Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te

HI Imaging of LGS 3 and an Apparently Interacting High-Velocity Cloud

We present a 93' by 93' map of the area near the Local Group dwarf galaxy LGS 3, centered on an HI cloud 30' away from the galaxy. Previous authors associated this cloud with LGS 3 but relied on observations made with a 36' beam. Our high-resolution (3.4'), wide-field Arecibo observations of the region reveal that the HI cloud is distinct from the galaxy and suggest an interaction between the two. We point out faint emission features in the map that may be gas that has been tidally removed from the HI cloud by LGS 3. We also derive the rotation curve of the cloud and find that it is in solid-body rotation out to a radius of 10', beyond which the rotation velocity begins to decline. Assuming a spherical geometry for the cloud, the implied mass is 2.8 x 10^7 (d/Mpc) M_{Sun}, where d is the distance in Mpc. The observed HI mass is 5.5 x 10^6 (d/Mpc)^2 M_{Sun}, implying that the cloud is dark-matter dominated unless its distance is at least 1.9 Mpc. We propose that the cloud is a high-velocity cloud that is undergoing a tidal interaction with LGS 3 and therefore is located roughly 700 kpc away from the Milky Way. The cloud then contains a total mass of ~2.0 x 10^7 M_{Sun}, 82% of which consists of dark matter.Comment: 5 pages, 2 color figures. Accepted for publication in ApJ Letter

Resonant laser tunnelling

We propose an experiment involving a gaussian laser tunneling through a twin barrier dielectric structure. Of particular interest are the conditions upon the incident angle for resonance to occur. We provide some numerical calculations for a particular choice of laser wave length and dielectric refractive index which confirm our expectations.Comment: 15 pages, 6 figure

Evidence of a new low field cross-over in the vortex critical velocity of type-II superconducting thin films

We measure current-voltage characteristics as function of magnetic field and temperature in Nb strips of different thickness and width. The instability voltage of the flux flow state related to the vortex critical velocity v* is studied and compared with the Larkin-Ovchinnikov theory. Beside the usual power-law dependence v* ~ B^-1/2, in the low field range a new cross-over field, Bcr1, is observed below which v* decreases by further lowering the external magnetic field B. We ascribe this unexpected cross-over to vortex channeling due to a fan-like penetration of the applied magnetic field as confirmed by magneto-optic imaging. The observation of Bcr1 becomes a direct evidence of a general feature in type-II superconducting films at low fields, that is a channel-like vortex motion induced by the inhomogeneous magnetic state caused by the relatively strong pinning

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Representations of U(1,q) and Constructive Quaternion Tensor Products

The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecc

Smectic order, pinning, and phase transition in a smectic liquid crystal cell with a random substrate

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.Comment: 30 pages, 11 figures, Published in PRE, with minor typos correcte

Phases and Transitions in Phantom Nematic Elastomer Membranes

Motivated by recently discovered unusual properties of bulk nematic elastomers, we study a phase diagram of liquid-crystalline polymerized phantom membranes, focusing on in-plane nematic order. We predict that such membranes should enerically exhibit five phases, distinguished by their conformational and in-plane orientational properties, namely isotropic-crumpled, nematic-crumpled, isotropic-flat, nematic-flat and nematic-tubule phases. In the nematic-tubule phase, the membrane is extended along the direction of {\em spontaneous} nematic order and is crumpled in the other. The associated spontaneous symmetries breaking guarantees that the nematic-tubule is characterized by a conformational-orientational soft (Goldstone) mode and the concomitant vanishing of the in-plane shear modulus. We show that long-range orientational order of the nematic-tubule is maintained even in the presence of harmonic thermal luctuations. However, it is likely that tubule's elastic properties are ualitatively modified by these fluctuations, that can be studied using a nonlinear elastic theory for the nematic tubule phase that we derive at the end of this paper.Comment: 12 pages, 4 eps figures. To appear in PR