Abstract:
This work focuses on understanding the nonlinear-optical response of a 1-D quantum wire embedded in 2-D space when quantum-size effects in the transverse direction are minimized using an extremely weighted delta function potential. Our aim is to establish the fundamental basis for understanding the effect of geometry on the nonlinear-optical response of quantum loops that are formed into a network of quantum wires. Using the concept of leaky quantum wires, it is shown that in the limit of full confinement, the sum rules are obeyed when the transverse infinite-energy continuum states are included. While the continuum states associated with the transverse wavefunction do not contribute to the nonlinear optical response, they are essential to preserving the validity of the sum rules. This work is a building block for future studies of nonlinear-optical enhancement of quantum graphs (which include loops and bent wires) based on their geometry. These properties are important in quantum mechanical modeling of any response function of quantum-confined systems, including the nonlinear-optical response of any system in which there is confinement in at leat one dimension, such as nanowires, which provide confinement in two dimensions.

Abstract:
The calculation of the fundamental limits of nonlinear susceptibilities posits that when a quantum system has a nonlinear response at the fundamental limit, only three energy eigenstates contribute to the first and second hyperpolarizability. This is called the three-level ansatz and is the only unproven assumption in the theory of fundamental limits. All calculations that are based on direct solution of the Schrodinger equation yield intrinsic hyperpolarizabilities less than 0.709 and intrinsic second hyperpolarizabilities less than 0.6. In this work, we show that relaxing the three-level ansatz and allowing an arbitrary number of states to contribute leads to divergence of the optimized intrinsic hyperpolarizability in the limit of an infinite number of states - what we call the many-state catastrophe. This is not surprising given that the divergent systems are most likely not derivable from the Schrodinger equation, yet obey the sum rules. The sums rules are the second ingredient in limit theory, and apply also to systems with more general Hamiltonians. These exotic Hamiltonians may not model any real systems found in nature. Indeed, a class of transition moments and energies that come form the sum rules do not have a corresponding Hamiltonian that is expressible in differential form. In this work, we show that the three-level ansatz acts as a constraint that excludes many of the nonphysical Hamiltonians and prevents the intrinsic hyperpolarizability from diverging. We argue that this implies that the true fundamental limit is smaller than previously calculated. Since the three-level ansatz does not lead to the largest possible nonlinear response, contrary to its assertion, we propose the intriguing possibility that the three-level ansatz is true for any system that obeys the Schrodinger equation, yet this assertion may be unprovable.

Abstract:
Studies aimed at understanding the global properties of the hyperpolarizabilities have focused on identifying universal properties when the hyperpolarizabilities are at the fundamental limit. These studies have taken two complimentary approaches: (1) Monte Carlo techniques that statistically probe the full parameter space of the Schrodinger Equation using the sum rules as a constraint; and, (2) numerical optimization studies of the first and second hyperpolarizability where models of the scalar and vector potentials are parameterized and the optimized parameters determined, from which universal properties are investigated. Here, we employ an energy spectrum constraint on the Monte Carlo method to bridge the divide between these two approaches. The results suggest an explanation for the origin of the factor of 20-30 gap between the best molecules and the fundamental limits and establishes the basis for the three-level ansatz.

Abstract:
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the fundamental limit. Loop topologies have modest responses, while bent wires have larger responses, even when the bent wire and loop geometries are identical. Topological enhancement of the nonlinear response of quantum graphs is even greater for star graphs, for which the first hyperpolarizability can exceed half the fundamental limit. In this paper, we investigate the nonlinear optical properties of quantum graphs with the star vertex topology, introduce motifs and develop new methods for computing the spectra of composite graphs. We show that this class of graphs consistently produces intrinsic optical nonlinearities near the limits predicted by potential optimization. All graphs of this type have universal behavior for the scaling of their spectra and transition moments as the nonlinearities approach the fundamental limit.

Abstract:
We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is always negative or zero. We use a one-electron model with tight transverse confinement. In the limit of infinite transverse confinement, the transverse wavefunctions drop out of the hyperpolarizabilities, but their residual effects are essential to include in the sum rules. The effects of geometry are manifested in the projections of the transition moments of each wire segment onto the 2-D lab frame. Numerical optimization of the geometry of a loop leads to hyperpolarizabilities that rival the best chromophores. We suggest that a combination of geometry and quantum-confinement effects can lead to systems with ultralarge nonlinear response.

Abstract:
The hyperpolarizability has been extensively studied to identify universal properties when it is near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the hyperpolarizability, the largest values of the second hyperpolarizability approaches the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability's upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.

Abstract:
We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. Changes in geometry result in smooth variations of the nonlinearities. Topological changes between geometrically-similar systems cause profound changes in the nonlinear susceptibilities that include a discontinuity due to abrupt changes in the boundary conditions. This work may inform the design of new molecules or nano- scale structures for nonlinear optics and hints at the same universal behavior for quantum graph models in nonlinear optics that is observed in other systems.

Abstract:
This article focuses on the concept of ‘intertext’ in Harun Aminurrashid’s novels. The concept appears in Malay literary tradition for example in lipurlara, manuscript writing and the novel itself. This tendency relates to ‘intertextuality’ as a phenomenon on the existence of ‘a text within a text’ or ‘dialogue between texts’. Julia Kristeva coined the term ‘intertextuality’ in her readings of the work of Mikhail Mikhailovich Bakhtin and Ferdinand de Saussure’s sign system and later followed by several scholars such as Roland Barthes, Gerard Genette, Michael Riffaterre and Harold Bloom. Harun Aminurrashid demonstrates his inclination towards historical themes and settings through his novels such as Darah Kedayan, Jong Batu, Siapakah Bersalah?, Sebelum Ajal, Merebut Gadis Jelita, Wak Cantuk, Panglima Awang and Anak Panglima Awang. Explicitly, Panglima Awang, portrays its intertextuality with the historical elements. The hypotexts incorporated several articles on the Portuguese in Malacca and Ferdinand de Magalhaes @ Magellan’s circumnavigation. Some intertextual processes involve transformation, modification and demitefication. Intertextuality could be said to denote authorship strategy, reflecting an attempt to ‘modify’ history to channel Malay aspirations and the spirit to uphold the self-worth of the Malays.

Abstract:
The growing increase in the number of small towns, brought about as a result of Iran’s demographic changes in recent decades, has necessitated due consideration of these towns in the country’s hierarchical urban system on the one hand and their economic function in their immediate periphery on the other. In the present article, an analysis has been conducted of the economic role Zahedshahr has played as a small town in its rural periphery by using the Jacqueline Beaujeu Garnier and George Shapou’s Model, as well as the Locational Coefficient and the Abscissa-Ordinate Graphic Models. Results obtained from the analysis showed that the above town, in spite of its small size, has played an effective role in providing services to the inhabitants of its surrounding areas, as well as acting as a center for sale of surplus agricultural products, thanks to its relatively equipped administrative, educational, commercial, etc., centers. The find- ings of this research also showed the development of Zahedshahr to be directly dependent on the social and economic conditions of its periphery, so that rural population and agricultural products stability can influence such development.

Abstract:
We calculate various properties of pseudoscalar mesons in partially quenched QCD using chiral perturbation theory through next-to-leading order. Our results can be used to extrapolate to QCD from partially quenched simulations, as long as the latter use three light dynamical quarks. In other words, one can use unphysical simulations to extract physical quantities - in this case the quark masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our proposal for determining L_7 makes explicit use of an unphysical (yet measurable) effect of partially quenched theories, namely the double-pole that appears in certain two-point correlation functions. Most of our calculations are done for sea quarks having up to three different masses, except for our result for L_7, which is derived for degenerate sea quarks.