29 research outputs found
Strings from position-dependent noncommutativity
We introduce a new set of noncommutative space-time commutation relations in
two space dimensions. The space-space commutation relations are deformations of
the standard flat noncommutative space-time relations taken here to have
position dependent structure constants. Some of the new variables are
non-Hermitian in the most natural choice. We construct their Hermitian
counterparts by means of a Dyson map, which also serves to introduce a new
metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps,
respected by these deformations. We compute minimal lengths and momenta arising
in this space from generalized versions of Heisenberg's uncertainty relations
and find that any object in this two dimensional space is string like,
i.e.having a fundamental length in one direction beyond which a resolution is
impossible. Subsequently we formulate and partly solve some simple models in
these new variables, the free particle, its PT-symmetric deformations and the
harmonic oscillator.Comment: 11 pages, Late
Observation of a red-blue detuning asymmetry in matter-wave superradiance
We report the first experimental observations of strong suppression of
matter-wave superradiance using blue-detuned pump light and demonstrate a
pump-laser detuning asymmetry in the collective atomic recoil motion. In
contrast to all previous theoretical frameworks, which predict that the process
should be symmetric with respect to the sign of the pump-laser detuning, we
find that for condensates the symmetry is broken. With high condensate
densities and red-detuned light, the familiar distinctive multi-order,
matter-wave scattering pattern is clearly visible, whereas with blue-detuned
light superradiance is strongly suppressed. In the limit of a dilute atomic
gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let
Three dimensional quadratic algebras: Some realizations and representations
Four classes of three dimensional quadratic algebras of the type \lsb Q_0 ,
Q_\pm \rsb , \lsb Q_+ , Q_- \rsb ,
where are constants or central elements of the algebra, are
constructed using a generalization of the well known two-mode bosonic
realizations of and . The resulting matrix representations and
single variable differential operator realizations are obtained. Some remarks
on the mathematical and physical relevance of such algebras are given.Comment: LaTeX2e, 23 pages, to appear in J. Phys. A: Math. Ge
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Quantum superintegrable systems in two dimensions are obtained from their
classical counterparts, the quantum integrals of motion being obtained from the
corresponding classical integrals by a symmetrization procedure. For each
quantum superintegrable systema deformed oscillator algebra, characterized by a
structure function specific for each system, is constructed, the generators of
the algebra being functions of the quantum integrals of motion. The energy
eigenvalues corresponding to a state with finite dimensional degeneracy can
then be obtained in an economical way from solving a system of two equations
satisfied by the structure function, the results being in agreement to the ones
obtained from the solution of the relevant Schrodinger equation. The method
shows how quantum algebraic techniques can simplify the study of quantum
superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn
PT-symmetric noncommutative spaces with minimal volume uncertainty relations
We provide a systematic procedure to relate a three dimensional q-deformed
oscillator algebra to the corresponding algebra satisfied by canonical
variables describing noncommutative spaces. The large number of possible free
parameters in these calculations is reduced to a manageable amount by imposing
various different versions of PT-symmetry on the underlying spaces, which are
dictated by the specific physical problem under consideration. The
representations for the corresponding operators are in general non-Hermitian
with regard to standard inner products and obey algebras whose uncertainty
relations lead to minimal length, areas or volumes in phase space. We analyze
in particular one three dimensional solution which may be decomposed to a two
dimensional noncommutative space plus one commuting space component and also
into a one dimensional noncommutative space plus two commuting space
components. We study some explicit models on these type of noncommutative
spaces.Comment: 18 page
On boson algebras as Hopf algebras
Certain types of generalized undeformed and deformed boson algebras which
admit a Hopf algebra structure are introduced, together with their Fock-type
representations and their corresponding -matrices. It is also shown that a
class of generalized Heisenberg algebras including those algebras including
those underlying physical models such as that of Calogero-Sutherland, is
isomorphic with one of the types of boson algebra proposed, and can be
formulated as a Hopf algebra.Comment: LaTex, 18 page
QUANTUM GROUPS AND LIE-ADMISSIBLE TIME EVOLUTION
The time evolution of operators for q-oscillators is derived for the first time by exploiting the connection between q-deformation algebras and Lie-admissible algebras
BOSE REALIZATION OF A NONCANONICAL HEISENBERG ALGEBRA
We find out the Bose realization of a generalized Heisenberg algebra, in which the bracket of the annihilation and creation operators is proportional to a polynomial function of the number operator. The eigenvalues of the corresponding oscillator are derived in a special case. We stress also the connection between non-canonical commutation relations and q-algebras