215 research outputs found
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 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
Towards democratic foundations: a Habermasian perspective on the politics of education
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
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