1,994 research outputs found
Spin Distribution in Diffraction Pattern of Two-dimensional Electron Gas with Spin-orbit Coupling
Spin distribution in the diffraction pattern of two-dimensional electron gas
by a split gate and a quantum point contact is computed in the presence of the
spin-orbit coupling. After diffracted, the component of spin perpendicular to
the two-dimensional plane can be generated up to 0.42 . The non-trivial
spin distribution is the consequence of a pure spin current in the transverse
direction generated by the diffraction. The direction of the spin current can
be controlled by tuning the chemical potential.Comment: 9 page
Central Limit Theorems for some Set Partition Statistics
We prove the conjectured limiting normality for the number of crossings of a
uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel
stochastic representation and are also used to prove central limit theorems for
the dimension index and the number of levels
Partial order from disorder in a classical pyrochlore antiferromagnet
We investigate theoretically the phase diagram of a classical Heisenberg
antiferromagnet on the pyrochlore lattice perturbed by a weak second-neighbor
interaction J_2. The huge ground state degeneracy of the nearest-neighbor
Heisenberg spins is lifted by J_2 and a magnetically ordered ground state sets
in upon approaching zero temperature. We have found a new, partially ordered
phase with collinear spins at finite temperatures for a ferromagnetic J_2. In
addition to a large nematic order parameter, this intermediate phase also
exhibits a layered structure and a bond order that breaks the sublattice
symmetry. Thermodynamic phase boundaries separating it from the fully
disordered and magnetically ordered states scale as 1.87 J_2 S^2 and 0.26 J_2
S^2 in the limit of small J_2. The phase transitions are discontinuous. We
analytically examine the local stability of the collinear state and obtain a
boundary T ~ J_2^2/J_1 in agreement with Monte Carlo simulations.Comment: 14 pages revtex, revised phase diagram, references adde
Tilings, Chern-Simons Theories and M2 Branes
A new infinite class of Chern-Simons theories is presented using brane
tilings. The new class reproduces all known cases so far and introduces many
new models that are dual to M2 brane theories which probe a toric non-compact
CY 4-fold. The master space of the quiver theory is used as a tool to construct
the moduli space for this class and the Hilbert Series is computed for a
selected set of examples.Comment: 23 pages, minor changes, references adde
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition
The transport properties of disordered systems are known to depend critically
on dimensionality. We study the diffusion coefficient of a quantum particle
confined to a lattice on the surface of a tube, where it scales between the 1D
and 2D limits. It is found that the scaling relation is universal and
independent of the disorder and noise parameters, and the essential order
parameter is the ratio between the localization length in 2D and the
circumference of the tube. Phenomenological and quantitative expressions for
transport properties as functions of disorder and noise are obtained and
applied to real systems: In the natural chlorosomes found in light-harvesting
bacteria the exciton transfer dynamics is predicted to be in the 2D limit,
whereas a family of synthetic molecular aggregates is found to be in the
homogeneous limit and is independent of dimensionality.Comment: 10 pages, 6 figure
Topological defects in flat nanomagnets: the magnetostatic limit
We discuss elementary topological defects in soft magnetic nanoparticles in
the thin-film geometry. In the limit dominated by magnetostatic forces the
low-energy defects are vortices (winding number n = +1), cross ties (n = -1),
and edge defects with n = -1/2. We obtain topological constraints on the
possible composition of domain walls. The simplest domain wall in this regime
is composed of two -1/2 edge defects and a vortex, in accordance with
observations and numerics.Comment: 3 pages, eps figures. Proceedings of MMM 0
Lagrangian Symmetries of Chern-Simons Theories
This paper analyses the Noether symmetries and the corresponding conservation
laws for Chern-Simons Lagrangians in dimension . In particular, we find an
expression for the superpotential of Chern-Simons gravity. As a by-product the
general discussion of superpotentials for 3rd order natural and quasi-natural
theories is also given.Comment: 16 pages in LaTeX, some comments and references added. to appear in
Journal of Physics A: Mathematical and Genera
Yang-Mills, Complex Structures and Chern's Last Theorem
Recently Shiing-Shen Chern suggested that the six dimensional sphere
has no complex structure. Here we explore the relations between
his arguments and Yang-Mills theories. In particular, we propose that Chern's
approach is widely applicable to investigate connections between the geometry
of manifolds and the structure of gauge theories. We also discuss several
examples of manifolds, both with and without a complex structure.Comment: Chern's proof remains incomplete, and we have edited some statements
in our article accordingl
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