7,620 research outputs found
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
Octonionic Representations of GL(8,R) and GL(4,C)
Octonionic algebra being nonassociative is difficult to manipulate. We
introduce left-right octonionic barred operators which enable us to reproduce
the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an
interesting connection between the structure of left-right octonionic barred
operators and generic 4x4 complex matrices. As an application we give an
octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted
Dirac Equation Studies in the Tunnelling Energy Zone
We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional
potential within the Dirac equation. We find the appearance of superluminal
transit times akin to the Hartman effect.Comment: 12 pages, 4 figure
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
Sea waves transport of inertial micro-plastics: Mathematical model and applications
Plastic pollution in seas and oceans has recently been recognized as one of the most impacting threats for the environment, and the increasing number of scientific studies proves that this is an issue of primary concern. Being able to predict plastic paths and concentrations within the sea is therefore fundamental to properly face this challenge. In the present work, we evaluated the effects of sea waves on inertial micro-plastics dynamics. We hypothesized a stationary input number of particles in a given control volume below the sea surface, solving their trajectories and distributions under a second-order regular wave. We developed an exhaustive group of datasets, spanning the most plausible values for particles densities and diameters and wave characteristics, with a specific focus on the Mediterranean Sea. Results show how the particles inertia significantly affects the total transport of such debris by waves
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
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
Quantum models related to fouled Hamiltonians of the harmonic oscillator
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator
which provide, at the classical level, the same equation of motion as the
conventional Hamiltonian. These Hamiltonians, say and , result
to be explicitly time-dependent and can be expressed as a formal rotation of
two cubic polynomial functions, and , of the canonical variables
(q,p).
We investigate the role of these fouled Hamiltonians at the quantum level.
Adopting a canonical quantization procedure, we construct some quantum models
and analyze the related eigenvalue equations. One of these models is described
by a Hamiltonian admitting infinite self-adjoint extensions, each of them has a
discrete spectrum on the real line. A self-adjoint extension is fixed by
choosing the spectral parameter of the associated eigenvalue
equation equal to zero. The spectral problem is discussed in the context of
three different representations. For , the eigenvalue equation is
exactly solved in all these representations, in which square-integrable
solutions are explicity found. A set of constants of motion corresponding to
these quantum models is also obtained. Furthermore, the algebraic structure
underlying the quantum models is explored. This turns out to be a nonlinear
(quadratic) algebra, which could be applied for the determination of
approximate solutions to the eigenvalue equations.Comment: 24 pages, no figures, accepted for publication on JM
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