1,175,498 research outputs found
Berezin transform on the quantum unit ball
We introduce and study, in the framework of a theory of quantum Cartan
domains, a q-analogue of the Berezin transform on the unit ball. We construct
q-analogues of weighted Bergman spaces, Toeplitz operators and covariant symbol
calculus. In studying the analytical properties of the Berezin transform we
introduce also the q-analogue of the SU(n,1)-invariant Laplace operator (the
Laplace-Beltrami operator) and present related results on harmonic analysis on
the quantum ball. These are applied to obtain an analogue of one result by
A.Unterberger and H.Upmeier. An explicit asymptotic formula expressing the
q-Berezin transform via the q-Laplace-Beltrami operator is also derived. At the
end of the paper, we give an application of our results to basic hypergeometric
q-orthogonal polynomials.Comment: 38 pages, accepted by Journal of Mathematical Physic
Excited Heavy Quarkonium Production at the LHC through -Boson Decays
Sizable amount of heavy-quarkonium events can be produced through -boson
decays at the LHC. Such channels will provide a suitable platform to study the
heavy-quarkonium properties. The "improved trace technology", which disposes
the amplitude at the amplitude-level, is helpful for deriving
compact analytical results for complex processes. As an important new
application, in addition to the production of the lower-level Fock states
and , we make a further study on the
production of higher-excited -quarkonium Fock states
, and . Here
stands for the -charmonium,
-quarkonium and -bottomonium respectively. We show
that sizable amount of events for those higher-excited states can also be
produced at the LHC. Therefore, we need to take them into consideration for a
sound estimation.Comment: 7 pages, 9 figures and 6 tables. Typo errors are corrected, more
discussions and two new figures have been adde
Unified pictures of Q-balls and Q-tubes
While Q-balls have been investigated intensively for many years, another type
of nontopological solutions, Q-tubes, have not been understood very well. In
this paper we make a comparative study of Q-balls and Q-tubes. First, we
investigate their equilibrium solutions for four types of potentials. We find,
for example, that in some models the charge-energy relation is similar between
Q-balls and Q-tubes while in other models the relation is quite different
between them. To understand what determines the charge-energy relation, which
is a key of stability of the equilibrium solutions, we establish an analytical
method to obtain the two limit values of the energy and the charge. Our
prescription indicates how the existent domain of solutions and their stability
depends on their shape as well as potentials, which would also be useful for a
future study of Q-objects in higher-dimensional spacetime.Comment: 11 pages, 14 figure
Q-stars in 2+1 dimensions
We study q-stars with one or two scalar fields, non-abelian, and
fermion-scalar q-stars in 2+1 dimensions in an anti de Sitter or flat
spacetime. We fully investigate their properties, such as mass, particle
number, radius, numerically, and focus on the matter of their stability against
decay to free particles and gravitational collapse. We also provide analytical
solutions in the case of flat spacetime and other special cases.Comment: 37 pg, to appear in Nucl. Phys.
Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson
The high density Frenkel exciton which interacts with a single mode
microcavity field is dealed with in the framework of the q-deformed boson. It
is shown that the q-defomation of bosonic commutation relations is satisfied
naturally by the exciton operators when the low density limit is deviated. An
analytical expression of the physical spectrum for the exciton is given by
using of the dressed states of the cavity field and the exciton. We also give
the numerical study and compare the theoretical results with the experimental
resultsComment: 6 pages, 2 figure
QCD Corrections to Flavor Changing Neutral Coupling Mediated Rare Top Quark Decays
Recently we have presented an analysis of flavor changing neutral coupling
mediated radiative top quark decays at next-to-leading order in QCD. In the
present paper we provide the details of the calculation of QCD corrections to
t-> q gamma and t-> q Z decays within the effective theory approach including
operator mixing. In particular, we calculate virtual matrix element corrections
and the corresponding bremsstrahlung contributions. In the case of t-> q gamma
we study the effects of kinematic cuts on the extracted branching ratios.
Analytical formulae are given at all stages of the calculation. We find that
the t-> q gamma decay can be used to probe also the effective operators
mediating t-> q g processes, since these can naturally contribute 10% or more
to the radiative decay, given typical experimental cuts on the decay kinematics
at hadron colliders. Conversely, we argue that any positive experimental signal
of the t-> q g process would indicate a natural lower bound on t-> q gamma
decay rate.Comment: 12 page
Competitive random sequential adsorption of point and fixed-sized particles: analytical results
We study the kinetics of competitive random sequential adsorption (RSA) of
particles of binary mixture of points and fixed-sized particles within the
mean-field approach. The present work is a generalization of the random car
parking problem in the sense that it considers the case when either a car of
fixed size is parked with probability q or the parking space is partitioned
into two smaller spaces with probability (1-q) at each time event. This allows
an interesting interplay between the classical RSA problem at one extreme
(q=1), and the kinetics of fragmentation processes at the other extreme (q=0).
We present exact analytical results for coverage for a whole range of q values,
and physical explanations are given for different aspects of the problem. In
addition, a comprehensive account of the scaling theory, emphasizing on
dimensional analysis, is presented, and the exact expression for the scaling
function and exponents are obtained.Comment: 7 pages, latex, 3 figure
Exercises in exact quantization
The formalism of exact 1D quantization is reviewed in detail and applied to
the spectral study of three concrete Schr\"odinger Hamiltonians [-\d^2/\d q^2
+ V(q)]^\pm on the half-line , with a Dirichlet (-) or Neumann (+)
condition at q=0. Emphasis is put on the analytical investigation of the
spectral determinants and spectral zeta functions with respect to singular
perturbation parameters. We first discuss the homogeneous potential
as vs its (solvable) limit (an infinite square well):
useful distinctions are established between regular and singular behaviours of
spectral quantities; various identities among the square-well spectral
functions are unraveled as limits of finite-N properties. The second model is
the quartic anharmonic oscillator: its zero-energy spectral determinants
\det(-\d^2/\d q^2 + q^4 + v q^2)^\pm are explicitly analyzed in detail,
revealing many special values, algebraic identities between Taylor
coefficients, and functional equations of a quartic type coupled to asymptotic
properties of Airy type. The third study addresses the
potentials of even degree: their zero-energy spectral
determinants prove computable in closed form, and the generalized eigenvalue
problems with v as spectral variable admit exact quantization formulae which
are perfect extensions of the harmonic oscillator case (corresponding to N=2);
these results probably reflect the presence of supersymmetric potentials in the
family above.Comment: latex txt.tex, 2 files, 34 pages [SPhT-T00/078]; v2: corrections and
updates as indicated by footnote
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