Polarized micro-Raman studies of femtosecond laser written stress-induced optical waveguides in diamond

Understanding the physical mechanisms of the refractive index modulation induced by femtosecond laser writing is crucial for tailoring the properties of the resulting optical waveguides. In this work we apply polarized Raman spectroscopy to study the origin of stress-induced waveguides in diamond, produced by femtosecond laser writing. The change in the refractive index induced by the femtosecond laser in the crystal is derived from the measured stress in the waveguides. The results help to explain the waveguide polarization sensitive guiding mechanism, as well as providing a technique for their optimization.Comment: 5 pages, 4 figure

Frequencies of Lipopolysaccharide Core Types among Clinical Isolates of Escherichia coli Defined with Monoclonal Antibodies

Mouse monoclonal antibodies (MAbs) specific for the lipopolysaccharide (LPS) core types R1, R2, and R3 of Escherichia coli and a cross-reactive MAb that binds to the LPS core of almost all E. coli were used in ELISA to determine the frequency of cores resembling R1, R2, and R3 in strains of E. coli isolated from clinical samples (blood and urine specimens) and from the feces of asymptomatic individuals. Of the 180 wild-type isolates, 123 were assigned to R1 core type, 14 to R2, and 18 to R3. Twenty-five wild-type E. coli isolates could not be assigned to a particular core type and may have either an R4 or K12 core or a previously unrecognized core type. R1 core type was associated with O types 1, 4, 6, 8, and 18 and with K1 or K5 capsules. R3 was associated with O15.O75 isolates could be of either R1 or R2 core typ

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.Comment: 8pages, Te

Accuracy of Semiclassical Methods for Shape Invariant Potentials

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.Comment: 7 pages, Latex, and two tables in postscrip

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

On Exactness Of The Supersymmetric WKB Approximation Scheme

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.Comment: 11 pages, latex, 1 figure available on reques

The benefits of being seen to help others: indirect reciprocity and reputation-based partner choice

When one individual helps another, it benefits the recipient and may also gain a reputation for being cooperative. This may induce others to favour the helper in subsequent interactions, so investing in being seen to help others may be adaptive. The best-known mechanism for this is indirect reciprocity (IR), in which the profit comes from an observer who pays a cost to benefit the original helper. IR has attracted considerable theoretical and empirical interest, but it is not the only way in which cooperative reputations can bring benefits. Signalling theory proposes that paying a cost to benefit others is a strategic investment which benefits the signaller through changing receiver behaviour, in particular by being more likely to choose the signaller as a partner. This reputation-based partner choice can result in competitive helping whereby those who help are favoured as partners. These theories have been confused in the literature. We therefore set out the assumptions, the mechanisms and the predictions of each theory for how developing a cooperative reputation can be adaptive. The benefits of being seen to be cooperative may have been a major driver of sociality, especially in humans. This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints

Conditional Allocation of Control Rights in Venture Capital Finance

When a young entrepreneurial firm matures, it is often necessary to replace the founding entrepreneur by a professional manager. This replacement decision can be affected by the private benefits of control enjoyed by the entrepreneur which gives rise to a conflict of interest between the entrepreneur and the venture capitalist. We show that a combination of convertible securities and contingent control rights can be used to resolve this conflict efficiently. This contractual arrangement is frequently observed in venture capital finance