Aspects of the decoherence in high spin environments: Breakdown of the mean-field approximation

The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-$\frac{1}{2}$ particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg $XY$ and Ising interactions. It is shown that while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg $XY$ interactions. In the case of a transverse Ising model, we find that the mean field approximation breaks down for high values of the spin.Comment: Preprint; 27 pages, 8 figure

On the partial trace over collective spin-degrees of freedom

We derive analytical properties for the degeneracy $\nu(N,j)$ occurring in the decomposition $\bigoplus\limits_{j}^\frac{N}{2}\nu(N,j)\mathbb C^{2j+1}$ of the state space $\mathbb C^{2\otimes N}$. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.Comment: 14 pages, 6 figures, minor typographical errors fixe

Consequences of Symmetries on the Analysis and Construction of Turbulence Models

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A nontrivial bosonic representation of large spin systems at high temperatures

We report on a nontrivial bosonization scheme for spin operators. It is shown that in the large $N$ limit, at infinite temperature, the operators $\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$ behave like the creation and annihilation operators, $a^\dag$ and $a$, corresponding to a harmonic oscillator in thermal equilibrium, whose temperature and frequency are related by $\hbar\omega/k_B T=\ln 3$. The $z$ component is found to be equivalent to the position variable of another harmonic oscillator occupying its ground Gaussian state at zero temperature. The obtained results are applied to the Heisenberg XY Hamiltonian at finite temperature.Comment: 12 pages, preprint, we have included a brief discussion of the antiferromagnetic cas

À propos de l'arrêt de la CIJ relatif aux exceptions préliminaires de l'incident aérien de Lockerbie (Note)

En dehors des développements récents de « l'affaire de Lockerbie », la Cour internationale de Justice (CIJ), dans son arrêt du 28.02.1998 relatif aux exceptions préliminaires, s'est prononcée sur sa propre compétence et sur la recevabilité de la requête libyenne. La problématique globale de ce travail va au-delà de l'analyse des questions juridiques, évoquées lors de l'instruction de cette affaire, pour soulever la finalité du jugement de la Cour. La démarche multidisciplinaire (philosophique, juridique et politique) permet, d'une part, de recadrer le contexte du différend entre le demandeur (la Libye) et les défendeurs des États-Unis et le Royaume-Uni) et relate, d'autre part, l'une des fonctions de la CIJ à savoir l'application du droit et la contribution au maintien de la paix et de la sécurité internationales. Derrière ce procès et cet arrêt, s'esquisse la détermination de la Cour à évincer l'utilisation de la force ou de la violence dans la solution dudit différend. Plus encore, l'arrêt rendu par la CIJ consiste à neutraliser l'éventualité d'un recours à « la justice vengeance » par les défendeurs.Apart from the development in « Lockerbie affair », the International Court of Justice (ICJ), by the decision taken on the 28th of February 1998, relating to the preliminary exceptions, has revealed its competence and come down in favour of libyan request. The global problematic of this work goes beyond the analysis of the legal questions, called up during the pretrial investigation of this affair, to bring up the aim of the Court judgement. The multidisciplinary procedure (philosophic, legal and politic) allows, on one hand, to tally the context of the disagreement between the plaintiff (Libya) and the defendants (USA, and GB) and record, on the other hand, one of the functions of the International Court of Justice in enforcing the law and contributing in the upholding of peace and international security. Behind this lawsuit and decision, one can feel the determination of the Court to evict the use of force and violence in the resolution of the stated disagreement. More yet, the decision pronounced by the ICJ neutralizes the eventuality to resort to « the justice of vengeance » by the defendants