8,576 research outputs found
The quantum dynamics of atomic magnets, co-tunneling and dipolar-biased tunneling
Multi-spins tunneling cross-relaxations in an ensemble of weakly-coupled
Ho ions, mediated by weak anisotropic dipolar interactions, can be
evidenced by ac-susceptibility measurements in a high temperature regime. Based
on a four-body representation, including the rare-earth nuclear spin, two-ions
tunneling mechanisms can be attributed to both dipolar-biased tunneling and
co-tunneling processes. The co-reversal involving entangled pairs of magnetic
moments is discussed with a particular emphasis, giving new evidences to
elucidate the many-body quantum dynamics.Comment: 4 figure
Elementary Derivative Tasks and Neural Net Multiscale Analysis of Tasks
Neural nets are known to be universal approximators. In particular, formal
neurons implementing wavelets have been shown to build nets able to approximate
any multidimensional task. Such very specialized formal neurons may be,
however, difficult to obtain biologically and/or industrially. In this paper we
relax the constraint of a strict ``Fourier analysis'' of tasks. Rather, we use
a finite number of more realistic formal neurons implementing elementary tasks
such as ``window'' or ``Mexican hat'' responses, with adjustable widths. This
is shown to provide a reasonably efficient, practical and robust,
multifrequency analysis. A training algorithm, optimizing the task with respect
to the widths of the responses, reveals two distinct training modes. The first
mode induces some of the formal neurons to become identical, hence promotes
``derivative tasks''. The other mode keeps the formal neurons distinct.Comment: latex neurondlt.tex, 7 files, 6 figures, 9 pages [SPhT-T01/064],
submitted to Phys. Rev.
Continuum Singularities of a Mean Field Theory of Collisions
Consider a complex energy for a -particle Hamiltonian and let
be any wave packet accounting for any channel flux. The time independent
mean field (TIMF) approximation of the inhomogeneous, linear equation
consists in replacing by a product or Slater
determinant of single particle states This results, under the
Schwinger variational principle, into self consistent TIMF equations
in single particle space. The method is a
generalization of the Hartree-Fock (HF) replacement of the -body homogeneous
linear equation by single particle HF diagonalizations
We show how, despite strong nonlinearities in this mean
field method, threshold singularities of the {\it inhomogeneous} TIMF equations
are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure
Antisymmetrization of a Mean Field Calculation of the T-Matrix
The usual definition of the prior(post) interaction between
projectile and target (resp. ejectile and residual target) being contradictory
with full antisymmetrization between nucleons, an explicit antisymmetrization
projector must be included in the definition of the transition
operator, We derive the
suitably antisymmetrized mean field equations leading to a non perturbative
estimate of . The theory is illustrated by a calculation of forward
- scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14
Existence of Density Functionals for Excited States and Resonances
We show how every bound state of a finite system of identical fermions,
whether a ground state or an excited one, defines a density functional.
Degeneracies created by a symmetry group can be trivially lifted by a
pseudo-Zeeman effect. When complex scaling can be used to regularize a
resonance into a square integrable state, a DF also exists.Comment: 4 pages, no figure
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
Fractal dimensions of eigenfunctions for various critical random matrix
ensembles are investigated in perturbation series in the regimes of strong and
weak multifractality. In both regimes we obtain expressions similar to those of
the critical banded random matrix ensemble extensively discussed in the
literature. For certain ensembles, the leading-order term for weak
multifractality can be calculated within standard perturbation theory. For
other models such a direct approach requires modifications which are briefly
discussed. Our analytical formulas are in good agreement with numerical
calculations.Comment: 28 pages, 7 figure
Phonon-assisted tunneling in the quantum regime of Mn12-ac
Longitudinal or transverse magnetic fields applied on a crystal of Mn12-ac
allows to observe independent tunnel transitions between m=-S+p and m=S-n-p
(n=6-10, p=0-2 in longitudinal field and n=p=0 in transverse field). We observe
a smooth transition (in longitudinal) from coherent ground-state to thermally
activated tunneling. Furthermore two ground-state relaxation regimes showing a
crossover between quantum spin relaxation far from equilibrium and near
equilibrium, when the environment destroys multimolecule correlations. Finally,
we stress that the complete Hamiltonian of Mn12 should contain odd spin
operators of low order
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