The quantum dynamics of atomic magnets, co-tunneling and dipolar-biased tunneling

Multi-spins tunneling cross-relaxations in an ensemble of weakly-coupled Ho$^{3+}$ 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 $z$ for a $N$-particle Hamiltonian $H$ and let $\chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater determinant $\phi$ of single particle states $\phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|\phi_i>=0.$ 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 $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ 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