2,520 research outputs found
Universality and Non-Perturbative Definitions of 2D Quantum Gravity from Matrix Models
The universality of the non-perturbative definition of Hermitian one-matrix
models following the quantum, stochastic, or -like stabilization is
discussed in comparison with other procedures. We also present another
alternative definition, which illustrates the need of new physical input for
matrix models to make contact with 2D quantum gravity at the
non-perturbative level.Comment: 20 page
BPS submodels of the Skyrme model
We show that the standard Skyrme model without pion mass term can be
expressed as a sum of two BPS submodels, i.e., of two models whose static field
equations, independently, can be reduced to first order equations. Further,
these first order (BPS) equations have nontrivial solutions, at least locally.
These two submodels, however, cannot have common solutions. Our findings also
shed some light on the rational map approximation. Finally, we consider certain
generalisations of the BPS submodels.Comment: Latex, 12 page
Integrability from an abelian subgroup of the diffeomorphism group
It has been known for some time that for a large class of non-linear field
theories in Minkowski space with two-dimensional target space the complex
eikonal equation defines integrable submodels with infinitely many conservation
laws. These conservation laws are related to the area-preserving
diffeomorphisms on target space. Here we demonstrate that for all these
theories there exists, in fact, a weaker integrability condition which again
defines submodels with infinitely many conservation laws. These conservation
laws will be related to an abelian subgroup of the group of area-preserving
diffeomorphisms. As this weaker integrability condition is much easier to
fulfil, it should be useful in the study of those non-linear field theories.Comment: 13 pages, Latex fil
k-defects as compactons
We argue that topological compactons (solitons with compact support) may be
quite common objects if -fields, i.e., fields with nonstandard kinetic term,
are considered, by showing that even for models with well-behaved potentials
the unusual kinetic part may lead to a power-like approach to the vacuum, which
is a typical signal for the existence of compactons. The related approximate
scaling symmetry as well as the existence of self-similar solutions are also
discussed. As an example, we discuss domain walls in a potential Skyrme model
with an additional quartic term, which is just the standard quadratic term to
the power two. We show that in the critical case, when the quadratic term is
neglected, we get the so-called quartic model, and the corresponding
topological defect becomes a compacton. Similarly, the quartic sine-Gordon
compacton is also derived. Finally, we establish the existence of topological
half-compactons and study their properties.Comment: the stability proof of Section 4.4 corrected, some references adde
Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations
The solutions of a large class of hierarchies of zero-curvature equations
that includes Toda and KdV type hierarchies are investigated. All these
hierarchies are constructed from affine (twisted or untwisted) Kac-Moody
algebras~. Their common feature is that they have some special ``vacuum
solutions'' corresponding to Lax operators lying in some abelian (up to the
central term) subalgebra of~; in some interesting cases such subalgebras
are of the Heisenberg type. Using the dressing transformation method, the
solutions in the orbit of those vacuum solutions are constructed in a uniform
way. Then, the generalized tau-functions for those hierarchies are defined as
an alternative set of variables corresponding to certain matrix elements
evaluated in the integrable highest-weight representations of~. Such
definition of tau-functions applies for any level of the representation, and it
is independent of its realization (vertex operator or not). The particular
important cases of generalized mKdV and KdV hierarchies as well as the abelian
and non abelian affine Toda theories are discussed in detail.Comment: 27 pages, plain Te
Origin of transition metal clustering tendencies in GaAs based dilute magnetic semiconductors
While isovalent doping of GaAs (e.g. by In) leads to a repulsion between the
solute atoms, two Cr, Mn, or Fe atoms in GaAs are found to have lower energy
than the well-separated pair, and hence attract each other. The strong bonding
interaction between levels with t2 symmetry on the transition metal (TM) atoms
results in these atoms exhibiting a strong tendency to cluster. Using
first-principles calculations, we show that this attraction is maximal for Cr,
Mn and Fe while it is minimal for V. The difference is attributed to the
symmetry of the highest occupied levels. While the intention is to find
possible choices of spintronic materials that show a reduced tendency to
cluster, one finds that the conditions that minimize clustering tendencies also
minimize the stabilization of the magnetic state.Comment: To appear in Appl. Phys. Let
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