Four-Parameter Point-Interaction in 1-D Quantum Systems

We construct a four-parameter point-interaction for a non-relativistic particle moving on a line as the limit of a short range interaction with range tending toward zero. For particular choices of the parameters, we can obtain a delta-interaction or the so-called delta'-interaction. The Hamiltonian corresponding to the four-parameter point-interaction is shown to correspond to the four-parameter self-adjoint Hamiltonian of the free particle moving on the line with the origin excluded.Comment: 6 pages, Plain Tex file. BU-HEP-92-

Perturbation Theory for Singular Potentials in Quantum Mechanics

We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of the unusual techniques which are required to obtain perturbative expansions of the energies in such cases. These include a point-splitting prescription for expansions around the Dirichlet (fermionic) limit of the $\delta$-function potential, and performing a similarity transformation to a non-Hermitian potential in the Calogero-Sutherland model. As an application of the first technique, we study the ground state of the $\delta$-function Bose gas near the fermionic limit.Comment: LaTeX, 19 pages, no figure

The regulated four parameter one dimensional point interaction

The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We then propose a different breakup of unperturbed theory and interaction, which now is asymptotically free but leads to the same physics. The corresponding regulated potential can be solved both exactly and perturbatively, in agreement with the conjecture.Comment: 17 pages, no figures, Tex fil

Spectral properties on a circle with a singularity

We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.Comment: TeX, 26 pages. v2: one reference added and two update

Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems

A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories constructions is exhibited and the physical equivalence or inequivalence of different such schemes is analyzed. The discussion focuses on comparing constructions based on the Klein-Gordon product with those based on the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral Analysis) inner product. It is shown that the Klein-Gordon and induced products can be simply related for the models of interest. This fact is then used to establish isomorphisms between certain decoherence schemes based on these products.Comment: 21 pages ReVTe

Nanoparticle Interactions and Molecular Relaxation in PLA/PBAT/Nanoclay Blends

ABSTRACT: Organo-modified clay nanoparticles were mixed at 1 and 5 wt% concentrations with a molten blend of 75 wt% of polylactide (PLA) and 25 wt% poly[(butylene adipate)-co-terephthalate] (PBAT). Three mixing strategies were used to control the localization of nanoclay. Small amplitude oscillatory shear (SAOS) and stress growth tests were conducted to clarify the nanoclay interactions with the blend components and its effect on the molecular relaxation behavior. SAOS and weighted relaxation spectra properties were determined before and after pre-shearing at a rate of 0.01 s−1. Molecular relaxation and its characteristics were influenced by PLA degradation, PBAT droplet coalescence, and nanoclay localization

Quantum mechanics of a free particle on a pointed plane revisited

The detailed study of a quantum free particle on a pointed plane is performed. It is shown that there is no problem with a mysterious ``quantum anticentrifugal force" acting on a free particle on a plane discussed in a very recent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we deal with a purely topological efect related to distinguishing a point on a plane. The new results are introduced concerning self-adjoint extensions of operators describing the free particle on a pointed plane as well as the role played by discrete symmetries in the analysis of such extensions.Comment: 4 figure

Holographic renormalization as a canonical transformation

The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equations of motion that inherits a well defined symplectic form from that on phase space. The requirement of a well defined symplectic form is essential and often leads to a necessary repackaging of the degrees of freedom. (ii) Once the space of asymptotic solutions has been constructed in terms of the correct degrees of freedom, then there exists a boundary term that is obtained as a certain solution of the Hamilton-Jacobi equation which simultaneously makes the variational problem well defined and preserves the symplectic form. This procedure is identical to holographic renormalization in the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a footnote on Palatini gravity added. Version to appear in JHE

Enhanced ERbeta immunoexpression and apoptosis in the germ cells of cimetidine-treated rats

<p>Abstract</p> <p>Background</p> <p>Cimetidine, refereed as antiandrogenic drug, causes hormonal changes in male patients such as increased testosterone and FSH levels. In the rat testis, structural alterations in the seminiferous tubules have been related to germ cell loss and Sertoli cell death by apoptosis. Regarding the important role of Sertoli cells in the conversion of testosterone into estrogen, via aromatase, the immunoexpression of estrogen receptors-beta (ERbeta) was evaluated in the germ cells of untreated and treated rats with cimetidine. A relationship between ERbeta immunoreactivity and apoptosis was also investigated in the germ cells of damaged tubules.</p> <p>Methods</p> <p>Immunohistochemistry for detection of ERbeta and TUNEL method were performed in testicular sections of adult male rats treated with 50 mg/Kg of cimetidine (CmG) or saline solution (CG) for 52 days.</p> <p>Results</p> <p>In CG, a cytoplasmic immunoexpression for ERbeta was observed in spermatogonia, primary spermatocytes and spermatids. An evident ERbeta immunoreactivity was always observed in the flagellum and residual bodies of late spermatids. In CmG, the cytoplasm or cytoplasm and nuclei of germ cells of the damaged tubules by cimetidine showed enhanced ERbeta immunostaining. TUNEL-labeling was usually observed in the same germ cell types exhibiting enhanced ERbeta immunoreactivity.</p> <p>Conclusion</p> <p>The presence of ERbeta immunolabeling in the flagellum and residual bodies of spermatids reinforces the role of estrogen in spermiogenesis. The overexpression of ERbeta in the germ cells of CmG could be related to a possible interference of cimetidine on tubular androgenization and/or on the intratubular aromatase due to Sertoli cell damage. The parallelism between ERbeta overexpression and apoptosis indicates a participation of ERbeta on germ cell death.</p