258 research outputs found
Crystallization in a model glass: influence of the boundary conditions
Using molecular dynamics calculations and the Voronoi tessellation, we study
the evolution of the local structure of a soft-sphere glass versus temperature
starting from the liquid phase at different quenching rates. This study is done
for different sizes and for two different boundary conditions namely the usual
cubic periodic boundary conditions and the isotropic hyperspherical boundary
conditions for which the particles evolve on the surface of a hypersphere in
four dimensions. Our results show that for small system sizes, crystallization
can indeed be induced by the cubic boundary conditions. On the other hand we
show that finite size effects are more pronounced on the hypersphere and that
crystallization is artificially inhibited even for large system sizes.Comment: 11 pages, 2 figure
Borcherds symmetries in M-theory
It is well known but rather mysterious that root spaces of the Lie
groups appear in the second integral cohomology of regular, complex, compact,
del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms)
of toroidal compactifications of M theory. Their Borel subgroups are actually
subgroups of supergroups of finite dimension over the Grassmann algebra of
differential forms on spacetime that have been shown to preserve the
self-duality equation obeyed by all bosonic form-fields of the theory. We show
here that the corresponding duality superalgebras are nothing but Borcherds
superalgebras truncated by the above choice of Grassmann coefficients. The full
Borcherds' root lattices are the second integral cohomology of the del Pezzo
surfaces. Our choice of simple roots uses the anti-canonical form and its known
orthogonal complement. Another result is the determination of del Pezzo
surfaces associated to other string and field theory models. Dimensional
reduction on corresponds to blow-up of points in general position
with respect to each other. All theories of the Magic triangle that reduce to
the sigma model in three dimensions correspond to singular del Pezzo
surfaces with (normal) singularity at a point. The case of type I and
heterotic theories if one drops their gauge sector corresponds to non-normal
(singular along a curve) del Pezzo's. We comment on previous encounters with
Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real
fermionic simple roots when they would naively aris
Multiple CSLs for the body centered cubic lattice
Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of
a lattice with a rotated copy of itself. They are useful for
classifying grain boundaries and have been studied extensively since the mid
sixties. Recently the interests turned to so-called multiple CSLs, i.e.
intersections of rotated copies of a given lattice , in particular
in connection with lattice quantizers. Here we consider multiple CSLs for the
3-dimensional body centered cubic lattice. We discuss the spectrum of
coincidence indices and their multiplicity, in particular we show that the
latter is a multiplicative function and give an explicit expression of it for
some special cases.Comment: 4 pages, SSPCM (31 August - 7 September 2005, Myczkowce, Poland
Vison states and confinement transitions of Z2 spin liquids on the kagome lattice
We present a projective symmetry group (PSG) analysis of the spinless
excitations of Z2 spin liquids on the kagome lattice. In the simplest case,
vortices carrying Z2 magnetic flux ('visons') are shown to transform under the
48 element group GL(2, Z3). Alternative exchange couplings can also lead to a
second case with visons transforming under 288 element group GL(2, Z3) \times
D3. We study the quantum phase transition in which visons condense into
confining states with valence bond solid order. The critical field theories and
confining states are classified using the vison PSGs.Comment: 25 pages, 13 figure
Quaterionic Construction of the W(F_4) Polytopes with Their Dual Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)
4-dimensional polytopes and their dual polytopes have been
constructed as the orbits of the Coxeter-Weyl group where the group
elements and the vertices of the polytopes are represented by quaternions.
Branchings of an arbitrary \textbf{} orbit under the Coxeter groups
and have been presented. The role of
group theoretical technique and the use of quaternions have been emphasizedComment: 26 pages, 10 figure
Classification and stability of simple homoclinic cycles in R^5
The paper presents a complete study of simple homoclinic cycles in R^5. We
find all symmetry groups Gamma such that a Gamma-equivariant dynamical system
in R^5 can possess a simple homoclinic cycle. We introduce a classification of
simple homoclinic cycles in R^n based on the action of the system symmetry
group. For systems in R^5, we list all classes of simple homoclinic cycles. For
each class, we derive necessary and sufficient conditions for asymptotic
stability and fragmentary asymptotic stability in terms of eigenvalues of
linearisation near the steady state involved in the cycle. For any action of
the groups Gamma which can give rise to a simple homoclinic cycle, we list
classes to which the respective homoclinic cycles belong, thus determining
conditions for asymptotic stability of these cycles.Comment: 34 pp., 4 tables, 30 references. Submitted to Nonlinearit
Hunting for the New Symmetries in Calabi-Yau Jungles
It was proposed that the Calabi-Yau geometry can be intrinsically connected
with some new symmetries, some new algebras. In order to do this it has been
analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive
polyhedra. The graphs can be naturally get in the frames of Universal
Calabi-Yau algebra (UCYA) and may be decode by universal way with changing of
some restrictions on the generalized Cartan matrices associated with the Dynkin
diagrams that characterize affine Kac-Moody algebras. We propose that these new
Berger graphs can be directly connected with the generalizations of Lie and
Kac-Moody algebras.Comment: 29 pages, 15 figure
Ultrametric spaces of branches on arborescent singularities
Let be a normal complex analytic surface singularity. We say that is
arborescent if the dual graph of any resolution of it is a tree. Whenever
are distinct branches on , we denote by their intersection
number in the sense of Mumford. If is a fixed branch, we define when and
otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of
surfaces, by proving that whenever is arborescent, then is an
ultrametric on the set of branches of different from . We compute the
maximum of , which gives an analog of a theorem of Teissier. We show that
encodes topological information about the structure of the embedded
resolutions of any finite set of branches. This generalizes a theorem of Favre
and Jonsson concerning the case when both and are smooth. We generalize
also from smooth germs to arbitrary arborescent ones their valuative
interpretation of the dual trees of the resolutions of . Our proofs are
based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has
a new section 4.3, accompanied by 2 new figures. Several passages were
clarified and the typos discovered in the meantime were correcte
Interacting Preformed Cooper Pairs in Resonant Fermi Gases
We consider the normal phase of a strongly interacting Fermi gas, which can
have either an equal or an unequal number of atoms in its two accessible spin
states. Due to the unitarity-limited attractive interaction between particles
with different spin, noncondensed Cooper pairs are formed. The starting point
in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory,
which approximates the pairs as being noninteracting. Here, we consider the
effects of the interactions between the Cooper pairs in a Wilsonian
renormalization-group scheme. Starting from the exact bosonic action for the
pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism
with the Wilsonian approach. We compare our findings with the recent
experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and
Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good
agreement. We also make predictions for the population-imbalanced case, that
can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the
imbalanced Fermi gas added, new figure and references adde
The Beta Ansatz: A Tale of Two Complex Structures
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges
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