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

Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime

We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions Delta(q)=Delta(1-q), recently conjectured for critical models where an analogue of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.Comment: 12 pages, 12 figure

Existence of a Density Functional for an Intrinsic State

A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.Comment: 6 page

Random matrix ensembles associated with Lax matrices

A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics

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

Open problems in nuclear density functional theory

This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.Comment: 10 page

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

TEMPORAL PAYMENT ISSUES IN CONTINGENT VALUATION ANALYSIS

We analyze agent response to disparate payment schedules for protection of critical habitat units for the Seller sea lion in Alaska. The model allows for identification of implicit and explicit discount rates using information from a system of maximum likelihood equations. Testing is done using data for one, five, and fifteen year payment treatments.Research Methods/ Statistical Methods,

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