N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX

Testing new physics with the electron g-2

We argue that the anomalous magnetic moment of the electron (a_e) can be used to probe new physics. We show that the present bound on new-physics contributions to a_e is 8*10^-13, but the sensitivity can be improved by about an order of magnitude with new measurements of a_e and more refined determinations of alpha in atomic-physics experiments. Tests on new-physics effects in a_e can play a crucial role in the interpretation of the observed discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large class of models, new contributions to magnetic moments scale with the square of lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in which this scaling is violated and larger effects in a_e are expected. In such models the value of a_e is correlated with specific predictions for processes with violation of lepton number or lepton universality, and with the electric dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde

Double Shape Invariance of Two-Dimensional Singular Morse Model

A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part of the spectrum and corresponding wave functions, starting from {\it one} definite state, which can be obtained by the method of $SUSY$-separation of variables, proposed recently.Comment: 9 page

Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin note: substantial text overlap with arXiv:1007.088

Avaliação da toxicidade do diflubenzuron e P-cloroanilina em indicadores bioquímicos de organismos não-alvo aquáticos.

Resumo: O uso de produtos agrícolas vem sendo a principal forma de combater parasitas na aquicultura, sendo que o Diflubenzuron, (DFB) é o mais utilizado. Este composto inibe a síntese de quitina, componente do exoesqueleto dos parasitas, e apresenta baixa toxicidade aos peixes. Porém, no ambiente aquático, o DFB pode ser tóxico às espécies não-alvo e, quando degradado, gera p-cloroanilina, (PCA), metabólito potencialmente cancerígeno e mutagênico para o ser humano. Tendo em vista a necessidade de se obter mais informações sobre a toxicidade destes compostos nos organismos aquáticos não-alvo, a proposta deste trabalho foi analisar a atividade enzimática de fosfatases ácida (FAT) e alcalina (Fale), catalase (CAT) e superoxido dismutase (SOD) de microalga Pseudokirchneriella subcapitata, microcrustáceo Daphnia similis e o peixe Oreochromis niloticus com base na concentração efetiva 50% (CE50) com vistas a suprir a necessidade de dados na literatura acerca da toxicidade destes produtos e analisar o possível uso da análise enzimática como indicador de poluição de recursos hídricos em programas de biomonitoramento

Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Irreducible second order SUSY transformations between real and complex potentials

Second order SUSY transformations between real and complex potentials for three important from physical point of view Sturm-Liouville problems, namely, problems with the Dirichlet boundary conditions for a finite interval, for a half axis and for the whole real line are analyzed. For every problem conditions on transformation functions are formulated when transformations are irreducible, i.e. when either the intermediate Hamiltonian is not well defined in the same Hilbert space as the initial and final Hamiltonians or its eigenfunctions cannot be obtained by applying transformation operator either on eigenfunctions of the initial Hamiltonian or on these of the final Hamiltonian. Obtained results are illustrated by numerous simple examples.Comment: Thanks to M.V. Ioffee Ref. [13] is corrected in the second versio