Canonical-grandcanonical ensemble in-equivalence in Fermi systems?

I discuss the effects of fermionic condensation in systems of constant density of states. I show that the condensation leads to a correction of the chemical potential and of the Fermi distribution in canonical Fermi systems at low temperatures. This implies that the canonical and grandcanonical ensembles are not equivalent even for Fermi systems.Comment: 4 pages and 1 figur

Fluctuations of the Fermi condensate in ideal gases

We calculate numerically and analytically the fluctuations of the fermionic condensate and of the number of particles above the condensate for systems of constant density of states. We compare the canonical fluctuations, obtained from the equivalent Bose condensate fluctuation, with the grandcanonical fermionic calculation. The fluctuations of the condensate are almost the same in the two ensembles, with a small correction comming from the total particle number fluctuation in the grandcanonical ensemble. On the other hand the number of particles above the condensate and its fluctuation is insensitive to the choice of ensemble.Comment: 10 pages with 3 figs. IOP styl

Formation of gold(III) alkyls from gold alkoxide complexes

The gold(III) methoxide complex (C^N^C)AuOMe 1 reacts with tris(p-tolyl)phosphine in benzene at room temperature under O-abstraction to give methylgold product (C^N^C)AuMe 2 together with O=P(p-tol)3 {(C^N^C) = [2,6-(C6H3tBu-4)2¬pyridine]2 }. Calculations show that this reaction is energetically favourable (ΔG = 32.3 kcal mol 1). The side-products in this reaction, the Au(II) complex [Au(C^N^C)]2 3 and the phosphorane (p-tol)3P(OMe)2, suggest that at least two reaction pathways may operate, including one involving (C^N^C)Au• radicals. Attempts to model the reaction by DFT methods showed that PPh3 can approach 1 to give a near-linear Au-O-P arrangement, without phosphine coordination to gold. The analogous reaction of (C^N^C)AuOEt, on the other hand, gives exclusively a mixture of 3 and (p-tol)3P(OEt)2. Whereas the reaction of (C^N^C)AuOR (R = But, p-C6H4F) with P(p-tol)3 proceeds over a period of hours, compounds with R = CH2CF3 or CH(CF3)2 react almost instantaneously, to give 3 and O=P(p-tol)3. In chlorinated solvents, treatment of the alkoxides (C^N^C)AuOR with phosphines generates [(C^N^C)Au(PR3)]Cl, via Cl-abstraction from the solvent. Attempts to extend the synthesis of gold(III) alkoxides to allyl alcohols were unsuccessful; the reaction of (C^N^C)AuOH with an excess of CH2=CHCH2OH in toluene led instead to allyl alcohol isomerization to give a mixture of gold alkyls, (C^N^C)AuR′ (R′ = -CH2CH2CHO 10 and CH2CH(CH2OH)¬OCH2¬CH=CH2 11), while 2-methallyl alcohol affords R′ = CH2CH(Me)CHO 12. The crystal structure of 11 was determined. The formation of Au-C instead of the expected Au-O products is in line with the trend in metal-ligand bond dissociation energies for Au(III), M-H > M-C > M-O

The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution

Reactivity of Gold Hydrides: O2 Insertion into the Au–H Bond

Dioxygen reacts with the gold(I) hydride (IPr)AuH under insertion to give the hydroperoxide, (IPr)AuOOH, a long-postulated reaction in gold catalysis and the first demonstration of O2 activation by Au-H in a well-defined system. Subsequent condensation gave the peroxide (IPr)Au-OO-Au(IPr) (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazole-2-ylidene). The reaction kinetics are reported, as well as the reactivity of Au(I) hydrides with radical scavengers