1,565 research outputs found
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking
We develop a uniform semiclassical trace formula for the density of states of
a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term
. This term breaks the U(3) symmetry of the HO, resulting in a
spherical system with SO(3) symmetry. We first treat the anharmonic term in
semiclassical perturbation theory by integration of the action of the perturbed
periodic HO orbits over the manifold P which characterizes
their 4-fold degeneracy. Then we obtain an analytical uniform trace formula
which in the limit of strong perturbations (or high energy) asymptotically goes
over into the correct trace formula of the full anharmonic system with SO(3)
symmetry, and in the limit (or energy) restores the HO trace
formula with U(3) symmetry. We demonstrate that the gross-shell structure of
this anharmonically perturbed system is dominated by the two-fold degenerate
diameter and circular orbits, and {\it not} by the orbits with the largest
classical degeneracy, which are the three-fold degenerate tori with rational
ratios of radial and angular frequencies. The same
holds also for the limit of a purely quartic spherical potential .Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be
published in J. Phys. A (without appendices C and D
Comment on ``Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation''
This is a comment on the work of Kolomeisky et al., Phys. Rev. Lett. 85, 1146
(2000). We point out that they are using the wrong form of the energy
functional for one-dimensional fermions. We point out two possible forms of the
energy functional, both of which can be derived from first principles but using
different methods. One is obtained from the collective field theory method,
while the other is derived from the extended Thomas-Fermi method. These two
forms of the energy functional do not support the soliton solutions which are
obtained by Kolomeisky et al.Comment: Revtex, 2 page
Semiclassical description of shell effects in finite fermion systems
A short survey of the semiclassical periodic orbit theory, initiated by M.
Gutzwiller and generalized by many other authors, is given. Via so-called
semiclassical trace formmulae, gross-shell effects in bound fermion systems can
be interpreted in terms of a few periodic orbits of the corresponding classical
systems. In integrable systems, these are usually the shortest members of the
most degenerate families or orbits, but in some systems also less degenerate
orbits can determine the gross-shell structure. Applications to nuclei, metal
clusters, semiconductor nanostructures, and trapped dilute atom gases are
discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite
Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200
Optical response of two-dimensional electron fluids beyond the Kohn regime: strong non-parabolic confinement and intense laser light
We investigate the linear and non-linear optical response of two-dimensional
(2D) interacting electron fluids confined by a strong non-parabolic potential.
We show that such fluids may exhibit higher-harmonic spectra under realistic
experimental conditions. Higher harmonics arise as the electrons explore
anharmonicities of the confinement potential (electron-electron interactions
reduce this non-linear effect). This opens the possibility of controlling the
optical functionality of such systems by engineering the confinement potential.
Our results were obtained within time-dependent density-functional theory,
employing the adiabatic local-density approximation. A classical hydrodynamical
model is in good agreement with the quantum-mechanical results.Comment: 4 pages, 4 figure
Semiclassical theory of spin-orbit interaction in the extended phase space
We consider the semiclassical theory in a joint phase space of spin and
orbital degrees of freedom. The method is developed from the path integrals
using the spin-coherent-state representation, and yields the trace formula for
the density of states. We discuss special cases, such as weak and strong
spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B;
minor corrections elsewher
Nuclear Scissors Mode with Pairing
The coupled dynamics of the scissors mode and the isovector giant quadrupole
resonance are studied using a generalized Wigner function moments method taking
into account pair correlations. Equations of motion for angular momentum,
quadrupole moment and other relevant collective variables are derived on the
basis of the time dependent Hartree-Fock-Bogoliubov equations. Analytical
expressions for energy centroids and transitions probabilities are found for
the harmonic oscillator model with the quadrupole-quadrupole residual
interaction and monopole pairing force. Deformation dependences of energies and
values are correctly reproduced. The inclusion of pair correlations
leads to a drastic improvement in the description of qualitative and
quantitative characteristics of the scissors mode.Comment: 36 pages, 5 figures, the results of calculation by another method and
the section concerning currents are adde
Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism
We obtain the band edge eigenfunctions and the eigenvalues of solvable
periodic potentials using the quantum Hamilton - Jacobi formalism. The
potentials studied here are the Lam{\'e} and the associated Lam{\'e} which
belong to the class of elliptic potentials. The formalism requires an
assumption about the singularity structure of the quantum momentum function
, which satisfies the Riccati type quantum Hamilton - Jacobi equation, in the complex plane. Essential
use is made of suitable conformal transformations, which leads to the
eigenvalues and the eigenfunctions corresponding to the band edges in a simple
and straightforward manner. Our study reveals interesting features about the
singularity structure of , responsible in yielding the band edge
eigenfunctions and eigenvalues.Comment: 21 pages, 5 table
Transport through open quantum dots: making semiclassics quantitative
We investigate electron transport through clean open quantum dots (quantum
billiards). We present a semiclassical theory that allows to accurately
reproduce quantum transport calculations. Quantitative agreement is reached for
individual energy and magnetic field dependent elements of the scattering
matrix. Two key ingredients are essential: (i) inclusion of pseudo-paths which
have the topology of linked classical paths resulting from diffraction in
addition to classical paths and (ii) a high-level approximation to diffractive
scattering. Within this framework of the pseudo-path semiclassical
approximation (PSCA), typical shortcomings of semiclassical theories such as
violation of the anti-correlation between reflection and transmission and the
overestimation of conductance fluctuations are overcome. Beyond its predictive
capabilities the PSCA provides deeper insights into the quantum-to-classical
crossover.Comment: 20 pages, 19 figure
Palomar adaptive optics project: status and performance
We describe the current performance of the Palomar 200 inch (5 m) adaptive optics system, which in December of 1998 achieved its first high order (241 actuators) lock on a natural guide star. In the K band (2.2 micrometer), the system has achieved Strehl ratios as high as 50% in the presence of 1.0 arcsecond seeing (0.5 micrometer). Predictions of the system's performance based on the analysis of real-time wavefront sensor telemetry data and an analysis based on a fitted Kolmogorov atmospheric model are shown to both agree with the observed science image performance. Performance predictions for various seeing conditions are presented and an analysis of the error budget is used to show which subsystems limit the performance of the AO system under various atmospheric conditions
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