PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Numbers,scale and symbols: the public understanding of nanotechnology

Nanotechnology will be an increasing part of the everyday lives of most people in the world. There is a general recognition that few people understand the implications of the technology, the technology itself or even the definition of the word. This lack of understanding stems from a lack of knowledge about science in general but more specifically difficulty in grasping the size scale and symbolism of nanotechnology. A potential key to informing the general public is establishing the ability to comprehend the scale of nanotechnology. Transitioning from the macro to the nanoscale seems to require an ability to comprehend scales of one-billion. Scaling is a skill not common in most individuals and tests of their ability to extrapolate size based upon scaling a common object demonstrates that most individuals cannot scale to the extent needed to make the transition to nanoscale. Symbolism is another important vehicle to providing the general public with a basis to understand the concepts of nanotechnology. With increasing age, individuals are able to draw representations of atomic scale objects, but these tend to be iconic and the different representations not easily translated. Ball and stick models are most recognized by the public, which provides an opportunity to present not only useful symbolism but also a reference point for the atomic scale.     

Determining the efficacy of a nanotechnology media product in enhancing children’s engagement with nanotechnology

Public engagement in nanotechnology media products can lead to a greater interest in understanding of nanotechnology. A study was undertaken to determine middle school student engagement in Nanooze, a magazine featuring nanotechnology research that has been developed for a young adult audience. Teachers at 116 Detroit middle schools distributed two issues of the magazine to their students, and surveys were collected from 870 students after reading the magazines. Results suggest that the majority of students liked reading the magazine and learned something about nanotechnology. Engagement in nanotechnology led to understanding of nanotechnology. The Nanooze magazine was an effective medium for engaging middle school students in learning about nanotechnology.     

Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

Vibro-acoustic noise control treatments for payload bays of launch vehicles: Discrete to fuzzy solutions

Sound transmitted through an enclosing structure into a cavity has been minimised by optimising the locations, numbers and properties of tuned mass dampers placed on the structure and Helmholtz resonators placed in the cavity. Most of the results presented in the literature show the effect of a few well selected acoustic or vibration absorbers on simple vibro-acoustic systems, whereas the results presented here indicate the trends that occur when a few absorbers are replaced by a large number. The results indicate that for low numbers of absorbers, the result of the optimal configuration is to reduce the response of discrete modes, and for a large number of absorbers the result of the optimal configuration is a tendency for the vibro-acoustic energy to be smeared over a range of frequencies, which is similar to the results seen in fuzzy structures. The enormous computational task was achieved using a distributed computing network and an asynchronous parallel genetic algorithm.     

Macrolide antibiotics—VIII The absolute configuration of certain centers in neomethymycin, erythromycin and related antibiotics

Neomethymycin (I) has been transformed into “anhydrocycloneomethynolide” (V) which could be degraded via (−)--methyllevulinic acid to (−)--methylsuccinic acid, thus establishing the absolute configuration of positions 4 and 6 in the lactonic acid (XIII). This acid is a common degradation product of methymycin, neomethymycin, pikromycin and narbomycin and there is thus available a standard of absolute configuration for these macrolide antibiotics. By a different sequence of reactions, erythromycin (XXIII) has been converted into (+)--methyllevulinic acid and (+)--methylsuccinic acid. Coupled with earlier results reported in the literature, it is now possible to assign absolute configurations to positions 10 (R) and 8 (R) of erythromycin and this applies most likely also to positions 4 (R) and 2 (S). Attention is called to the biogenetic significance of these observations.     

Optical rotatory dispersion studies—CIV Low-temperature circular dichroism behavior of various chromophoric derivatives of alcohols and amines

The low-temperature circular dichroism behavior of various cyclic and alicyclic systems containing the methyl xanthato-, N,N-diethyl-N′-acylthioureyl-, N-phthalimido-, nitrito- and dithio-carbalkoxy- chromophores is discussed. Rotational strength (R₀^T) values are reported where possible and changes in this parameter upon variation of the temperature are interpreted, where relevant, in terms of the degree of steric inhibition to free rotation about the various bonds connected to the asymmetric center bearing (or nearest to) the chromophore moiety.     

Anionic Graft Copolymers. ll. Styrene Grafts on EPT Rubbers

Rubbers containing a low level of unsaturation such as EPT may be metalated with a chelate made from s-butyllithium and N,N,N′- N′ -tetramethylethylethylenediamine. The lithiated polymers, reacted with styrene, result in polystyrene graft copolymers. The physical properties are affected by graft level and polystyrene content.     

Numerical analysis of nematic liquid crystal alignment on asymmetric surface grating structures

The influence of an asymmetric periodic grooved cell surface on the 2D static director configuration of a nematic liquid crystal has been investigated. The minimum in the Frank-Oseen free energy was solved numerically with the Rapini-Papoular form of the surface anchoring energy at the nematic-grating interface. Results are presented for the variation of pretilt angle in the tilted bulk director field as a function of the surface groove depth, pitch and asymmetry and the bulk parameters. The simulations demonstrate the existence of two energetically degenerate high and low pretilted bulk alignment configurations. The pretilt values in these two regimes and also for the low tilt regime with finite surface anchoring are consistent with experimental results. An effective increase in the resolution of the model is obtained by using an irregular grid to describe the surface profile.