Nuclear shape-phase diagrams

Ground-state energy functions of even-even and odd-A nuclei are derived from simple parameter-dependent Interacting Boson Model (IBM) and Interacting Boson-Fermion Model (IBFM) Hamiltonians. Exact nuclear shape-phase diagrams in the two-parameter (eta, chi) plane are explicitly described using the energy functions on the basis of the condition of phase equilibrium.

A tight binding model for water

We demonstrate for the first time a tight binding model for water incorporating polarizable oxygen atoms. A novel aspect is that we adopt a ``ground up'' approach in that properties of the monomer and dimer only are fitted. Subsequently we make predictions of the structure and properties of hexamer clusters, ice-XI and liquid water. A particular feature, missing in current tight binding and semiempirical hamiltonians, is that we reproduce the almost two-fold increase in molecular dipole moment as clusters are built up towards the limit of bulk liquid. We concentrate on properties of liquid water, particularly dielectric constant and self diffusion coefficient, which are very well rendered in comparison with experiment. Finally we comment on the question of the contrasting densities of water and ice which is central to an understanding of the subtleties of the hydrogen bond.

Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch. An open source version of the code can be found at: http://www.dmrg.it.

Implementation and testing of Lanczos-based algorithms for Random-Phase Approximation eigenproblems

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like time-dependent density functional theory or Bethe-Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian Hamiltonian counterparts, computational methods for the treatment of non-Hermitian Hamiltonians are often less efficient and less stable, sometimes leading to the breakdown of the method. Recently [Gruning et al. Nano Lett. 8 (2009) 28201, we have identified that such Hamiltonians are usually pseudo-Hermitian. Exploiting this property, we have implemented an algorithm of the Lanczos type for Random-Phase Approximation Hamiltonians that benefits from the same stability and computational load as its Hermitian counterpart, and applied it to the study of the optical response of carbon nanotubes. We present here the related theoretical grounds and technical details, and study the performance of the algorithm for the calculation of the optical absorption of a molecule within the Bethe-Salpeter equation framework. (C) 2011 Elsevier B.V. All rights reserved.

Gapped Two-Body Hamiltonian for Continuous-Variable Quantum Computation

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law. © 2011 American Physical Society.

Nonlocality of two- and three-mode continuous variable systems

We address the nonlocality of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing nonlocality are considered, in which the dichotomic Bell operator is represented by the displaced parity and by the pseudospin operator respectively. Three-mode states are also considered as a conditional source of two-mode non-Gaussian states, whose nonlocality properties are analysed. We found that the non-Gaussian character of the conditional states allows violation of Bell's inequalities (by parity and pseudospin tests) stronger than with a conventional twin-beam state. However, the non-Gaussian character is not sufficient to reveal nonlocality through a dichotomized quadrature measurement strategy.

Ferroelectric Vortices and Related Configurations

This chapter discusses that the theoretical studies, using both atomistic and phenomenological approaches, have made clear predictions about the existence and behaviour of ferroelectric (FE) vortices. Effective Hamiltonians can be implemented within both Monte Carlo (MC) and molecular dynamics (MD) simulations. In contrast to the effective Hamiltonian method, which is atomistic in nature, the phase field method employs a continuum approach, in which the polarization field is the order parameter. Properties of FE nanostructures are largely governed by the existence of a depolarization field, which is much stronger than the demagnetization field in magnetic nanosystems. The topological patterns seen in rare earth manganites are often referred to as vortices and yet this claim never seems to be explicitly justified. By inspection, the form of a vortex structure is such that there is a continuous rotation in the orientation of dipole vectors around the singularity at the centre of the vortex.

Monte Carlo studies of phase transitions and adsorption : application to n-6 Lennard-Jones, C60 and zeolite systems

The solid-fluid transition properties of the n - 6 Lennard-Jones system are studied by means of extensive free energy calculations. Different values of the parameter n which regulates the steepness of the short-range repulsive interaction are investigated. Furthermore, the free energies of the n < 12 systems are calculated using the n = 12 system as a reference. The method relies on a generalization of the multiple histogram method that combines independent canonical ensemble simulations performed with different Hamiltonians and computes the free energy difference between them. The phase behavior of the fullerene C60 solid is studied by performing NPT simulations using atomistic models which treat each carbon in the molecule as a separate interaction site with additional bond charges. In particular, the transition from an orientationally frozen phase at low temperatures to one where the molecules are freely rotating at higher temperatures is studied as a function of applied pressure. The adsorption of molecular hydrogen in the zeolite NaA is investigated by means of grand-canonical Monte Carlo, in a wide range of temperatures and imposed gas pressures, and results are compared with available experimental data. A potential model is used that comprises three main interactions: van der Waals, Coulomb and induced polarization by the permanent electric field in the zeolite.

Les systèmes super intégrables d’ordre trois séparables en coordonnées paraboliques

Ce mémoire est une poursuite de l’étude de la superintégrabilité classique et quantique dans un espace euclidien de dimension deux avec une intégrale du mouvement d’ordre trois. Il est constitué d’un article. Puisque les classifications de tous les Hamiltoniens séparables en coordonnées cartésiennes et polaires sont déjà complétées, nous apportons à ce tableau l’étude de ces systèmes séparables en coordonnées paraboliques. Premièrement, nous dérivons les équations déterminantes d’un système en coordonnées paraboliques et ensuite nous résolvons les équations obtenues afin de trouver les intégrales d’ordre trois pour un potentiel qui permet la séparation en coordonnées paraboliques. Finalement, nous démontrons que toutes les intégrales d’ordre trois pour les potentiels séparables en coordonnées paraboliques dans l’espace euclidien de dimension deux sont réductibles. Dans la conclusion de l’article nous analysons les différences entre les potentiels séparables en coordonnées cartésiennes et polaires d’un côté et en coordonnées paraboliques d’une autre côté. Mots clés: intégrabilité, superintégrabilité, mécanique classique, mécanique quantique, Hamiltonien, séparation de variable, commutation.

Le problème de Coulomb-Dunkl dans le plan

Ce mémoire, composé d'un article en collaboration avec Monsieur Luc Vinet et Vincent X. Genest, est la suite du travail effectué sur les systèmes quantiques super-intégrables définis par des Hamiltoniens de type Dunkl. Plus particulièrement, ce mémoire vise l'analyse du problème de Coulomb-Dunkl dans le plan qui est une généralisation du système quantique de l'atome d'hydrogène impliquant des opérateurs de réflexion sur les variables x et y. Le modèle est défini par un potentiel en 1/r. Nous avons tout d'abord remarqué que l'Hamiltonien est séparable en coordonnées polaires et que les fonctions d'onde s'écrivent en termes de produits de polynômes de Laguerre généralisés et des harmoniques de Dunkl sur le cercle. L'algèbre générée par les opérateurs de symétrie nous a également permis de confirmer le caractère maximalement super-intégrable du problème de Coulomb-Dunkl. Nous avons aussi pu écrire explicitement les représentations de cette même algèbre. Nous avons finalement trouvé le spectre de l'énergie de manière algébrique.

Ground-state self-consistent calculation of quantum dots under magnetic fields: Addition spectrum

A density-functional self-consistent calculation of the ground-state electronic density of quantum dots under an arbitrary magnetic field is performed. We consider a parabolic lateral confining potential. The addition energy, E(N+1)-E(N), where N is the number of electrons, is compared with experimental data and the different contributions to the energy are analyzed. The Hamiltonian is modeled by a density functional, which includes the exchange and correlation interactions and the local formation of Landau levels for different equilibrium spin populations. We obtain an analytical expression for the critical density under which spontaneous polarization, induced by the exchange interaction, takes place.

Ab initio theoretical comparative study of magnetic coupling in KNiF3 and K2NiF4s

The origin of magnetic coupling in KNiF3 and K2 NiF4 is studied by means of an ab initio cluster model approach. By a detailed study of the mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians it is possible to obtain the magnetic coupling constant J and to compare ab initio cluster-model values with those resulting from ab initio periodic Hartree-Fock calculations. This comparison shows that J is strongly determined by two-body interactions; this is a surprising and unexpected result. The importance of the ligands surrounding the basic metal-ligand-metal interacting unit is reexamined by using two different partitions and the constrained space orbital variation method of analysis. This decomposition enables us to show that this effect is basically environmental. Finally, dynamical electronic correlation effects have found to be critical in determining the final value of the magnetic coupling constant.

Absence of collective effects in Heisenberg systems with localized magnetic moments

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF3, K2NiF4, NiO, and La2CuO4. Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved.

Local character of magnetic coupling in ionic solids

Magnetic interactions in ionic solids are studied using parameter-free methods designed to provide accurate energy differences associated with quantum states defining the Heisenberg constant J. For a series of ionic solids including KNiF3, K2NiF4, KCuF3, K2CuF4, and high- Tc parent compound La2CuO4, the J experimental value is quantitatively reproduced. This result has fundamental implications because J values have been calculated from a finite cluster model whereas experiments refer to infinite solids. The present study permits us to firmly establish that in these wide-gap insulators, J is determined from strongly local electronic interactions involving two magnetic centers only thus providing an ab initio support to commonly used model Hamiltonians.