Stability of Local Quantum Dissipative Systems

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb–Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.     

Pd-catalysed regioselective C-H functionalisation of 2-pyrones

A new synthetic methodology for the catalytic C-H functionalisation of 2-pyrones is described which proceeds regioselectively at the C3 position, mirroring the observed regioselectivity in 6π-electrocyclisation/oxidative aromatisation reactions of related compounds. Insight into the reaction mechanism is provided, with support for a neutral palladium(II) pathway. Cationic palladium(II) complexes possessing 2-pyrones are unstable and readily undergo Pd(II)→P transfer at ambient temperature resulting in phosphonium salt formation (and Pd(0)L(n) species).     

Why does perfluorination render bicyclo[2.2.0]hex-1(4)-ene stable toward dimerization? Calculations provide the answers

B3LYP calculations with two different basis sets have been performed to understand why bicyclo[2.2.0]hex-1(4)-ene (1a) undergoes dimerization with DeltaH(++) = 11.5 kcal/mol, but dimerization of perfluorobicyclo[2.2.0]hex-1(4)-ene (1b) has never been observed. The former reaction is computed to be exothermic by 37.2 kcal/mol, whereas the latter is calculated to be endothermic by 7.4 kcal/mol. The 44.6 kcal/mol difference between the enthalpies of these two reactions can be dissected into contributions of 24.5 kcal/mol for the difference between the enthalpies for forming diradical intermediates 2a and 2b and 20.1 kcal/mol for cyclization of 2a and 2b to, respectively, 3a and 3b. The latter enthalpy difference is largely attributable to repulsions between the endo-fluorines in the dimer, although the exo-fluorines also are found to contribute. The former enthalpy difference is attributable to the difference between the dissociation enthalpies of the pi bonds in 1a and 1b, which is shown to amount to 16 +/- 1 kcal/mol. About 25% of the stronger pi bond in fluoroalkene 1b is found to be due to hyperconjugation of the eight C-F bonds in 1b with the filled pi orbital. However, the major contributor to the stronger pi bond in 1b is shown to be the unfavorable interaction that results when a pyramidalized radical center is syn to a C-F bond. Both of these effects, which contribute to the greater strength of the pi bond in 1b, relative to that in 1a, are analyzed and discussed.     

On free $${\mathbb{Z}_{p}}$$ actions on products of spheres

In this paper we consider free actions of large prime order cyclic groups on the product of any number of spheres of the same odd dimension and on products of two spheres of differing odd dimensions. We require only that the action be free on the product as a whole and not each sphere separately. In particular we determine equivariant homotopy type, and for both linear actions and for even numbers of spheres the simple homotopy type and simple structure sets. The results are compared to the analysis and classification done for lens spaces. Similar to lens spaces, the first k-invariant generally determines the homotopy type of many of the quotient spaces, however, the Reidemeister torsion frequently vanishes and many of the homotopy equivalent spaces are also simple homotopy equivalent. Unlike lens spaces, which are determined by their ρ-invariant and Reidemeister torsion, the ρ-invariant here vanishes for even numbers of spheres and linear actions and the Pontrjagin classes become p-localized homeomorphism invariants for a given dimension. The cohomology classes, Pontrjagin classes, and sets of normal invariants are computed in the process.     

Catalysis and acceleration of acyl transfer by aminocyclodextrins: a biomimetic system of use in enzyme modeling and drug design

[formula: see text] Aminocyclodextrins (ACDs), perfunctionalized at the 6-position with amino groups, bind phosphonoformate (PFA) diesters and accelerate acyl transfer reactions with high efficiency at neutral pH. Aminolysis and esterolysis are accelerated and hydrolysis of PFA diesters is catalyzed by ACDs. PFA diesters have significant antiviral activity. The rapid reactions observed with ACDs show that biological nucleophiles may undergo facile covalent modification by PFA esters at physiological pH, which has significant implications for prodrug and drug design strategies.     

Synthesis and application of crown ether tagged triarylphosphines

Crown ether tagged triarylphosphines 1 and 2 were synthesised and applied in Mitsunobu and Heck reactions, their reactivity being evaluated against triphenylphosphine- and polymer-bound triphenylphosphine. Purification of the reactions was effected by post-reaction sequestration onto an ammonium functionalised solid-phase.     

Selective substitution of vanadium for molybdenum in Sr2(Fe1−xVx)MoO6 double perovskites

The crystal and magnetic structures of Sr₂(Fe_1−xV_x)MoO₆ (0.03?x?0.1) compounds are refined by alternately using X-ray powder diffraction (XRD) and neutron powder diffraction (NPD) data collected at room temperature. The refinement results reveal that the V atoms selectively occupy the Mo sites instead of the Fe sites for x?0.1. The 3d/4d cation ordering decreases with the increase of the V content. Slight distortions in the lattice and metal octahedra are shown at 300 K, and the distortions increase at 4 K. The magnetic structure at 4 K can be modeled equally well with the moments aligning along [001], [110] or [111] directions. The total moments derived from the NPD data for the [110] and [111] direction models agree well with the magnetic measurements, whereas the [001] model leads to a smaller total moment. Bond valence analysis indicates that Sr ions are properly located in the structure and Mo ions are compatible with both the Fe sites and the Mo sites. The electronic effects are suggested to be responsible for the selective occupation of the V on the Mo sites due to the different distortions of the FeO₆ and MoO₆ octahedra.     

A B3LYP study of the effects of phenyl substituents on 1,5-hydrogen shifts in 3-(Z)-1,3-pentadiene provides evidence against a chameleonic transition structure

The effects of one or two phenyl substituents on the activation enthalpy for a 1,5-hydrogen shift in 3-(Z)-1,3-pentadiene (1) and on the geometry of the transition structure (TS) have been investigated by B3LYP/6-31G calculations. The phenyl-substituent effects on the experimentally measured activation enthalpies are predicted to be sizable, spanning a range of nearly 10 kcal/mol. However, if differences between steric effects in the transoid isomers of the reactants are factored out by comparing the activation enthalpies in the cisoid conformers, the electronic components of the phenyl-substituent effects on both the barrier heights and the TS geometries are found to be quite modest in size. Unlike the TS in the Cope rearrangement, the TS for a 1,5-hydrogen shift in 1 is not highly variable in nature, and the reason the 1,5-hydrogen shift TS is not chameleonic is discussed.     

Models for polyurethane hydrolysis under moderately acidic conditions: A comparative study of hydrolysis rates of urethanes,ureas, and amides

The hydrolysis of model structures found in the hard blocks of polyurethanes has been studied under moderately acidic and neutral conditions. These include a series of N-alkyl and N-phenyl urethanes and ureas; for comparison purposes the corresponding amides and a carbonate ester based on bisphenol A were also studied. Of all functional groups the urethane was the most resistant to hydrolysis and the amide the most labile. Also, the N-phenyl compounds were hydrolyzed faster than the corresponding alkyl derivatives. The carbonate ester underwent relatively rapid hydrolysis. Polyether containing polyurethanes, known to be relatively stable to hydrolysis, are discussed as to which polymer segments provide the weakest links under hydrolytic conditions.