact phase diagram and determine the
nature of the phase transitions as a function of the strength of the interlayer
interaction.Comment: 22 pages in Revtex, 6 PS files, submitted to PR
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Exact Solution of a Three-Dimensional Dimer System
We consider a three-dimensional lattice model consisting of layers of vertex
models coupled with interlayer interactions. For a particular non-trivial
interlayer interaction between charge-conserving vertex models and using a
transfer matrix approach, we show that the eigenvalues and eigenvectors of the
transfer matrix are related to those of the two-dimensional vertex model. The
result is applied to analyze the phase transitions in a realistic
three-dimensional dimer system.Comment: 11 pages in REVTex with 2 PS figure
Understanding I=2 pi-pi Interaction
A correct understanding and description of the I=2 pi-pi S-wave interaction
is important for the extraction of the I=0 pi-pi S-wave interaction from
experimental data and for understanding the I=0 pi-pi S-wave interaction
theoretically. With t-channel rho, f2(1270) exchange and the pi pi -> rho rho
-> pi pi box diagram contribution, we reproduce the pi-pi isotensor S-wave and
D-wave scattering phase shifts and inelasticities up to 2.2 GeV quite well in a
K-matrix formalism.Comment: Talk given at Hadron 03: 10th International Conference on Hadron
Spectroscopy, Aschaffenburg, Germany, 31 Aug - 6 Sep 200
Introduction to Graphene Electronics -- A New Era of Digital Transistors and Devices
The speed of silicon-based transistors has reached an impasse in the recent
decade, primarily due to scaling techniques and the short-channel effect.
Conversely, graphene (a revolutionary new material possessing an atomic
thickness) has been shown to exhibit a promising value for electrical
conductivity. Graphene would thus appear to alleviate some of the drawbacks
associated with silicon-based transistors. It is for this reason why such a
material is considered one of the most prominent candidates to replace silicon
within nano-scale transistors. The major crux here, is that graphene is
intrinsically gapless, and yet, transistors require a band-gap pertaining to a
well-defined ON/OFF logical state. Therefore, exactly as to how one would
create this band-gap in graphene allotropes is an intensive area of growing
research. Existing methods include nano-ribbons, bilayer and multi-layer
structures, carbon nanotubes, as well as the usage of the graphene substrates.
Graphene transistors can generally be classified according to two working
principles. The first is that a single graphene layer, nanoribbon or carbon
nanotube can act as a transistor channel, with current being transported along
the horizontal axis. The second mechanism is regarded as tunneling, whether
this be band-to-band on a single graphene layer, or vertically between adjacent
graphene layers. The high-frequency graphene amplifier is another talking point
in recent research, since it does not require a clear ON/OFF state, as with
logical electronics. This paper reviews both the physical properties and
manufacturing methodologies of graphene, as well as graphene-based electronic
devices, transistors, and high-frequency amplifiers from past to present
studies. Finally, we provide possible perspectives with regards to future
developments.Comment: This is an updated version of our review article, due to be published
in Contemporary Physics (Sept 2013). Included are updated references, along
with a few minor corrections. (45 pages, 19 figures
The Emergence of Superconducting Systems in Anti-de Sitter Space
In this article, we investigate the mathematical relationship between a (3+1)
dimensional gravity model inside Anti-de Sitter space , and a (2+1)
dimensional superconducting system on the asymptotically flat boundary of (in the absence of gravity). We consider a simple case of the Type II
superconducting model (in terms of Ginzburg-Landau theory) with an external
perpendicular magnetic field . An interaction potential is introduced
within the Lagrangian system. This provides more flexibility within the model,
when the superconducting system is close to the transition temperature .
Overall, our result demonstrates that the two Ginzburg-Landau differential
equations can be directly deduced from Einstein's theory of general relativity.Comment: 10 pages, 2 figure
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