1,649 research outputs found
Noncompact dynamical symmetry of a spin-orbit coupled oscillator
We explain the finite as well as infinite degeneracy in the spectrum of a
particular system of spin-1/2 fermions with spin-orbit coupling in three
spatial dimensions. Starting from a generalized Runge-Lenz vector, we
explicitly construct a complete set of symmetry operators, which span a
noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only
involves a particular, infinite, so called singleton representation. In the
branch where orbital and spin angular momentum are aligned the full
representation appears, constituting a 3D analogue of Landau levels.
Anti-aligning the spin leads to a finite degeneracy due to a truncation of the
singleton representation. We conclude the paper by constructing the spectrum
generating algebra of the problem
Tensor product representations of the quantum double of a compact group
We consider the quantum double D(G) of a compact group G, following an
earlier paper. We use the explicit comultiplication on D(G) in order to build
tensor products of irreducible *-representations. Then we study their behaviour
under the action of the R-matrix, and their decomposition into irreducible
*-representations. The example of D(SU(2)) is treated in detail, with explicit
formulas for direct integral decomposition (`Clebsch-Gordan series') and
Clebsch-Gordan coefficients. We point out possible physical applications.Comment: LaTeX2e, 27 pages, corrected references, accepted by Comm.Math.Phy
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Defect mediated melting and the breaking of quantum double symmetries
In this paper, we apply the method of breaking quantum double symmetries to
some cases of defect mediated melting. The formalism allows for a systematic
classification of possible defect condensates and the subsequent confinement
and/or liberation of other degrees of freedom. We also show that the breaking
of a double symmetry may well involve a (partial) restoration of an original
symmetry. A detailed analysis of a number of simple but representative examples
is given, where we focus on systems with global internal and external (space)
symmetries. We start by rephrasing some of the well known cases involving an
Abelian defect condensate, such as the Kosterlitz-Thouless transition and
one-dimensional melting, in our language. Then we proceed to the non-Abelian
case of a hexagonal crystal, where the hexatic phase is realized if
translational defects condense in a particular rotationally invariant state.
Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference
Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole
The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-NUT space with
the time trivially added, is the appropriate background of the Dirac magnetic
monopole without an explicit mass term. One remarks that there exists a very
simple five-dimensional metric of spacetimes carrying massive magnetic
monopoles that is an exact solution of the vacuum Einstein equations. Moreover,
the same isometry properties as the original Euclidean Taub-NUT space are
preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as
a combinations between the Gross-Perry-Sorkin and Schwarzschild ones. The
asymptotic motion of the scalar charged test particles is discussed, now by
accounting for the mixing between the gravitational and magnetic effects.Comment: 7 page
Bioinformatics
Motivation: Current methods that annotate conserved transcription factor binding sites in an alignment of two regulatory regions perform the alignment and annotation step separately and combine the results in the end. If the site descriptions are weak or the sequence similarity is low, the local gap structure of the alignment poses a problem in detecting the conserved sites. It is therefore desirable to have an approach that is able to simultaneously consider the alignment as well as possibly matching site locations. Results: With SimAnn we have developed a tool that serves exactly this purpose. By combining the annotation step and the alignment of the two sequences into one algorithm, it detects conserved sites more clearly. It has the additional advantage that all parameters are calculated based on statistical considerations. This allows for its successful application with any binding site model of interest. We present the algorithm and the approach for parameter selection and compare its performance with that of other, non-simultaneous methods on both simulated and real data. Availability: A command-line based C++ implementation of SimAnn is available from the authors upon request. In addition, we provide Perl scripts for calculating the input parameters based on statistical considerations
The Mn site in Mn-doped Ga-As nanowires: an EXAFS study
We present an EXAFS study of the Mn atomic environment in Mn-doped GaAs
nanowires. Mn doping has been obtained either via the diffusion of the Mn used
as seed for the nanowire growth or by providing Mn during the growth of
Au-induced wires. As a general finding, we observe that Mn forms chemical bonds
with As but is not incorporated in a substitutional site. In Mn-induced GaAs
wires, Mn is mostly found bonded to As in a rather disordered environment and
with a stretched bond length, reminiscent of that exhibited by MnAs phases. In
Au-seeded nanowires, along with stretched Mn-As coordination we have found the
presence of Mn in a Mn-Au intermetallic compound.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in Semiconductor Science and Technology. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
doi:10.1088/0268-1242/27/8/08500
Nested Topological Order
We introduce the concept of nested topological order in a class of exact
quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry.
The topological order present in the models can be partially destroyed by
introducing a gauge symmetry reduction mechanism. When symmetry is reduced in
several islands only, this imposes boundary conditions to the rest of the
system giving rise to topological ground state degeneracy. This degeneracy is
related to the existence of topological fluxes in between islands or,
alternatively, hidden charges at islands. Additionally, island deformations
give rise to an extension of topological quantum computation beyond
quasiparticles.Comment: revtex4, 4 page
Vortices on Higher Genus Surfaces
We consider the topological interactions of vortices on general surfaces. If
the genus of the surface is greater than zero, the handles can carry magnetic
flux. The classical state of the vortices and the handles can be described by a
mapping from the fundamental group to the unbroken gauge group. The allowed
configurations must satisfy a relation induced by the fundamental group. Upon
quantization, the handles can carry ``Cheshire charge.'' The motion of the
vortices can be described by the braid group of the surface. How the motion of
the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint
CALT-68-187
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