New Two-Dimensional Quantum Models with Shape Invariance

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional SUSY Quantum Mechanics. They are obtained using the expressions for known one-dimensional shape invariant potentials. The constructed Hamiltonians are integrable with symmetry operators of fourth order in momenta, and they are not amenable to the conventional separation of variables.Comment: 16 p.p., a few new references adde

Matrix Hamiltonians: SUSY approach to hidden symmetries

A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred to as a "hidden" symmetry operator) found to commute with the superhamiltonian. We discuss some physical interpretations of such dynamical systems in terms of spin 1/2 particle in a magnetic field or in terms of coupled channel problem. Particular attention is paid to the case of transparent matrix potentials.Comment: 20 pages, LaTe

On the relationship of the scaled phase space and Skyrme-coherent state treatments of proton antiproton annihilation at rest

We discuss pion multiplicities and single pion momentum spectra from proton antiproton annihilation at rest. Both the scaled phase space model and the Skyrme-coherent state approach describe these observables well. In the coherent state approach the puzzling size of the scale parameter relating the phase space integrals for different multiplicities is replaced by a well defined weight function. The strength of this function is determined by the intensity of the classical pion field and its spatial extent is of order 1 fm.Comment: 11 pages including 4 figures(postscript

Can One Distinguish Tau Neutrinos from Antineutrinos in Neutral-Current Pion Production Processes?

A potential way to distinguish tau-neutrinos from antineutrinos, below the tau-production threshold, but above the pion production one, is presented. It is based on the different behavior of the neutral current pion production off the nucleon, depending on whether it is induced by neutrinos or antineutrinos. This procedure for distinguishing tau-neutrinos from antineutrinos neither relies on any nuclear model, nor it is affected by any nuclear effect (distortion of the outgoing nucleon waves, etc...). We show that neutrino-antineutrino asymmetries occur both in the totally integrated cross sections and in the pion azimuthal differential distributions. To define the asymmetries for the latter distributions we just rely on Lorentz-invariance. All these asymmetries are independent of the lepton family and can be experimentally measured by using electron or muon neutrinos, due to the lepton family universality of the neutral current neutrino interaction. Nevertheless and to estimate their size, we have also used the chiral model of hep-ph/0701149 at intermediate energies. Results are really significant since the differences between neutrino and antineutrino induced reactions are always large in all physical channels.Comment: Revised version. 8 pages, 3 figures. The abstract has been changed and discussion extende

Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must include also the corresponding associated functions. In the specific case of anharmonic second-plus-fourth order interaction, expressions for the wave functions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wave functions is given.Comment: 17 p.

Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction

We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction $x_1x_2$ with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and oscillator frequences, the model {\it is not} amenable to a conventional separation of variables. The property of shape invariance allows to find analytically all eigenfunctions and the spectrum is found to be equidistant. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of the identity must include also the corresponding associated functions. These functions are constructed explicitly, and their properties are investigated. The problem of $R-$separation of variables in two-dimensional systems is discussed.Comment: 20 pages; minor corrections were made; new Appendix was adde

CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric.Comment: 25 page

Seismic and Infrasound Signals at Mt. Etna: Modelling the North-East Crater Conduit and its Relation with the 2008-2009 Eruption Feeding System

On 13 May 2008, an eruption began at Mt. Etna from an eruptive fissure that opened on the upper eastern flank of the volcano. During 12-13 May, 157 infrasonic events, together with the related seismic transients, were collected. We carried out several analyses to obtain dominant frequencies, pseudospectrograms, peak-to-peak amplitudes, source locations and time lags between infrasonic and seismic events. Spectra of the infrasonic events show two main spectral peaks in the frequency bands ~0.4-0.7 Hz and 1.5-2.0 Hz, respectively. Both infrasonic and seismic events were separately located below the North-East Crater, where no eruptive activity was observed. Moreover, significant changes in infrasound spectral content, as well as in the infrasonic-seismic lags, were found a few hours before the beginning of the eruption. On the basis of the collected information the infrasound source mechanism was modelled as a superposition of pipe and Helmholtz resonance, also leading to outline the geometry of the shallower portion of the North-East Crater plumbing system. The occurrence of these seismo-infrasonic events together with other geological and geophysical evidences, led us to inferring a direct link between North-East Crater activity and the eruptive fissure. Further, based on variations over time of both spectral features and seismicinfrasonic time lag, shallowing phenomena of the free magma column inside North-East Crater conduit were hypothesized. Such an uprise of magma was likely caused by a pressure increase inside the plumbing system occurring before the beginning of the 2008-2009 eruption

The shallow magma pathway geometry at Mt. Etna volcano

A fundamental goal of volcano seismology is to understand the dynamics of active magmatic systems in order to assess eruptive behavior and the associated hazard. Imaging of magma conduits, quantification of magma transport and investigation of long-period seismic sources, together with their temporal variations, are crucial for the comprehension of eruption-triggering mechanisms. At Mt. Etna volcano, several intense episodes of tremor activity were recorded during 2007, in association with strombolian activity and/or intense fire fountaining episodes occurring from the South East Crater (SEC). The locations of the tremor sources and of the long-period seismic events are used here to constrain both the area and the depth range of magma degassing, highlighting the geometry of the shallow conduits feeding SEC. The imaged conduits consist of two connected resonating dike-like bodies, NNW-SSE and NW-SE oriented, extending from sea level to the surface. In addition, we show how tremor, long-period (LP) and very-long-period (VLP) event locations and signatures reflect pressure fluctuations in the plumbing system associated with the ascent/discharge of gas-rich magma linked to the lava fountains. The evidence here reported, also corroborated by ground deformation variations, can help develop a better prediction and early-warning system for those eruptions (effusive or explosive) that apparently manifest no clear precursors