1,319 research outputs found
Keplerian Squeezed States and Rydberg Wave Packets
We construct minimum-uncertainty solutions of the three-dimensional
Schr\"odinger equation with a Coulomb potential. These wave packets are
localized in radial and angular coordinates and are squeezed states in three
dimensions. They move on elliptical keplerian trajectories and are appropriate
for the description of the corresponding Rydberg wave packets, the production
of which is the focus of current experimental effort. We extend our analysis to
incorporate the effects of quantum defects in alkali-metal atoms, which are
used in experiments.Comment: accepted for publication in Physical Review
Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect
The quantum Hall effect is necessarily accompanied by low-energy excitations
localized at the edge of a two-dimensional electron system. For the case of
electrons interacting via the long-range Coulomb interaction, these excitations
are edge magnetoplasmons. We address the time evolution of localized
edge-magnetoplasmon wave packets. On short times the wave packets move along
the edge with classical E cross B drift. We show that on longer times the wave
packets can have properties similar to those of the Rydberg wave packets that
are produced in atoms using short-pulsed lasers. In particular, we show that
edge-magnetoplasmon wave packets can exhibit periodic revivals in which a
dispersed wave packet reassembles into a localized one. We propose the study of
edge-magnetoplasmon wave packets as a tool to investigate dynamical properties
of integer and fractional quantum-Hall edges. Various scenarios are discussed
for preparing the initial wave packet and for detecting it at a later time. We
comment on the importance of magnetoplasmon-phonon coupling and on quantum and
thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was
originally 3Mbyte and had to be bitmapped for submission to archive; in the
process it acquired distracting artifacts, to upload the better version, see
http://physics.indiana.edu/~uli/publ/projects.htm
Fluctuation Superconductivity in Mesoscopic Aluminum Rings
Fluctuations are important near phase transitions, where they can be
difficult to describe quantitatively. Superconductivity in mesoscopic rings is
particularly intriguing because the critical temperature is an oscillatory
function of magnetic field. There is an exact theory for thermal fluctuations
in one-dimensional superconducting rings, which are therefore expected to be an
excellent model system. We measure the susceptibility of many rings, one ring
at a time, using a scanning SQUID that can isolate magnetic signals from seven
orders of magnitude larger background applied flux. We find that the
fluctuation theory describes the results and that a single parameter
characterizes the ways in which the fluctuations are especially important at
magnetic fields where the critical temperature is suppressed.Comment: Reprinted with permission from AAA
Elliptical Squeezed States and Rydberg Wave Packets
We present a theoretical construction for closest-to-classical wave packets
localized in both angular and radial coordinates and moving on a keplerian
orbit. The method produces a family of elliptical squeezed states for the
planar Coulomb problem that minimize appropriate uncertainty relations in
radial and angular coordinates. The time evolution of these states is studied
for orbits with different semimajor axes and eccentricities. The elliptical
squeezed states may be useful for a description of the motion of Rydberg wave
packets excited by short-pulsed lasers in the presence of external fields,
which experiments are attempting to produce. We outline an extension of the
method to include certain effects of quantum defects appearing in the
alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199
Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values
Uncertainty relations between a bounded coordinate operator and a conjugate
momentum operator frequently appear in quantum mechanics. We prove that
physically reasonable minimum-uncertainty solutions to such relations have
quantized expectation values of the conjugate momentum. This implies, for
example, that the mean angular momentum is quantized for any
minimum-uncertainty state obtained from any uncertainty relation involving the
angular-momentum operator and a conjugate coordinate. Experiments specifically
seeking to create minimum-uncertainty states localized in angular coordinates
therefore must produce packets with integer angular momentum.Comment: accepted for publication in Physical Review
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
, 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 . These
long-term periodicities result in the autocorrelation function at times greater
than having a self-similar resemblance to its structure for times
less than . 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 , 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
Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z
The motion of circular WP for one electron in central Coulomb field with high
Z is calculated. The WP is defined in terms of solutions of the Dirac equation
in order to take into account all possible relevant effects in particular the
spin-orbit potential. A time scale is defined within which spin dynamics must
be taken into account mainly in the atoms with high Z. Within this time scale
there exists a mechanism of collapses and revivals of the spin already shown by
the authors for harmonic oscillator potential and called the 'spin-orbit
pendulum'. However this effect has not the exact periodicity of the simpler
model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title
changed, one reference adde
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