8,936 research outputs found
A class of quadratic deformations of Lie superalgebras
We study certain Z_2-graded, finite-dimensional polynomial algebras of degree
2 which are a special class of deformations of Lie superalgebras, which we call
quadratic Lie superalgebras. Starting from the formal definition, we discuss
the generalised Jacobi relations in the context of the Koszul property, and
give a proof of the PBW basis theorem. We give several concrete examples of
quadratic Lie superalgebras for low dimensional cases, and discuss aspects of
their structure constants for the `type I' class. We derive the equivalent of
the Kac module construction for typical and atypical modules, and a related
direct construction of irreducible modules due to Gould. We investigate in
detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie
superalgebra sl(n/1). We formulate the general atypicality conditions at level
1, and present an analysis of zero-and one-step atypical modules for a certain
family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie
superalgebras"; abstract re-worded; text clarified; 3 references added;
rearrangement of minor appendices into text; new subsection 4.
Simple model of self-organized biological evolution as completely integrable dissipative system
The Bak-Sneppen model of self-organized biological evolution of an infinite
ecosystem of randomly interacting species is represented in terms of an
infinite set of variables which can be considered as an analog to the set of
integrals of motion of completely integrable system. Each of this variables
remains to be constant but its influence on the evolution process is restricted
in time and after definite moment its value is excluded from description of the
system dynamics.Comment: LaTeX, 7 page
Observation of a resonant four-body interaction in cold cesium Rydberg atoms
Cold Rydberg atoms subject to long-range dipole-dipole interactions represent
a particularly interesting system for exploring few-body interactions and
probing the transition from 2-body physics to the many-body regime. In this
work we report the direct observation of a resonant 4-body Rydberg interaction.
We exploit the occurrence of an accidental quasi-coincidence of a 2-body and a
4-body resonant Stark-tuned Forster process in cesium to observe a resonant
energy transfer requiring the simultaneous interaction of at least four
neighboring atoms. These results are relevant for the implementation of quantum
gates with Rydberg atoms and for further studies of many-body physics.Comment: 5 pages, 5 figure
Long-range potentials and molecular resonances in an ultracold rydberg gas
We have calculated long-range molecular potentials of the ,
and symmetries between highly-excited rubidium atoms. Strong
potentials characterized by these symmetries are important in
describing interaction-induced phenomena in the excitation spectra of high
Rydberg states. Long-range molecular resonances are such phenomena and they
were first reported in S.M. Farooqi {\it et al.}, Phys. Rev. Lett. {\bf 91}
183002. One class of these resonances occurs at energies corresponding to
excited atom pairs . Such resonances are attributed to -mixing
due to Rydberg-Rydberg interactions so that otherwise forbidden molecular
transitions become allowed. We calculate molecular potentials in Hund's case
(c), use them to find the resonance lineshape and compare to experimental
results.Comment: 11 pages, 7 figure
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