2,817 research outputs found
Bayesian Inverse Quantum Theory
A Bayesian approach is developed to determine quantum mechanical potentials
from empirical data. Bayesian methods, combining empirical measurements and "a
priori" information, provide flexible tools for such empirical learning
problems. The paper presents the basic theory, concentrating in particular on
measurements of particle coordinates in quantum mechanical systems at finite
temperature. The computational feasibility of the approach is demonstrated by
numerical case studies. Finally, it is shown how the approach can be
generalized to such many-body and few-body systems for which a mean field
description is appropriate. This is done by means of a Bayesian inverse
Hartree-Fock approximation.Comment: LaTex, 32 pages, 19 figure
Bayesian Reconstruction of Approximately Periodic Potentials at Finite Temperature
The paper discusses the reconstruction of potentials for quantum systems at
finite temperatures from observational data. A nonparametric approach is
developed, based on the framework of Bayesian statistics, to solve such inverse
problems. Besides the specific model of quantum statistics giving the
probability of observational data, a Bayesian approach is essentially based on
"a priori" information available for the potential. Different possibilities to
implement "a priori" information are discussed in detail, including
hyperparameters, hyperfields, and non--Gaussian auxiliary fields. Special
emphasis is put on the reconstruction of potentials with approximate
periodicity. The feasibility of the approach is demonstrated for a numerical
model.Comment: 18 pages, 17 figures, LaTe
Mean Field Methods for Atomic and Nuclear Reactions: The Link between Time--Dependent and Time--Independent Approaches
Three variants of mean field methods for atomic and nuclear reactions are
compared with respect to both conception and applicability: The time--dependent
Hartree--Fock method solves the equation of motion for a Hermitian density
operator as initial value problem, with the colliding fragments in a continuum
state of relative motion. With no specification of the final state, the method
is restricted to inclusive reactions. The time--dependent mean field method, as
developed by Kerman, Levit and Negele as well as by Reinhardt, calculates the
density for specific transitions and thus applies to exclusive reactions. It
uses the Hubbard--Stratonovich transformation to express the full
time--development operator with two--body interactions as functional integral
over one--body densities. In stationary phase approximation and with Slater
determinants as initial and final states, it defines non--Hermitian,
time--dependent mean field equations to be solved self--consistently as
boundary value problem in time. The time--independent mean field method of
Giraud and Nagarajan is based on a Schwinger--type variational principle for
the resolvent. It leads to a set of inhomogeneous, non--Hermitian equations of
Hartree--Fock type to be solved for given total energy. All information about
initial and final channels is contained in the inhomogeneities, hence the
method is designed for exclusive reactions. A direct link is established
between the time--dependent and time--independent versions. Their relation is
non--trivial due to the non--linear nature of mean field methods.Comment: 21 pages, to be published in European Physical Journal
Singularities in cascade models of the Euler equation
The formation of singularities in the three-dimensional Euler equation is
investigated. This is done by restricting the number of Fourier modes to a set
which allows only for local interactions in wave number space. Starting from an
initial large-scale energy distribution, the energy rushes towards smaller
scales, forming a universal front independent of initial conditions. The front
results in a singularity of the vorticity in finite time, and has scaling form
as function of the time difference from the singularity. Using a simplified
model, we compute the values of the exponents and the shape of the front
analytically. The results are in good agreement with numerical simulations.Comment: 33 pages (REVTeX) including eps-figures, Stylefile here.st
On the chemical equilibration of strangeness-exchange reaction in heavy-ion collisions
The strangeness-exchange reaction pi + Y -> K- + N is shown to be the
dynamical origin of chemical equilibration for K- production in heavy-ion
collisions up to beam energies of 10 A GeV. The hyperons occurring in this
process are produced associately with K+ in baryon-baryon and meson-baryon
interactions. This connection is demonstrated by the ratio K-/K+ which does not
vary with centrality and shows a linear correlation with the yield of pions per
participant. At incident energies above AGS this correlation no longer holds
due to the change in the production mechanism of kaons.Comment: 9 pages, 4 figure
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