3,916 research outputs found
Versatile Digital GHz Phase Lock for External Cavity Diode Lasers
We present a versatile, inexpensive and simple optical phase lock for
applications in atomic physics experiments. Thanks to all-digital phase
detection and implementation of beat frequency pre-scaling, the apparatus
requires no microwave-range reference input, and permits phase locking at
frequency differences ranging from sub-MHz to 7 GHz (and with minor extension,
to 12 GHz). The locking range thus covers ground state hyperfine splittings of
all alkali metals, which makes this system a universal tool for many
experiments on coherent interaction between light and atoms.Comment: 4.5 pages, 5 figures v3: fixed error in schematic: R10 connects to
other end of C
Exact Maps in Density Functional Theory for Lattice Models
In the present work, we employ exact diagonalization for model systems on a
real-space lattice to explicitly construct the exact density-to-potential and
for the first time the exact density-to-wavefunction map that underly the
Hohenberg-Kohn theorem in density functional theory. Having the explicit
wavefunction-to- density map at hand, we are able to construct arbitrary
observables as functionals of the ground-state density. We analyze the
density-to-potential map as the distance between the fragments of a system
increases and the correlation in the system grows. We observe a feature that
gradually develops in the density-to-potential map as well as in the
density-to-wavefunction map. This feature is inherited by arbitrary expectation
values as functional of the ground-state density. We explicitly show the
excited-state energies, the excited-state densities, and the correlation
entropy as functionals of the ground-state density. All of them show this exact
feature that sharpens as the coupling of the fragments decreases and the
correlation grows. We denominate this feature as intra-system steepening. We
show that for fully decoupled subsystems the intra-system steepening transforms
into the well-known inter-system derivative discontinuity. An important
conclusion is that for e.g. charge transfer processes between localized
fragments within the same system it is not the usual inter-system derivative
discontinuity that is missing in common ground-state functionals, but rather
the differentiable intra-system steepening that we illustrate in the present
work
Photons as quasi-charged particles
The Schrodinger motion of a charged quantum particle in an electromagnetic
potential can be simulated by the paraxial dynamics of photons propagating
through a spatially inhomogeneous medium. The inhomogeneity induces geometric
effects that generate an artificial vector potential to which signal photons
are coupled. This phenomenon can be implemented with slow light propagating
through an a gas of double-Lambda atoms in an electromagnetically-induced
transparency setting with spatially varied control fields. It can lead to a
reduced dispersion of signal photons and a topological phase shift of
Aharonov-Bohm type
A new proof that alternating links are non-trivial
We use a simple geometric argument and small cancellation properties of link
groups to prove that alternating links are non-trivial. This proof uses only
classic results in topology and combinatorial group theory.Comment: Minor changes. To appear in Fundamenta Mathematica
The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
We address and quantify the role of non-adiabaticity ("memory effects") in
the exchange-correlation (xc) functional of time-dependent density functional
theory (TDDFT) for describing non-linear dynamics of many-body systems.
Time-dependent resonant processes are particularly challenging for available
TDDFT approximations, due to their strong non-linear and non-adiabatic
character. None of the known approximate density functionals are able to cope
with this class of problems in a satisfactory manner. In this work we look at
the prototypical example of the resonant processes by considering Rabi
oscillations within the exactly soluble 2-site Hubbard model. We construct the
exact adiabatic xc functional and show that (i) it does not reproduce correctly
resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to
the exact xc potential, which turns out to be small only at the beginning and
at the end of the Rabi cycle when the ground state population is dominant. We
then propose a "two-level" approximation for the time-dependent xc potential
which can capture Rabi dynamics in the 2-site problem. It works well both for
resonant and for detuned Rabi oscillations and becomes essentially exact in the
linear response regime. This new, fully non-adiabatic and explicit density
functional constitutes one of the main results of the present work.Comment: 8 pages, 5 figure
A Prolonged Slump for ‘Plaintiff-Pitchers’: The Narrow ‘Strike Zone’ for Securities Plaintiffs in the Fourth Circuit
This article focuses on the narrow “strike zone” that plaintiffs must overcome in private securities actions instituted in the Fourth Circuit. Based on empirical data generated over a fourteen-year span, there emerges a clear finding that during that time period defendants were victorious in almost all cases, either on the merits of the case or due to procedural obstacles. The authors posit that this pattern of difficulty for plaintiffs arises, at least in part, from the Fourth Circuit’s restrictive interpretation of various requisite elements of these causes of action, such as materiality and scienter, as well as the Fourth Circuit’s approach to the pleading standards mandated by the PSLRA and the Federal Rules of Civil Procedure. The authors examine in detail some of the leading securities cases that establish Fourth Circuit precedent in these areas, as well as notable cases from the survey period, to illustrate the confines of the narrow “strike zone” available to plaintiffs to establish a meritorious claim
Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker
Since the proof of the four color theorem in 1976, computer-generated proofs
have become a reality in mathematics and computer science. During the last
decade, we have seen formal proofs using verified proof assistants being used
to verify the validity of such proofs.
In this paper, we describe a formalized theory of size-optimal sorting
networks. From this formalization we extract a certified checker that
successfully verifies computer-generated proofs of optimality on up to 8
inputs. The checker relies on an untrusted oracle to shortcut the search for
witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c
Coloring random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters and where the
proliferation of metastable states is responsible for the onset of complexity
in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR
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