8,460 research outputs found
Spectrum of a duality-twisted Ising quantum chain
The Ising quantum chain with a peculiar twisted boundary condition is
considered. This boundary condition, first introduced in the framework of the
spin-1/2 XXZ Heisenberg quantum chain, is related to the duality
transformation, which becomes a symmetry of the model at the critical point.
Thus, at the critical point, the Ising quantum chain with the duality-twisted
boundary is translationally invariant, similar as in the case of the usual
periodic or antiperiodic boundary conditions. The complete energy spectrum of
the Ising quantum chain is calculated analytically for finite systems, and the
conformal properties of the scaling limit are investigated. This provides an
explicit example of a conformal twisted boundary condition and a corresponding
generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style
Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra
Explicit expressions for three series of matrices which are related to a
``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of
those, one series is equivalent to the quantum matrices of the
generalised Toda systems whereas the remaining two series
appear to be new.Comment: 5 page
Spectral and Diffusive Properties of Silver-Mean Quasicrystals in 1,2, and 3 Dimensions
Spectral properties and anomalous diffusion in the silver-mean (octonacci)
quasicrystals in d=1,2,3 are investigated using numerical simulations of the
return probability C(t) and the width of the wave packet w(t) for various
values of the hopping strength v. In all dimensions we find C(t)\sim
t^{-\delta}, with results suggesting a crossover from \delta<1 to \delta=1 when
v is varied in d=2,3, which is compatible with the change of the spectral
measure from singular continuous to absolute continuous; and we find w(t)\sim
t^{\beta} with 0<\beta(v)<1 corresponding to anomalous diffusion. Results
strongly suggest that \beta(v) is independent of d. The scaling of the inverse
participation ratio suggests that states remain delocalized even for very small
hopping amplitude v. A study of the dynamics of initially localized wavepackets
in large three-dimensional quasiperiodic structures furthermore reveals that
wavepackets composed of eigenstates from an interval around the band edge
diffuse faster than those composed of eigenstates from an interval of the
band-center states: while the former diffuse anomalously, the latter appear to
diffuse slower than any power law.Comment: 11 pages, 10 figures, 1 tabl
Anomaly Cancelation in Field Theory and F-theory on a Circle
We study the manifestation of local gauge anomalies of four- and
six-dimensional field theories in the lower-dimensional Kaluza-Klein theory
obtained after circle compactification. We identify a convenient set of
transformations acting on the whole tower of massless and massive states and
investigate their action on the low-energy effective theories in the Coulomb
branch. The maps employ higher-dimensional large gauge transformations and
precisely yield the anomaly cancelation conditions when acting on the one-loop
induced Chern-Simons terms in the three- and five-dimensional effective theory.
The arising symmetries are argued to play a key role in the study of the
M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact
that all fully resolved F-theory geometries inducing multiple Abelian gauge
groups or non-Abelian groups admit a certain set of symmetries, we are able to
generally show the cancelation of pure Abelian or pure non-Abelian anomalies in
these models.Comment: 48 pages, 2 figures; v2: typos corrected, comments on circle fluxes
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Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
The extinction of a single species due to demographic stochasticity is
analyzed. The discrete nature of the individual agents and the Poissonian noise
related to the birth-death processes result in local extinction of a metastable
population, as the system hits the absorbing state. The Fokker-Planck
formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the
absorbing state become, in general, invalid as the population becomes large. To
connect these two regimes, a master equation based on a real space WKB method
is presented, and is shown to yield an excellent approximation for the decay
rate and the extreme events statistics all the way down to the absorbing state.
The details of the underlying microscopic process, smeared out in a mean field
treatment, are shown to be crucial for an exact determination of the extinction
exponent. This general scheme is shown to reproduce the known results in the
field, to yield new corollaries and to fit quite precisely the numerical
solutions. Moreover it allows for systematic improvement via a series expansion
where the small parameter is the inverse of the number of individuals in the
metastable state
Coherent optical transfer of Feshbach molecules to a lower vibrational state
Using the technique of stimulated Raman adiabatic passage (STIRAP) we have
coherently transferred ultracold 87Rb2 Feshbach molecules into a more deeply
bound vibrational quantum level. Our measurements indicate a high transfer
efficiency of up to 87%. As the molecules are held in an optical lattice with
not more than a single molecule per lattice site, inelastic collisions between
the molecules are suppressed and we observe long molecular lifetimes of about 1
s. Using STIRAP we have created quantum superpositions of the two molecular
states and tested their coherence interferometrically. These results represent
an important step towards Bose-Einstein condensation (BEC) of molecules in the
vibrational ground state.Comment: 4 pages, 5 figure
Dilute Birman--Wenzl--Murakami Algebra and models
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is
considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra.
The vertex models are examples of corresponding solvable
lattice models and can be regarded as the dilute version of the
vertex models.Comment: 11 page
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