Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states

We consider a quantum dot in the regime of the quantum Hall effect, particularly in Laughlin states and non-Abelian Read-Rezayi states. We find the location of the Coulomb blockade peaks in the conductance as a function of the area of the dot and the magnetic field. When the magnetic field is fixed and the area of the dot is varied, the peaks are equally spaced for the Laughlin states. In contrast, non-Abelian statistics is reflected in modulations of the spacing which depend on the magnetic field.     

Reliable Solution of Bidiagonal Systems with Applications

We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.     

Deterministic Percolation

This paper examines percolation questions in a deterministic setting. In particular, I consider , the set of elements of Z ² with greatest common divisor equal to 1, where two sites are connected if they are at distance 1. The main result of the paper proves that the infinite component has an asymptotic density. An “almost everywhere” sieve of J. Friedlander is used to obtain the result. Received: 1 November 1998 / Accepted: 1 April 1999     

Tetrazole Diversification of Amino Acids and Peptides via Silver-Catalyzed Intermolecular Cycloaddition with Aryldiazonium Salts

Selective structural modification of amino acids and peptides is a central strategy in organic chemistry, chemical biology but also in pharmacology and material science. In this context, the formation of tetrazole rings, known to possess significant therapeutic properties, would expand the chemical space of unnatural amino acids but has received less attention. In this study, we demonstrated that the classic unimolecular Wolff rearrangement of α-amino acid-derived diazoketones could be replaced by a faster intermolecular cycloaddition reaction with aryldiazonium salts under identical practical conditions. This strategy provides an efficient synthetic platform that could transform proteinogenic α-amino acids into a plethora of unprecedented tetrazole-decorated amino acid derivatives with preservation of the stereocenters. Density functional theory studies shed some light on the reaction mechanism and provided information regarding the origins of the chemo- and regioselectivity. Furthermore, this diazo-cycloaddition protocol was applied to construct tetrazole-modified peptidomimetics and drug-like amino acid derivatives.     

Selective Terminal Functionalization of Linear Alkanes**

A two-step sequential strategy involving a biocatalytic dehydrogenation/remote hydrofunctionalization, as a unified and versatile approach to selectively convert linear alkanes into a large array of valuable functionalized aliphatic derivatives is reported. The dehydrogenation is carried out by a mutant strain of a bacteria Rhodococcus and the produced alkenes are subsequently engaged in a remote functionalization through a metal-catalyzed hydrometalation/migration sequence that subsequently react with a large variety of electrophiles. The judicious implementation of this combined biocatalytic and organometallic approach enabled us to develop a high-yielding protocol to site-selectively functionalize unreactive primary C−H bonds.