The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part III. Idealizations. Hilbert space representation

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures.     

Linear Orders on General Algebras

We answer the question, when a partial order in a partially ordered algebraic structure has a compatible linear extension. The finite extension property enables us to show, that if there is no such extension, then it is caused by a certain finite subset in the direct square of the base set. As a consequence, we prove that a partial order can be linearly extended if and only if it can be linearly extended on every finitely generated subalgebra. Using a special equivalence relation on the above direct square, we obtain a further property of linearly extendible partial orders. Imposing conditions on the lattice of compatible quasi orders, the number of linear orders can be determined. Our general approach yields new results even in the case of semi-groups and groups.     

Atomicity and maximality in axiomatic quantum theory

The “weak-maximality” condition is proved to be equivalent to atomicity of the lattice of “propositions” (“decision effects”) in quantum axiomatics, satisfying certain simple conditions. In particular, it is shown that these conditions are fulfilled in Ludwig's axiomatic formulation of quantum mechanics. It is further proved that atomicity of the lattice of propositions follows from the condition of “strong maximality”. The maximality conditions have a clear physical interpretation. They are also fulfilled in the Hilbert space formulation of quantum mechanics. Since the atomicity property is used in theories based on Type I factors, the connection between atomicity and maximality seems of general interest. Useful theorems are proved.     

Intramolecular Diels–Alder reaction in enyne–allenes: a computational investigation and comparison with the Myers–Saito and Schmittel reactions

The reaction mechanisms as well as substituted effect and solvent effect of the enyne–allenes are investigated by Density Functional Theory (DFT) method and compared with the Myers–Saito and Schmittel reactions. The Myers–Saito reaction of non‐substituted enyne–allenes is kinetically and thermodynamically favored as compared to the Schmittel reaction; while the concerted [4 + 2] cycloaddition is only 1.32 kcal/mol higher than the C₂? C₇ cyclization and more exothermic (Δ_RE = ?69.38 kcal/mol). For R₁ = CH₃ and t‐Bu, the increasing barrier of the C₂? C₇ cyclization is higher than that for the C₂? C₆ cyclization because of the steric effect, so the increased barrier of the [4 + 2] cycloaddition is affected by such substituted electron‐releasing group. Moreover, the strong steric effect of R₁ = t‐Bu would shift the C₂? C₇ cyclization to the [4 + 2] cycloaddition. On the other hand, for R₁ = Ph, NH₂, O^?, NO₂, and CN substituents, the barrier of the C₂? C₆ cyclization would be more diminished than the C₂? C₇ cyclization due to strong mesomeric effect; the reaction path of C₂? C₇ cyclization would also shift to the [4 + 2] cycloaddition. The solvation does not lead to significant changes in the potential‐energy surface of the reaction except for the more polar surrounding solvent such as dimethyl sulfoxide (DMSO), or water. Copyright © 2009 John Wiley & Sons, Ltd.     

High-efficiency polymer light-emitting diodes using neutral surfactant modified aluminum cathode

High-efficiency polymer light-emitting diodes were fabricated by inserting a layer of nonionic neutral surfactant between the electroluminescent (EL) layer and the high-work-function aluminum cathode via spin coating. It was found that both the poly(ethylene glycol)- and poly(propylene glycol)-based surfactants as well as their copolymers can all demonstrate similar performance enhancement. Device performances comparable to or even better than those of the control devices using calcium as the cathode have been achieved for both poly(p-phenylene)-based and polyfluorene-based conjugated polymers with orange-red, green, and blue emission colors. It is possible that when both surfactant and aluminum are used as the cathode, the abundant hole injection through a hole-transporting layer and hole pile-up at the inner side of the EL/surfactant interface might cause an effective electric field to induce the realignment of the dipole moment of those polar surfactant molecules, thus lowering the barrier for electron injection. In addition, the coordination between the aluminum and oxygen atoms on the surfactant might cause n-type doping in the areas near surfactant in the EL polymer layer that causes the enhancement of electron injection.     

Facile synthesis of highly efficient phenyltetraene-based nonlinear optical chromophores for electrooptics

[reaction: see text] A facile synthetic route has been developed to convert an electron-rich, sterically hindered dialkylaminodienone into a conjugated dialkylaminotrienal with good yield. The derived dialkylaminotetraene-type nonlinear optical chromophores possess an all-trans conformation and can be functionalized with fluoro-dendron to provide proper shape modification for poling. Polymers doped with two examples of these chromophores in high concentrations have been poled to afford ultra-large electrooptic coefficients (r(33)) of 208 and 262 pm/V, respectively, at the measuring wavelength of 1.31 mum.     

Development of diamond-based X-ray detection for high-flux beamline diagnostics

High‐quality single‐crystal and polycrystalline chemical‐vapor‐deposition diamond detectors with platinum contacts have been tested at the white‐beam X28C beamline at the National Synchrotron Light Source under high‐flux conditions. The voltage dependence of these devices has been measured under both DC and pulsed‐bias conditions, establishing the presence or absence of photoconductive gain in each device. Linear response consistent with the theoretically determined ionization energy has been achieved over eleven orders of magnitude when combined with previous low‐flux studies. Temporal measurements with single‐crystal diamond detectors have resolved the nanosecond‐scale pulse structures of both the NSLS and the APS. Prototype single‐crystal quadrant detectors have provided the ability to simultaneously resolve the X‐ray beam position and obtain a quantitative measurement of the flux.