827 research outputs found
Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions
We study the baby Skyrme model as a theory that interpolates between two
distinct BPS systems. For this a near-BPS approximation can be used which,
however, involves a small deviation from each of the two BPS limits. We provide
analytical explanation and numerical support for the validity of this
approximation. We then study the set of all possible supersymmetric extensions
of the baby Skyrme model with and the particular ones with
extended supersymmetries and relate this to the above mentioned
almost-BPS approximation.Comment: 23 pages, 5 figures, v2: explanations adde
Mean field dynamics of superfluid-insulator phase transition in a gas of ultra cold atoms
A large scale dynamical simulation of the superfluid to Mott insulator
transition in the gas of ultra cold atoms placed in an optical lattice is
performed using the time dependent Gutzwiller mean field approach. This
approximate treatment allows us to take into account most of the details of the
recent experiment [Nature 415, 39 (2002)] where by changing the depth of the
lattice potential an adiabatic transition from a superfluid to a Mott insulator
state has been reported. Our simulations reveal a significant excitation of the
system with a transition to insulator in restricted regions of the trap.Comment: final version, correct Fig.7 (the published version contains wrong
fig.7 by mistake
Phase spaces related to standard classical -matrices
Fundamental representations of real simple Poisson Lie groups are Poisson
actions with a suitable choice of the Poisson structure on the underlying
(real) vector space. We study these (mostly quadratic) Poisson structures and
corresponding phase spaces (symplectic groupoids).Comment: 20 pages, LaTeX, no figure
Canonical surfaces associated with projectors in Grassmannian sigma models
We discuss the construction of higher-dimensional surfaces based on the harmonic maps of S2 into PN−1 and other Grassmannians. We show that there are two ways of implementing this procedure—both based on the use of the relevant projectors. We study various properties of such projectors and show that the Gaussian curvature of these surfaces, in general, is not constant. We look in detail at the surfaces corresponding to the Veronese sequence of such maps and show that for all of them this curvature is constant but its value depends on which mapping is used in the construction of the surface
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