Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

The cyclodimerisation of 3-methyl-2-butenenitrile

3-Methyl-2-butenenitrile (1) cyclodimerised on treatment with lithium diisopropylamide in dimethoxyethane at temperatures between ?78°C and 0°C to 3-amino-4-cyano-1,5,5-trimethyl-1,3-cyclohexadiene (2) the structure of which was established by acid hydrolysis to the known 4-cyano-1,5,5-trimethyl-1-cyclohexene-3-one (3).     

Tunable coupling of superconducting qubits

We study an LC circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge-phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

Statistical-mechanical predictions and Navier-Stokes dynamics of two-dimensional flows on a bounded domain

In this paper the applicability of a statistical-mechanical theory to freely decaying two-dimensional (2D) turbulence on a bounded domain is investigated. We consider an ensemble of direct numerical simulations in a square box with stress-free boundaries, with a Reynolds number that is of the same order as in experiments on 2D decaying Navier-Stokes turbulence. The results of these simulations are compared with the corresponding statistical equilibria, calculated from different stages of the evolution. It is shown that the statistical equilibria calculated from early times of the Navier-Stokes evolution do not correspond to the dynamical quasistationary states. At best, the global topological structure is correctly predicted from a relatively late time in the Navier-Stokes evolution, when the quasistationary state has almost been reached. This failure of the (basically inviscid) statistical-mechanical theory is related to viscous dissipation and net leakage of vorticity in the Navier-Stokes dynamics at moderate values of the Reynolds number.     

Self-chemical ionization of diethylzinc

The self-chemical ionization of diethylzinc is examined by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and semiempirical molecular orbital calculations. Electron impact of diethylzinc neutral produces the radical cation, C(4)H(15)Zn(+) (m/z x 122), which reacts further with the neutral (C(2)H(5))(2)Zn to give the following product ions: Zn(+) (m/z x 64), C(2)H(5)Zn(+) (m/z x 93), C(4)H(9)Zn(+) (m/z x 121), C(4)H(11)Zn(2)(+) (m/z x 187), and C(6)H(15)Zn(2)(+) (m/z x 215). To determine the structure and pathways for production of these ions, monoisotopic (12)C(4)H(15)(64)Zn(+), (64)Zn(+) and (12)C(2)H(5)(64)Zn(+) were individually isolated and reacted with the neutral background. We also performed semiempirical molecular orbital calculations (ZINDO/1). The molecular orbital calculations and experimental data are consistent in predicting that the ethyl group on the diethylzinc cation carries the positive charge. Copyright 1999 John Wiley & Sons, Ltd.     

Comparing the 2,2′‐Biphenylenedithiophosphinate Binding of Americium with Neodymium and Europium

Advancing our understanding of the minor actinides (Am, Cm) versus lanthanides is key for developing advanced nuclear‐fuel cycles. Herein, we describe the preparation of (NBu₄)Am[S₂P(^tBu₂C₁₂H₆)]₄ and two isomorphous lanthanide complexes, namely one with a similar ionic radius (i.e., Nd^III) and an isoelectronic one (Eu^III). The results include the first measurement of an Am?S bond length, with a mean value of 2.921(9) Å, by single‐crystal X‐ray diffraction. Comparison with the Eu^III and Nd^III complexes revealed subtle electronic differences between the complexes of Am^III and the lanthanides.     

Controllable coupling of superconducting flux qubits

We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.     

Charge separation in the excited state electron donor—acceptor compounds containing the piperazine moiety

Three bridged electron donor—acceptor systems are investigated containing a 4-cyano-1-ethenylnaphthalene electron-acceptor and piperidine (compound 1), phenylpiperazine (2) and 4-methoxyphenylpiperazine (3) electron-donating groups. In the intramolecular charge-transfer states of 1 and 2, the extent of charge separation is similar, but in compound 3 the positive charge is shifted towards the more powerful arylamine donor site, which results in a significantly greater dipole moment. Optical absorption spectra of model radical cations demonstrate that the predominant charge localization on the trialkyl nitrogen in 2 and on the aryl nitrogen in 3 are a consequence of the bistable nature of the piperazine donors.     

Reduction of Tosylamino Acids and Related Compounds with Sodium in Liquid Ammonia; stoichiometry and products

Using an extraction procedure which permits determination of end-points, the reduction of a number of tosylamino acids, their derivatives, and model compounds with sodium in liquid ammonia has been investigated. When the molecule contains a single acidic group in addition to the tosylamino group (as in the case of the simple mono-tosylamino monocarboxylic acids) reduction proceeds with the consumption of 2 g-at. Na per tosyl group and the formation of toluene-4-sulphinic acid. If the number of acidic groups in the products is insufficient to accommodate the number of electrons consumed in the reduction, the reduction of ionisable tosylamino groups is incomplete unless an acid is added. If the number of acidic groups is higher, or excess acid is added, the sulphur-containing products include thiocresol and sulphite. This last reaction course is also observed whenever calcium is used in place of sodium. A partial interpretation of the results is offered.