1,470 research outputs found
Extended phase space for a spinning particle
Extended phase space of an elementary (relativistic) system is introduced in
the spirit of the Souriau's definition of the `space of motions' for such
system. Our formulation is generally applicable to any homogeneous space-time
(e.g. de Sitter) and also to Poisson actions. Calculations concerning the
Minkowski case for non-zero spin particles show an intriguing alternative: we
should either accept two-dimensional trajectories or (Poisson) noncommuting
space-time coordinates.Comment: 12 pages, late
Free motion on the Poisson SU(n) group
SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the
symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the
free motion on SU(N) and solve the corresponding equations of motion. Velocity
is related to the momentum by a non-linear Legendre transformation.Comment: LaTeX, 10 page
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
Many body population trapping in ultracold dipolar gases
A system of interacting dipoles is of paramount importance for understanding
of many-body physics. The interaction between dipoles is {\it anisotropic} and
{\it long-range}. While the former allows to observe rich effects due to
different geometries of the system, long-range () interactions lead to
strong correlations between dipoles and frustration. In effect, interacting
dipoles in a lattice form a paradigmatic system with strong correlations and
exotic properties with possible applications in quantum information
technologies, and as quantum simulators of condensed matter physics, material
science, etc. Notably, such a system is extremely difficult to model due to a
proliferation of interaction induced multi-band excitations for sufficiently
strong dipole-dipole interactions. In this article we develop a consistent
theoretical model of interacting polar molecules in a lattice by applying the
concepts and ideas of ionization theory which allows us to include highly
excited Bloch bands. Additionally, by involving concepts from quantum optics
(population trapping), we show that one can induce frustration and engineer
exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a
system.Comment: many interesting page
Two component Bose-Hubbard model with higher angular momentum states
We study a Bose-Hubbard Hamiltonian of ultracold two component gas of spinor
Chromium atoms. Dipolar interactions of magnetic moments while tuned resonantly
by ultralow magnetic field can lead to spin flipping. Due to approximate axial
symmetry of individual lattice site, total angular momentum is conserved.
Therefore, all changes of the spin are accompanied by the appearance of the
angular orbital momentum. This way excited Wannier states with non vanishing
angular orbital momentum can be created. Resonant dipolar coupling of the two
component Bose gas introduces additional degree of control of the system, and
leads to a variety of different stable phases. The phase diagram for small
number of particles is discussed.Comment: 4 pages, 2 figure
Low Energy States in the SU(N) Skyrme Models
We show that any solution of the SU(2) Skyrme model can be used to give a
topologically trivial solution of the SU(4) one. In addition, we extend the
method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1)
to construct low energy configurations of the SU(N) Skyrme models. We show that
one of such maps gives an exact, topologically trivial, solution of the SU(3)
model. We study various properties of these maps and show that, in general,
their energies are only marginally higher than the energies of the
corresponding SU(2) embeddings. Moreover, we show that the baryon (and energy)
densities of the SU(3) configurations with baryon number B=2-4 are more
symmetrical than their SU(2) analogues. We also present the baryon densities
for the B=5 and B=6 configurations and discuss their symmetries.Comment: latex : 25 pages, 9 Postscript figures, uses eps
A discrete phi^4 system without Peierls-Nabarro barrier
A discrete phi^4 system is proposed which preserves the topological lower
bound on the kink energy. Existence of static kink solutions saturating this
lower bound and occupying any position relative to the lattice is proved.
Consequently, kinks of the model experience no Peierls-Nabarro barrier, and can
move freely through the lattice without being pinned. Numerical simulations
reveal that kink dynamics in this system is significantly less dissipative than
that of the conventional discrete phi^4 system, so that even on extremely
coarse lattices the kink behaves much like its continuum counterpart. It is
argued, therefore, that this is a natural discretization for the purpose of
numerically studying soliton dynamics in the continuum phi^4 model.Comment: 8 pages, LaTeX, 8 postscript figure
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