10,985 research outputs found
PT-Symmetric Representations of Fermionic Algebras
A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum
mechanics from bosonic systems (systems for which ) to fermionic systems
(systems for which ). The current paper shows how the formalism
developed by Jones-Smith and Mathur can be used to construct PT-symmetric
matrix representations for operator algebras of the form ,
, , where
. It is easy to construct matrix
representations for the Grassmann algebra (). However, one can only
construct matrix representations for the fermionic operator algebra
() if ; a matrix representation does not exist for the
conventional value .Comment: 5 pages, 2 figure
Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
In a recent paper Bender and Mannheim showed that the unequal-frequency
fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in
which the energy eigenvalues are real and bounded below, the Hilbert-space
inner product is positive definite, and time evolution is unitary. Central to
that analysis was the recognition that the Hamiltonian of the
model is PT symmetric. This Hamiltonian was mapped to a conventional
Dirac-Hermitian Hamiltonian via a similarity transformation whose form was
found exactly. The present paper explores the equal-frequency limit of the same
model. It is shown that in this limit the similarity transform that was used
for the unequal-frequency case becomes singular and that becomes a
Jordan-block operator, which is nondiagonalizable and has fewer energy
eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart.
Thus, the equal-frequency PT theory emerges as a distinct realization of
quantum mechanics. The quantum mechanics associated with this Jordan-block
Hamiltonian can be treated exactly. It is shown that the Hilbert space is
complete with a set of nonstationary solutions to the Schr\"odinger equation
replacing the missing stationary ones. These nonstationary states are needed to
establish that the Jordan-block Hamiltonian of the equal-frequency
Pais-Uhlenbeck model generates unitary time evolution.Comment: 39 pages, 0 figure
Characterization of low thermal conductivity PAN-based carbon fibers
The microstructure and surface chemistry of eight low thermal conductivity (LTC) PAN-based carbon fibers were determined and compared with PAN-based fibers heat treated to higher temperatures. Based on wide-angle x ray diffraction, the LTC PAN fibers all appear to have a similar turbostratic structure with large 002 d-spacings, small crystallite sizes, and moderate preferred orientation. Limited small-angle x ray scattering (SAXS) results indicate that, with the exception of LTC fibers made by BASF, the LTC fibers do not have well developed pores. Transmission electron microscopy shows that the texture of the two LTC PAN-based fibers studied (Amoco T350/23X and /25X) consists of multiple sets of parallel, wavy, bent layers that interweave with each other forming a complex three dimensional network oriented randomly around the fiber axis. X ray photoelectron spectroscopy (XPS) analysis finds correlations between heat treated temperatures and the surface composition chemistry of the carbon fiber samples
Generation of interface for an Allen-Cahn equation with nonlinear diffusion
In this note, we consider a nonlinear diffusion equation with a bistable
reaction term arising in population dynamics. Given a rather general initial
data, we investigate its behavior for small times as the reaction coefficient
tends to infinity: we prove a generation of interface property
Complex Correspondence Principle
Quantum mechanics and classical mechanics are two very different theories,
but the correspondence principle states that quantum particles behave
classically in the limit of high quantum number. In recent years much research
has been done on extending both quantum mechanics and classical mechanics into
the complex domain. This letter shows that these complex extensions continue to
exhibit a correspondence, and that this correspondence becomes more pronounced
in the complex domain. The association between complex quantum mechanics and
complex classical mechanics is subtle and demonstrating this relationship
prequires the use of asymptotics beyond all orders.Comment: 4 pages, 6 figure
Nuevos conceptos en el ensayo Varestraint
En este trabajo se describen las modificaciones que se han hecho al ensayo Varesrrainr para obrener el máximo de información de una probeta. Se ensayaron aceros inoxidables del tipo 347 estándar y modificado, encontrando que la técnica usada puede detectar diferencias en la tendencia al agrietamiento de la zona fundida, zona afectada térmicamente del metal previamente fundido y del metal base
Modelling and experimental investigation of carangiform locomotion for control
We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior to that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system
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