4,883 research outputs found
The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
We have observed the production of strings (disclination lines and loops) via
the Kibble mechanism of domain (bubble) formation in the isotropic to nematic
phase transition of a sample of uniaxial nematic liquid crystal. The probablity
of string formation per bubble is measured to be . This is in
good agreement with the theoretical value expected in two dimensions
for the order parameter space of a simple uniaxial nematic
liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request
Consequences of Zeeman Degeneracy for van der Waals Blockade between Rydberg Atoms
We analyze the effects of Zeeman degeneracies on the long-range interactions
between like Rydberg atoms, with particular emphasis on applications to quantum
information processing using van der Waals blockade. We present a general
analysis of how degeneracies affect the primary error sources in blockade
experiments, emphasizing that blockade errors are sensitive primarily to the
weakest possible atom-atom interactions between the degenerate states, not the
mean interaction strength. We present explicit calculations of the van der
Waals potentials in the limit where the fine-structure interaction is large
compared to the atom-atom interactions. The results are presented for all
potential angular momentum channels invoving s, p, and d states. For most
channels there are one or more combinations of Zeeman levels that have
extremely small dipole-dipole interactions and are therefore poor candidates
for effective blockade experiments. Channels with promising properties are
identified and discussed. We also present numerical calculations of Rb and Cs
dipole matrix elements and relevant energy levels using quantum defect theory,
allowing for convenient quantitative estimates of the van der Waals
interactions to be made for principal quantum numbers up to 100. Finally, we
combine the blockade and van der Waals results to quantitatively analyze the
angular distribution of the blockade shift and its consequence for angular
momentum channels and geometries of particular interest for blockade
experiments with Rb.Comment: 16 figure
Loop Groups and Discrete KdV Equations
A study is presented of fully discretized lattice equations associated with
the KdV hierarchy. Loop group methods give a systematic way of constructing
discretizations of the equations in the hierarchy. The lattice KdV system of
Nijhoff et al. arises from the lowest order discretization of the trivial,
lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are
also given, the lowest order discretization of the first nontrivial equation in
the hierarchy, and a "second order" discretization of b_t=b_x. The former,
which is given the name "full lattice KdV" has the (potential) KdV equation as
a standard continuum limit. For each discretization a Backlund transformation
is given and soliton content analyzed. The full lattice KdV system has, like
KdV itself, solitons of all speeds, whereas both other discretizations studied
have a limited range of speeds, being discretizations of an equation with
solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur
The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
The usual quantitative condition has been widely used in the practical
applications of the adiabatic theorem. However, it had never been proved to be
sufficient or necessary before. It was only recently found that the
quantitative condition is insufficient, but whether it is necessary remains
unresolved. In this letter, we prove that the quantitative condition is
necessary in guaranteeing the validity of the adiabatic approximation.Comment: 4 pages,1 figue
Hydrogen production by photoelectrolytic decomposition of H2O using solar energy
Photoelectrochemical systems for the efficient decomposition of water are discussed. Semiconducting d band oxides which would yield the combination of stability, low electron affinity, and moderate band gap essential for an efficient photoanode are sought. The materials PdO and Fe-xRhxO3 appear most likely. Oxygen evolution yields may also be improved by mediation of high energy oxidizing agents, such as CO3(-). Examination of several p type semiconductors as photocathodes revealed remarkable stability for p-GaAs, and also indicated p-CdTe as a stable H2 photoelectrode. Several potentially economical schemes for photoelectrochemical decomposition of water were examined, including photoelectrochemical diodes and two stage, four photon processes
Evolution of a localized electron spin in a nuclear spin environment
Motivated by recent interest in the role of the hyperfine interaction in
quantum dots we study the dynamics of a localized electron spin coupled to many
nuclei. An important feature of the model is that the coupling to an individual
nuclear spin depends on its position in the quantum dot. We introduce a
semi-classical description of the system valid in the limit of a large number
of nuclei and analyze the resulting classical dynamics. Contrary to a natural
assumption, the correlation functions of electron spin with an arbitrary
initial condition show no decay in time. Rather, they exhibit complicated
undamped oscillations. This may be attributed to the fact that the system has
many integrals of motion and is close to an integrable one. The ensemble
averaged correlation functions do exhibit a slow decay (1/ln(t)) for t ->
\infty.Comment: 11 pages, 11 figures, revtex4 styl
Atom cooling by non-adiabatic expansion
Motivated by the recent discovery that a reflecting wall moving with a
square-root in time trajectory behaves as a universal stopper of classical
particles regardless of their initial velocities, we compare linear in time and
square-root in time expansions of a box to achieve efficient atom cooling. For
the quantum single-atom wavefunctions studied the square-root in time expansion
presents important advantages: asymptotically it leads to zero average energy
whereas any linear in time (constant box-wall velocity) expansion leaves a
non-zero residual energy, except in the limit of an infinitely slow expansion.
For finite final times and box lengths we set a number of bounds and cooling
principles which again confirm the superior performance of the square-root in
time expansion, even more clearly for increasing excitation of the initial
state. Breakdown of adiabaticity is generally fatal for cooling with the linear
expansion but not so with the square-root expansion.Comment: 4 pages, 4 figure
The Universal Gaussian in Soliton Tails
We show that in a large class of equations, solitons formed from generic
initial conditions do not have infinitely long exponential tails, but are
truncated by a region of Gaussian decay. This phenomenon makes it possible to
treat solitons as localized, individual objects. For the case of the KdV
equation, we show how the Gaussian decay emerges in the inverse scattering
formalism.Comment: 4 pages, 2 figures, revtex with eps
Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations
We study the effects of Kondo correlations on the transmission phase shift of
a quantum dot coupled to two leads in comparison with the experimental
determinations made by Aharonov-Bohm (AB) quantum interferometry. We propose
here a theoretical interpretation of these results based on scattering theory
combined with Bethe ansatz calculations. We show that there is a factor of 2
difference between the phase of the S-matrix responsible for the shift in the
AB oscillations, and the one controlling the conductance. Quantitative
agreement is obtained with experimental results for two different values of the
coupling to the leads.Comment: 4 pages, 4 figures, accepted for publication in Physical Review
Letter
Locality and topology in the molecular Aharonov-Bohm effect
It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor
topological in the sense of the standard magnetic Aharonov-Bohm effect. It is
further argued that there is a close relationship between the molecular
Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral
spin particle encircling a line of charge.Comment: 3 pages, no figure
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