3,495 research outputs found
Conserving and gapless approximations for the composite bosons in terms of the constituent fermions
A long-standing problem with the many-body approximations for interacting
condensed bosons has been the dichotomy between the ``conserving'' and
``gapless'' approximations, which either obey the conservations laws or satisfy
the Hugenholtz-Pines condition for a gapless excitation spectrum, in the order.
It is here shown that such a dichotomy does not exist for a system of composite
bosons, which form as bound-fermion pairs in the strong-coupling limit of the
fermionic attraction. By starting from the constituent fermions, for which
conserving approximations can be constructed for any value of the mutual
attraction according to the Baym-Kadanoff prescriptions, it is shown that these
approximations also result in a gapless excitation spectrum for the boson-like
propagators in the broken-symmetry phase. This holds provided the corresponding
equations for the fermionic single- and two-particle Green's functions are
solved self-consistently.Comment: 4 pages, 1 figur
Identification of the Beutler-Fano formula in eigenphase shifts and eigentime delays near a resonance
Eigenphase shifts and eigentime delays near a resonance for a system of one
discrete state and two continua are shown to be functionals of the Beutler-
Fano formulas using appropriate dimensionless energy units and line profile
indices. Parameters responsible for the avoided crossing of eigenphase shifts
and eigentime delays are identified. Similarly, parameters responsible for the
eigentime delays due to a frame change are identified. With the help of new
parameters, an analogy with the spin model is pursued for the S matrix and time
delay matrix. The time delay matrix is shown to comprise three terms, one due
to resonance, one due to a avoided crossing interaction, and one due to a frame
change. It is found that the squared sum of time delays due to the avoided
crossing interaction and frame change is unity.Comment: 17 pages, 3 figures, RevTe
Numerical Studies of Fano Resonance in Quantum dots Embedded in AB Rings
The Fano resonance in quantum dots embedded in Aharonov-Bohm rings is
examined theoretically, using two models of non-interacting electrons. The
first model yields an analytical expression for the conductance G. G is written
in an extended Fano form with a complex parameter. The shape of the resonance
can be asymmetric or symmetric, depending on the magnetic flux enclosed in the
ring. The "phase" of the resonance is changed continuously with increasing the
flux in two-terminal situations. These are in accordance with recent
experimental results. In the second model, we consider the dephasing effect on
the Fano resonance by numerical calculations.Comment: 2 pages, 4 figures, to appear in J. Phys. Soc. Jpn., proceedings of
International Conference on Quantum Transport and Quantum Coherence
(Localisation 2002, Tokyo
Transverse excitations of ultracold matter waves upon propagation past abrupt waveguide changes
The propagation of ultracold atomic gases through abruptly changing waveguide
potentials is examined in the limit of non-interacting atoms. Time-independent
scattering calculations of microstructured waveguides with discontinuous
changes in the transverse harmonic binding potentials are used to mimic
waveguide perturbations and imperfections. Three basic configurations are
examined: step-like, barrier-like and well-like with waves incident in the
ground mode. At low energies, the spectra rapidly depart from single-moded,
with significant transmission and reflection of excited modes. The high-energy
limit sees 100 percent transmission, with the distribution of the transmitted
modes determined simply by the overlap of the mode wave functions and
interference.Comment: 20 pages, 7 figures, under review PR
Efficient and Effective Query Auto-Completion
Query Auto-Completion (QAC) is an ubiquitous feature of modern textual search
systems, suggesting possible ways of completing the query being typed by the
user. Efficiency is crucial to make the system have a real-time responsiveness
when operating in the million-scale search space. Prior work has extensively
advocated the use of a trie data structure for fast prefix-search operations in
compact space. However, searching by prefix has little discovery power in that
only completions that are prefixed by the query are returned. This may impact
negatively the effectiveness of the QAC system, with a consequent monetary loss
for real applications like Web Search Engines and eCommerce. In this work we
describe the implementation that empowers a new QAC system at eBay, and discuss
its efficiency/effectiveness in relation to other approaches at the
state-of-the-art. The solution is based on the combination of an inverted index
with succinct data structures, a much less explored direction in the
literature. This system is replacing the previous implementation based on
Apache SOLR that was not always able to meet the required
service-level-agreement.Comment: Published in SIGIR 202
Long range scattering resonances in strong-field seeking states of polar molecules
We present first steps toward understanding the ultracold scattering
properties of polar molecules in strong electric field-seeking states. We have
found that the elastic cross section displays a quasi-regular set of potential
resonances as a function of the electric field, which potentially offers
intimate details about the inter-molecular interaction. We illustrate these
resonances in a ``toy'' model composed of pure dipoles, and in more physically
realistic systems. To analyze these resonances, we use a simple WKB
approximation to the eigenphase, which proves both reasonably accurate and
meaningful. A general treatment of the Stark effect and dipolar interactions is
also presented
Precise Variational Calculation For The Doubly Excited State (2p^2)^3P^e of Helium
Highly precise variational calculations of non-relativistic energies of the
(2p^2)^3P^e state of Helium atom are presented.We get an upper bound energy
E=-0.71050015565678 a.u.,the lowest yet obtained.Comment: 5 pages, 1 tabl
Processing and Transmission of Information
Contains research objectives.Lincoln Laboratory, Purchase Order DDL B-00306U. S. ArmyU. S. NavyU. S. Air Force under Air Force Contract AFI 9(604)-520
Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
The Lorentz law of force is the fifth pillar of classical electrodynamics,
the other four being Maxwell's macroscopic equations. The Lorentz law is the
universal expression of the force exerted by electromagnetic fields on a volume
containing a distribution of electrical charges and currents. If electric and
magnetic dipoles also happen to be present in a material medium, they are
traditionally treated by expressing the corresponding polarization and
magnetization distributions in terms of bound-charge and bound-current
densities, which are subsequently added to free-charge and free-current
densities, respectively. In this way, Maxwell's macroscopic equations are
reduced to his microscopic equations, and the Lorentz law is expected to
provide a precise expression of the electromagnetic force density on material
bodies at all points in space and time. This paper presents incontrovertible
theoretical evidence of the incompatibility of the Lorentz law with the
fundamental tenets of special relativity. We argue that the Lorentz law must be
abandoned in favor of a more general expression of the electromagnetic force
density, such as the one discovered by A. Einstein and J. Laub in 1908. Not
only is the Einstein-Laub formula consistent with special relativity, it also
solves the long-standing problem of "hidden momentum" in classical
electrodynamics.Comment: 7 pages, 1 figur
Geometry and symmetries of multi-particle systems
The quantum dynamical evolution of atomic and molecular aggregates, from
their compact to their fragmented states, is parametrized by a single
collective radial parameter. Treating all the remaining particle coordinates in
d dimensions democratically, as a set of angles orthogonal to this collective
radius or by equivalent variables, bypasses all independent-particle
approximations. The invariance of the total kinetic energy under arbitrary
d-dimensional transformations which preserve the radial parameter gives rise to
novel quantum numbers and ladder operators interconnecting its eigenstates at
each value of the radial parameter.
We develop the systematics and technology of this approach, introducing the
relevant mathematics tutorially, by analogy to the familiar theory of angular
momentum in three dimensions. The angular basis functions so obtained are
treated in a manifestly coordinate-free manner, thus serving as a flexible
generalized basis for carrying out detailed studies of wavefunction evolution
in multi-particle systems.Comment: 37 pages, 2 eps figure
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