627 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
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
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
Superrevivals in the quantum dynamics of a particle confined in a finite square well potential
We examine the revival features in wave packet dynamics of a particle
confined in a finite square well potential. The possibility of tunneling
modifies the revival pattern as compared to an infinite square well potential.
We study the dependence of the revival times on the depth of the square well
and predict the existence of superrevivals. The nature of these superrevivals
is compared with similar features seen in the dynamics of wavepackets in an
anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in
Physical Review
Comments on Non-Commutative Phenomenology
It is natural to ask whether non-commutative geometry plays a role in four
dimensional physics. By performing explicit computations in various toy models,
we show that quantum effects lead to violations of Lorentz invariance at the
level of operators of dimension three or four. The resulting constraints are
very stringent.Comment: Correction of an error in the U(1) and U(N) calculation leads to
stronger limits than those given previously Clarifying comments and reference
adde
Dynamic Nuclear Polarization in Double Quantum Dots
We theoretically investigate the controlled dynamic polarization of lattice
nuclear spins in GaAs double quantum dots containing two electrons. Three
regimes of long-term dynamics are identified, including the build up of a large
difference in the Overhauser fields across the dots, the saturation of the
nuclear polarization process associated with formation of so-called "dark
states," and the elimination of the difference field. We show that in the case
of unequal dots, build up of difference fields generally accompanies the
nuclear polarization process, whereas for nearly identical dots, build up of
difference fields competes with polarization saturation in dark states. The
elimination of the difference field does not, in general, correspond to a
stable steady state of the polarization process.Comment: 4 pages, 2 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
, 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
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
Nambu-Goldstone Modes in Gravitational Theories with Spontaneous Lorentz Breaking
Spontaneous breaking of Lorentz symmetry has been suggested as a possible
mechanism that might occur in the context of a fundamental Planck-scale theory,
such as string theory or a quantum theory of gravity. However, if Lorentz
symmetry is spontaneously broken, two sets of questions immediately arise: what
is the fate of the Nambu-Goldstone modes, and can a Higgs mechanism occur? A
brief summary of some recent work looking at these questions is presented here.Comment: 6 pages. Presented at the meeting "From Quantum to Cosmos,"
Washington, D.C., May 2006; published in Int. J. Mod. Phys. D16:2357-2363,
200
Threshold Corrections and Gauge Symmetry in Twisted Superstring Models
Threshold corrections to the running of gauge couplings are calculated for
superstring models with free complex world sheet fermions. For two N=1
models, the threshold corrections lead to a small increase
in the unification scale. Examples are given to illustrate how a given particle
spectrum can be described by models with different boundary conditions on the
internal fermions. We also discuss how complex twisted fermions can enhance the
symmetry group of an N=4 model to the gauge group
. It is then shown how a mixing angle analogous
to the Weinberg angle depends on the boundary conditions of the internal
fermions.Comment: easier to Tex version, figures to be sent separatel
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