710 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
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
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
Degrees of Freedom of the Quark Gluon Plasma, tested by Heavy Mesons
Heavy quarks (charm and bottoms) are one of the few probes which are
sensitive to the degrees of freedom of a Quark Gluon Plasma (QGP), which cannot
be revealed by lattice gauge calculations in equilibrium. Due to the rapid
expansion of the QGP energetic heavy quarks do not come to an equilibrium with
the QGP. Their energy loss during the propagation through the QGP medium
depends strongly on the modelling of the interaction of the heavy quarks with
the QGP quarks and gluons, i.e. on the assuption of the degrees of freedom of
the plasma. Here we compare the results of different models, the pQCD based
Monte-Carlo (MC@sHQ), the Dynamical Quasi Particle Model (DQPM) and the
effective mass approach, for the drag force in a thermalized QGP and discuss
the sensitivity of heavy quark energy loss on the properties of the QGP as well
as on non-equilibrium dynamicsComment: proceedings symposion "New Horizons" Makutsi, South Africa, Nov 201
Barnett-Pegg formalism of angle operators, revivals, and flux lines
We use the Barnett-Pegg formalism of angle operators to study a rotating
particle with and without a flux line. Requiring a finite dimensional version
of the Wigner function to be well defined we find a natural time quantization
that leads to classical maps from which the arithmetical basis of quantum
revivals is seen. The flux line, that fundamentally alters the quantum
statistics, forces this time quantum to be increased by a factor of a winding
number and determines the homotopy class of the path. The value of the flux is
restricted to the rational numbers, a feature that persists in the infinite
dimensional limit.Comment: 5 pages, 0 figures, Revte
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
Test of CPT and Lorentz invariance from muonium spectroscopy
Following a suggestion of Kostelecky et al. we have evaluated a test of CPT
and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian
terms beyond the standard model violating CPT and Lorentz invariance would
contribute frequency shifts and to
and , the two transitions involving muon spin flip, which were
precisely measured in ground state muonium in a strong magnetic field of 1.7 T.
The shifts would be indicated by anti-correlated oscillations in and
at the earth's sidereal frequency. No time dependence was found in
or at the level of 20 Hz, limiting the size of some CPT
and Lorentz violating parameters at the level of GeV,
representing Planck scale sensitivity and an order of magnitude improvement in
sensitivity over previous limits for the muon.Comment: 4 pages, 4 figures, uses REVTeX and epsf, submitted to Phys. Rev.
Let
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
Three Questions on Lorentz Violation
We review the basics of the two most widely used approaches to Lorentz
violation - the Stardard Model Extension and Noncommutative Field Theory - and
discuss in some detail the example of the modified spectrum of the synchrotron
radiation. Motivated by touching upon such a fundamental issue as Lorentz
symmetry, we ask three questions: What is behind the search for Lorentz
violation? Is String Theory a physical theory? Is there an alternative to
Supersymmetry?Comment: 16 pages; invited luecture at DICE2006 - Piombino, Italy - September
200
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