1,821 research outputs found
Monotonicity of quantum ground state energies: Bosonic atoms and stars
The N-dependence of the non-relativistic bosonic ground state energy is
studied for quantum N-body systems with either Coulomb or Newton interactions.
The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the
Newton systems are "bosonic stars". In either case there exists some third
order polynomial in N such that the ratio of the ground state energy to the
respective polynomial grows monotonically in N. Some applications of these new
monotonicity results are discussed
Improved lower bounds for the ground-state energy of many-body systems
New lower bounds for the binding energy of a quantum-mechanical system of
interacting particles are presented. The new bounds are expressed in terms of
two-particle quantities and improve the conventional bounds of the Hall-Post
type. They are constructed by considering not only the energy in the
two-particle system, but also the structure of the pair wave function. We apply
the formal results to various numerical examples, and show that in some cases
dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.
About the stability of the dodecatoplet
A new investigation is done of the possibility of binding the "dodecatoplet",
a system of six top quarks and six top antiquarks, using the Yukawa potential
mediated by Higgs exchange. A simple variational method gives a upper bound
close to that recently estimated in a mean-field calculation. It is
supplemented by a lower bound provided by identities among the Hamiltonians
describing the system and its subsystems.Comment: 5 pages, two figures merged, refs. added, typos correcte
Approximate Deadline-Scheduling with Precedence Constraints
We consider the classic problem of scheduling a set of n jobs
non-preemptively on a single machine. Each job j has non-negative processing
time, weight, and deadline, and a feasible schedule needs to be consistent with
chain-like precedence constraints. The goal is to compute a feasible schedule
that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan
[Annals of Disc. Math., 1977] in their seminal work introduced this problem and
showed that it is strongly NP-hard, even when all processing times and weights
are 1. We study the approximability of the problem and our main result is an
O(log k)-approximation algorithm for instances with k distinct job deadlines
On Convergence Properties of Shannon Entropy
Convergence properties of Shannon Entropy are studied. In the differential
setting, it is shown that weak convergence of probability measures, or
convergence in distribution, is not enough for convergence of the associated
differential entropies. A general result for the desired differential entropy
convergence is provided, taking into account both compactly and uncompactly
supported densities. Convergence of differential entropy is also characterized
in terms of the Kullback-Liebler discriminant for densities with fairly general
supports, and it is shown that convergence in variation of probability measures
guarantees such convergence under an appropriate boundedness condition on the
densities involved. Results for the discrete setting are also provided,
allowing for infinitely supported probability measures, by taking advantage of
the equivalence between weak convergence and convergence in variation in this
setting.Comment: Submitted to IEEE Transactions on Information Theor
Extended quantum conditional entropy and quantum uncertainty inequalities
Quantum states can be subjected to classical measurements, whose
incompatibility, or uncertainty, can be quantified by a comparison of certain
entropies. There is a long history of such entropy inequalities between
position and momentum. Recently these inequalities have been generalized to the
tensor product of several Hilbert spaces and we show here how their derivations
can be shortened to a few lines and how they can be generalized. All the
recently derived uncertainty relations utilize the strong subadditivity (SSA)
theorem; our contribution relies on directly utilizing the proof technique of
the original derivation of SSA.Comment: 4 page
Impact of career paths on MEPs’ activities
The increasing powers of the European Parliament in recent decades have made it a more attractive institution for ambitious politicians keen to build their political career in the EU's multi-level system. A key contribution to the debate about the career paths of MEPs is made by Scarrow (1997). Her work, which identified three different career paths taken by MEPs, has been widely cited and used as a basis for other studies on this topic. Building on Scarrow's work, this paper describes two additional categories of MEPs – former national politicians and ‘one-off’ MEPs – and links MEPs’ careers with their activities in Parliament. It finds that over and above the factors that have previously been identified as influential on an MEP's behaviour, his or her career path and ambitions are relevant in explaining certain legislative behaviour across Member States and party groups
Hadrons with Charm and Beauty
By combining potential models and QCD spectral sum rules (QSSR), we discuss
the spectroscopy of the mesons and of the , and
baryons ( or ), the decay constant and the
(semi)leptonic decay modes of the meson. For the masses, the best
predictions come from potential models and read: ~MeV,
~MeV, ~GeV,
~GeV, ~GeV
and ~GeV. The decay constant is well determined from QSSR and leads to:
s.The uses of the vertex sum rules for the semileptonic decays of the
show that the -dependence of the form factors is much stronger than
predicted by vector meson dominance. It also predicts the almost equal strength
of about 0.30 sec for the semileptonic rates into
and J/. Besides these phenomenological results, we
also show explicitly how the Wilson coefficients of the and gluon condensates already contain the full
heavy quark- () and mixed- ()
condensate contributions in the OPE.}Comment: 32 pages, LaTeX, no changes in the 1994 paper, latex errors corrected
in 201
- …