236 research outputs found
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Des equations de Dirac et de Schrodinger pour la transformation de Fourier
Dyson a associe aux determinants de Fredholm des noyaux de Dirichlet pairs
(resp. impairs) une equation de Schrodinger sur un demi-axe et a employe les
methodes du scattering inverse de Gel'fand-Levitan et de Marchenko, en tandem,
pour etudier l'asymptotique de ces determinants. Nous avons propose suite a
notre mise-au-jour de l'operateur conducteur de chercher a realiser la
transformation de Fourier elle-meme comme un scattering, et nous obtenons ici
dans ce but deux systemes de Dirac sur l'axe reel tout entier et qui sont
associes intrinsequement, respectivement, aux transformations en cosinus et en
sinus.
(Dyson has associated with the Fredholm determinants of the even (resp. odd)
Dirichlet kernels a Schrodinger equation on the half-axis and has used, in
tandem, the Gel'fand-Levitan and Marchenko methods of inverse scattering theory
to study the asymptotics of these determinants. We have proposed following our
unearthing of the conductor operator to seek to realize the Fourier transform
itself as a scattering, and we obtain here to this end two Dirac systems on the
entire real axis which are intrinsically associated, respectively, to the
cosine and to the sine transforms.)Comment: 8 pages, with a summary in English. One or two things adde
Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
The Hall--Post inequalities provide lower bounds on -body energies in
terms of -body energies with . They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillatorComment: 7 pages, Latex2e, 2 .eps figure
Velocity fluctuations in forced Burgers turbulence
We propose a simple method to compute the velocity difference statistics in
forced Burgers turbulence in any dimension. Within a reasonnable assumption
concerning the nucleation and coalescence of shocks, we find in particular that
the `left' tail of the distribution decays as an inverse square power, which is
compatible with numerical data. Our results are compared to those of various
recent approaches: instantons, operator product expansion, replicas.Comment: 10 pages latex, one postcript figur
New Lower Bound on Fermion Binding Energies
We derive a new lower bound for the ground state energy of N
fermions with total spin S in terms of binding energies of (N-1) fermions. Numerical examples are provided for some simple
short-range or confining potentials.Comment: 4 pages, 1 eps figur
Physics of accretion flows around compact objects
Several physical and astrophysical problems related to accretion onto black
holes and neutron stars are shortly reviewed. I discuss the observed
differences between these two types of compact objects in quiescent Soft X-ray
Transients. Then I review the status of various non-standard objects suggested
as an alternative to black-holes. Finally I present new results and suggestions
about the nature of the jet activity in Active Galactic Nuclei. {To cite this
article: J.-P. Lasota, C. R. Physique 6 (2006).}Comment: Submitted to Elsevier Scienc
Robust High-performance Dye-sensitized Solar Cells Based on Ionic Liquid-sulfolane Composite Electrolytes
Novel ionic liquid-sulfolane composite electrolytes based on the 1,2,3-triazolium family of ionic liquids were developed for dye-sensitized solar cells. The best performing device exhibited a short-circuit current density of 13.4 mA cm(-2), an open-circuit voltage of 713 mV and a fill factor of 0.65, corresponding to an overall power conversion efficiency (PCE) of 6.3%. In addition, these devices are highly stable, retaining more than 95% of the initial device PCE after 1000 hours of light-and heat-stress. These composite electrolytes show great promise for industrial application as they allow for a 14.5% improvement in PCE, compared to the solvent-free eutectic ionic liquid electrolyte system, without compromising device stability
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Implementation of U.K. Earth system models for CMIP6
We describe the scientific and technical implementation of two models for a core set of
experiments contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6).
The models used are the physical atmosphere-land-ocean-sea ice model HadGEM3-GC3.1 and the
Earth system model UKESM1 which adds a carbon-nitrogen cycle and atmospheric chemistry to
HadGEM3-GC3.1. The model results are constrained by the external boundary conditions (forcing data)
and initial conditions.We outline the scientific rationale and assumptions made in specifying these.
Notable details of the implementation include an ozone redistribution scheme for prescribed ozone
simulations (HadGEM3-GC3.1) to avoid inconsistencies with the model's thermal tropopause, and land use
change in dynamic vegetation simulations (UKESM1) whose influence will be subject to potential biases in
the simulation of background natural vegetation.We discuss the implications of these decisions for
interpretation of the simulation results. These simulations are expensive in terms of human and CPU
resources and will underpin many further experiments; we describe some of the technical steps taken to
ensure their scientific robustness and reproducibility
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
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