Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

Chiral conducting salts of nickel dithiolene complexes

Conducting and chiral [Ni(dmit)(2)] dithiolene salts were obtained by electrocrystallization of the radical [n-Bu(4)N][Ni(dmit)(2)] salt in the presence of chiral, enantiopure trimethylammonium cations. Three different cations were investigated, namely, (R)-Ph(Me)HC*-NMe(3)(+), (S)-((t)Bu)(Me)HC*-NMe(3)(+), and (S)-(1-Napht)MeHC*-NMe(3)(+), noted (R)-1, (S)-2, and (S)-3. Salts of 1:3 stoichiometry were obtained with (R)-1 and (S)-2, formulated as [(R)-1][Ni(dmit)(2)](3) and [(S)-2][Ni(dmit)(2)](3)·(CH(3)CN)(2). They both crystallize in the P2(1)2(1)2(1) chiral space group, with three crystallographically independent complexes exhibiting different oxidation degrees. Another salt with 2:5 stoichiometry was isolated with (S)-3. The semiconducting character of the three salts (σ(RT) = 20-30 × 10(-3) S cm(-1)) finds its origin in a strong electron localization, favored by the large number of crystallographically independent [Ni(dmit)(2)] complexes in these chiral structures and their association into weakly interacting dimeric or trimeric motifs. Racemic salts with the same cations, obtained only with difficulties with the tert-butyl-containing (rac)-2 cation, afforded similar trimerized structures. The observed unusual stoichiometry and strong charge localization is tentatively assigned to the size and anisotropic charge distribution of the cations.     

Variation of radiative lifetimes of NH2(Ã2A1) with rotational levels in the (0, 8, 0) and (0, 9, 0) vibration bands

Radiative lifetimes from the first electronically excited state of the amidogen free radical, NH(2)(A?(2)A(1)), are reported for rotational states in selected vibrational levels ν(2)' using laser-induced fluorescence. Thermal collision of argon, Ar(?)((3)P(0), (3)P(2)) metastable atoms in a microwave discharge-flow system with ammonia (NH(3)) molecules produced ground state NH(2)(X?(2)B(1)). The radiative lifetimes for the deactivation of NH(2)(A?(2)A(1)) were determined by measuring the decay profiles of NH(2)(A?(2)A(1)?→?X?(2)B(1)). In addition to the Fermi resonances with the ground state that lengthen the radiative lifetimes, a systematic increase in the radiative lifetimes with rotational quantum number was observed. Furthermore, the average radiative lifetimes of the (0, 9, 0) Γ, τ(1) = 18.65 ± 0.47 μs and (0, 8, 0) Φ, τ(2) = 23.72 ± 0.65 μs levels were much longer than those of the (0, 9, 0) Σ, τ(3) = 10.62 ± 0.47 μs, and (0, 8, 0) Π, τ(4) = 13.55 ± 0.55 μs states suggesting increased mixing of the first electronic excited and the ground states.     

Combined experimental-theoretical characterization of the hydrido-cobaloxime [HCo(dmgH)2(PnBu3)

A combined theoretical and experimental approach has been employed to characterize the hydrido-cobaloxime [HCo(dmgH)(2)(PnBu(3))] compound. This complex was originally investigated by Schrauzer et al. [Schrauzer et al., J. Am. Chem. Soc. 1971, 93,1505] and has since been referred to as a key, stable analogue of the hydride intermediate involved in hydrogen evolution catalyzed by cobaloxime compounds [Artero, V. et al. Angew. Chem., Int. Ed. 2011, 50, 7238-7266]. We employed quantum chemical calculations, using density functional theory and correlated RI-SCS-MP2 methods, to characterize the structural and electronic properties of the compound and observed important differences between the calculated (1)H NMR spectrum and that reported in the original study by Schrauzer and Holland. To calibrate the theoretical model, the stable hydrido tetraamine cobalt(III) complex [HCo(tmen)(2)(OH(2))](2+) (tmen = 2,3-dimethyl-butane-2,3-diamine) [Rahman, A. F. M. M. et al. Chem. Commun. 2003, 2748-2749] was subjected to a similar analysis, and, in this case, the calculated results agreed well with those obtained experimentally. As a follow-up to the computational work, the title hydrido-cobaloxime compound was synthesized and recharacterized experimentally, together with the Co(I) derivative, giving results that were in agreement with the theoretical predictions.     

Fourteen-electron ring model and the anomalous magnetic circular dichroism of meso-triarylsubporphyrins

The MCD spectra of meso-triarylsubporphyrins show a sign anomaly which is correlated with the acceptor properties of the aryl substituent. From the spectra, magnetic moments of the excited states are determined. In the context of a simplified orbital model, the sign change is attributed to the quenching of the magnetic moment of the LUMO by acceptor orbitals of the substituent. The actual calculation of this moment presents a major challenge to computational methods. It is shown that wave function techniques based on CASSCF underestimate the covalency effects that are responsible for the quenching. In contrast, a CI method based on DFT orbitals yields excellent results, which fully support the orbital model.     

When is the Uvarov transformation positive definite?

Let L\cal{L} be a positive definite bilinear functional, then the Uvarov transformation of L\cal{L} is given by  U(p,q) = L(p,q) + m p(a)[`(q)](a<sup>-1</sup>) +[`(m)] p([`(a)]<sup>-1</sup>)\,\mathcal{U}(p,q) = \mathcal{L}(p,q) + m\,p(\alpha)\overline{q}(\alpha^{-1}) + \overline{m}\,p(\overline{\alpha}^{-1}) [`(q)]([`(a)])\overline{q}(\overline{\alpha}) where $|\alpha| > 1, m \in \mathbb{C}$|\alpha| > 1, m \in \mathbb{C}. In this paper we analyze conditions on m for U\cal{U} to be positive definite in the linear space of polynomials of degree less than or equal to n. In particular, we show that m has to lie inside a circle in the complex plane defined by α, n and the moments associated with L\cal{L}. We also give an upper bound for the radius of this circle that depends only on α and n. This and other conditions on m are visualized for some examples.     

Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.     

Generalizations of the Finite Element Method

This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.     

Characterizing dusky dolphin sounds from Argentina and New Zealand

Dusky dolphin (Lagenorhynchus obscurus) acoustic sounds were characterized by analyzing narrowband recordings [0-16 kHz in New Zealand (NZ) and 0-24 kHz in Argentina], and sounds in broadband recordings (0-200 kHz) were compared to their counterparts in down-sampled narrowband recordings (0-16 kHz). The most robust similarity between sounds present in broadband recordings and their counterparts in the down-sampled narrowband recordings was inter-click interval (ICI); ICI was therefore primarily used to characterize click sounds in narrowband recordings. In NZ and Argentina, distribution of ICIs was a continuum, although the distribution of ICIs in NZ had a somewhat bimodal tendency. In NZ, sounds that had smaller mean ICIs were more likely to have constant ICIs, and less likely to have increasing or decreasing ICIs. Similar to some other delphinids, dusky dolphins may use single, short duration sounds that have a constant ICI and closely spaced clicks for communication. No whistles were documented at either study site. Temporally structured sequences of burst pulses (i.e., sounds with ICI < about 10 ms) also occurred at both study sites, and these sequences contained 2-14 burst pulses that appeared closely matched aurally and in spectrograms and waveforms.