Non-relativistic Lee Model on two Dimensional Riemannian Manifolds

This work is a continuation of our previous work (JMP, Vol. 48, 12, pp. 122103-1-122103-20, 2007), where we constructed the non-relativistic Lee model in three dimensional Riemannian manifolds. Here we renormalize the two dimensional version by using the same methods and the results are shortly given since the calculations are basically the same as in the three dimensional model. We also show that the ground state energy is bounded from below due to the upper bound of the heat kernel for compact and Cartan-Hadamard manifolds. In contrast to the construction of the model and the proof of the lower bound of the ground state energy, the mean field approximation to the two dimensional model is not similar to the one in three dimensions and it requires a deeper analysis, which is the main result of this paper.Comment: 18 pages, no figure

The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

A Many-body Problem with Point Interactions on Two Dimensional Manifolds

A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the $\beta$ function is exactly calculated for the general case, which includes all particle numbers.Comment: 28 pages; typos are corrected, three figures are adde

Point Interaction in two and three dimensional Riemannian Manifolds

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator. In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for general class of manifolds, e.g., for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the beta-function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by S. G. Rajeev.Comment: 43 page

Existence of Hamiltonians for Some Singular Interactions on Manifolds

The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.Comment: 33 pages, no figure

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure

Competition between decay and dissociation of core-excited OCS studied by X-ray scattering

We show the first evidence of dissociation during resonant inelastic soft X-ray scattering. Carbon and oxygen K-shell and sulfur L-shell resonant and non-resonant X-ray emission spectra were measured using monochromatic synchrotron radiation for excitation and ionization. After sulfur, L2,3 -> {\pi}*, {\sigma}* excitation, atomic lines are observed in the emission spectra as a consequence of competition between de-excitation and dissociation. In contrast the carbon and oxygen spectra show weaker line shape variations and no atomic lines. The spectra are compared to results from ab initio calculations and the discussion of the dissociation paths is based on calculated potential energy surfaces and atomic transition energies.Comment: 12 pages, 6 pictures, 2 tables, http://link.aps.org/doi/10.1103/PhysRevA.59.428

2016 ACR-EULAR adult dermatomyositis and polymyositis and juvenile dermatomyositis response criteria-methodological aspects

Objective. The objective was to describe the methodology used to develop new response criteria for adult DM/PM and JDM. Methods. Patient profiles from prospective natural history data and clinical trials were rated by myositis specialists to develop consensus gold-standard ratings of minimal, moderate and major improvement. Experts completed a survey regarding clinically meaningful improvement in the core set measures (CSM) and a conjoint-analysis survey (using 1000Minds software) to derive relative weights of CSM and candidate definitions. Six types of candidate definitions for response criteria were derived using survey results, logistic regression, conjoint analysis, application of conjoint-analysis weights to CSM and published definitions. Sensitivity, specificity and area under the curve were defined for candidate criteria using consensus patient profile data, and selected definitions were validated using clinical trial data. Results. Myositis specialists defined the degree of clinically meaningful improvement in CSM for minimal, moderate and major improvement. The conjoint-analysis survey established the relative weights of CSM, with muscle strength and Physician Global Activity as most important. Many candidate definitions showed excellent sensitivity, specificity and area under the curve in the consensus profiles. Trial validation showed that a number of candidate criteria differentiated between treatment groups. Top candidate criteria definitions were presented at the consensus conference. Conclusion. Consensus methodology, with definitions tested on patient profiles and validated using clinical trials, led to 18 definitions for adult PM/DM and 14 for JDM as excellent candidates for consideration in the final consensus on new response criteria for myositis