2,749 research outputs found
Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra
The ladder operator formalism of a general quantum state for su(1,1) Lie
algebra is obtained. The state bears the generally deformed oscillator
algebraic structure. It is found that the Perelomov's coherent state is a
su(1,1) nonlinear coherent state. The expansion and the exponential form of the
nonlinear coherent state are given. We obtain the matrix elements of the
su(1,1) displacement operator in terms of the hypergeometric functions and the
expansions of the displaced number states and Laguerre polynomial states are
followed. Finally some interesting su(1,1) optical systems are discussed.Comment: 16 pages, no figures, accepted by Int. J. Mod. Phy.
Semileptonic decays of meson to S-wave charmonium states in the perturbative QCD approach
Inspired by the recent measurement of the ratio of branching fractions
to and final states at the LHCb
detector, we study the semileptonic decays of meson to the S-wave ground
and radially excited 2S and 3S charmonium states with the perturbative QCD
approach. After evaluating the form factors for the transitions , where and denote pseudoscalar and vector S-wave charmonia,
respectively, we calculate the branching ratios for all these semileptonic
decays. The theoretical uncertainty of hadronic input parameters are reduced by
utilizing the light-cone wave function for meson. It is found that the
predicted branching ratios range from up to and could be
measured by the future LHCb experiment. Our prediction for the ratio of
branching fractions is in good
agreement with the data. For decays, the relative
contributions of the longitudinal and transverse polarization are discussed in
different momentum transfer squared regions. These predictions will be tested
on the ongoing and forthcoming experiments.Comment: 12 pages, 3 figures, 5 table
Entangled SU(2) and SU(1,1) coherent states
Entangled SU(2) and SU(1,1) coherent states are developed as superpositions
of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are
coherent states with respect to generalized su(2) and su(1,1) generators, and
multiparticle parity states arise as a special case. As a special example of
entangled SU(2) coherent states, entangled binomial states are introduced and
these entangled binomial states enable the contraction from entangled SU(2)
coherent states to entangled harmonic oscillator coherent states. Entangled
SU(2) coherent states are discussed in the context of pairs of qubits. We also
introduce the entangled negative binomial states and entangled squeezed states
as examples of entangled SU(1,1) coherent states. A method for generating the
entangled SU(2) and SU(1,1) coherent states is discussed and degrees of
entanglement calculated. Two types of SU(1,1) coherent states are discussed in
each case: Perelomov coherent states and Barut-Girardello coherent states.Comment: 31 pages, no figure
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