179 research outputs found

### Dimensional Renormalization in phi^3 theory: ladders and rainbows

The sum of all ladder and rainbow diagrams in $\phi^3$ theory near 6
dimensions leads to self-consistent higher order differential equations in
coordinate space which are not particularly simple for arbitrary dimension D.
We have now succeeded in solving these equations, expressing the results in
terms of generalized hypergeometric functions; the expansion and representation
of these functions can then be used to prove the absence of renormalization
factors which are transcendental for this theory and this topology to all
orders in perturbation theory. The correct anomalous scaling dimensions of the
Green functions are also obtained in the six-dimensional limit.Comment: 11 pages, LaTeX, no figure

### On the evaluation formula for Jack polynomials with prescribed symmetry

The Jack polynomials with prescribed symmetry are obtained from the
nonsymmetric polynomials via the operations of symmetrization,
antisymmetrization and normalization. After dividing out the corresponding
antisymmetric polynomial of smallest degree, a symmetric polynomial results. Of
interest in applications is the value of the latter polynomial when all the
variables are set equal. Dunkl has obtained this evaluation, making use of a
certain skew symmetric operator. We introduce a simpler operator for this
purpose, thereby obtaining a new derivation of the evaluation formula. An
expansion formula of a certain product in terms of Jack polynomials with
prescribed symmetry implied by the evaluation formula is used to derive a
generalization of a constant term identity due to Macdonald, Kadell and Kaneko.
Although we don't give the details in this work, the operator introduced here
can be defined for any reduced crystallographic root system, and used to
provide an evaluation formula for the corresponding Heckman-Opdam polynomials
with prescribed symmetry.Comment: 18 page

### Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the
bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ
the Hopf duality arguments to provide the dually conjugate function algebra
Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a
closed form expression of the universal T matrix that caps the duality and
generalizes the familiar exponential map relating a Lie algebra with its
corresponding group. Subsequently, using an inverse Mellin transform approach,
the coherent states of single-node systems subject to the U_(h(1)) symmetry
are found to be complete with a positive-definite integration measure.
Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to
generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur

### Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and
continuous spectra of the hydrogen atom. These systems are expressed in
elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum)
and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group
$SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular
cases of the kernel of integral operator which interwines irreducible
representations of the $SO(4, 2)$ group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.

### Temporally stable coherent states in energy degenerate systems: The hydrogen atom

Klauder's recent generalization of the harmonic oscillator coherent states
[J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems,
requiring some additional structure if applied to systems with degeneracies.
The author suggests how this structure could be added, and applies the complete
method to the hydrogen atom problem. To illustrate how a certain degree of
freedom in the construction may be exercised, states are constructed which are
initially localized and evolve semi-classically, and whose long time evolution
exhibits "fractional revivals."Comment: 9 pages, 3 figure

### Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms

This paper begins with an examination of the revival structure and long-term
evolution of Rydberg wave packets for hydrogen. We show that after the initial
cycle of collapse and fractional/full revivals, which occurs on the time scale
$t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of
the new revivals is different from that of the fractional revivals. The new
revivals are characterized by periodicities in the motion of the wave packet
with periods that are fractions of the revival time scale $t_{\rm rev}$. These
long-term periodicities result in the autocorrelation function at times greater
than $t_{\rm rev}$ having a self-similar resemblance to its structure for times
less than $t_{\rm rev}$. The new sequence of revivals culminates with the
formation of a single wave packet that more closely resembles the initial wave
packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival
forms. Explicit examples of the superrevival structure for both circular and
radial wave packets are given. We then study wave packets in alkali-metal
atoms, which are typically used in experiments. The behavior of these packets
is affected by the presence of quantum defects that modify the hydrogenic
revival time scales and periodicities. Their behavior can be treated
analytically using supersymmetry-based quantum-defect theory. We illustrate our
results for alkali-metal atoms with explicit examples of the revival structure
for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199

### Radial Squeezed States and Rydberg Wave Packets

We outline an analytical framework for the treatment of radial Rydberg wave
packets produced by short laser pulses in the absence of external electric and
magnetic fields. Wave packets of this type are localized in the radial
coordinates and have p-state angular distributions. We argue that they can be
described by a particular analytical class of squeezed states, called radial
squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of
the corresponding hydrogenic radial squeezed states. They are found to undergo
decoherence and collapse, followed by fractional and full revivals. We also
present their uncertainty product and uncertainty ratio as functions of time.
Our results show that hydrogenic radial squeezed states provide a suitable
analytical description of hydrogenic Rydberg atoms excited by short-pulsed
laser fields.Comment: published in Physical Review

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