869 research outputs found
Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes
Observable effects due to trembling motion (Zitterbewegung, ZB) of charge
carriers in bilayer graphene, monolayer graphene and carbon nanotubes are
calculated. It is shown that, when the charge carriers are prepared in the form
of gaussian wave packets, the ZB has a transient character with the decay time
of femtoseconds in graphene and picoseconds in nanotubes. Analytical results
for bilayer graphene allow us to investigate phenomena which accompany the
trembling motion. In particular, it is shown that the transient character of ZB
in graphene is due to the fact that wave subpackets related to positive and
negative electron energies move in opposite directions, so their overlap
diminishes with time. This behavior is analogous to that of the wave packets
representing relativistic electrons in a vacuum.Comment: 7 pages, 3 figures, augmented versio
Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation
Non-localities of Foldy-Wouthuysen and related transformations, which are
used to separate positive and negative energy states in the Dirac equation, are
investigated. Second moments of functional kernels generated by the
transformations are calculated, the transformed functions and their variances
are computed. It is shown that all the transformed quantities are smeared in
the coordinate space by the amount comparable to the Compton wavelength
.Comment: 7 pages, two figure
Zitterbewegung of Klein-Gordon particles and its simulation by classical systems
The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB,
trembling motion) of spin-zero particles in absence of fields and in the
presence of an external magnetic field. Both Hamiltonian and wave formalisms
are employed to describe ZB and their results are compared. It is demonstrated
that, if one uses wave packets to represent particles, the ZB motion has a
decaying behavior. It is also shown that the trembling motion is caused by an
interference of two sub-packets composed of positive and negative energy states
which propagate with different velocities. In the presence of a magnetic field
the quantization of energy spectrum results in many interband frequencies
contributing to ZB oscillations and the motion follows a collapse-revival
pattern. In the limit of non-relativistic velocities the interband ZB
components vanish and the motion is reduced to cyclotron oscillations. The
exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic
field is described on an operator level. The trembling motion of a KG particle
in absence of fields is simulated using a classical model proposed by Morse and
Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB
oscillations.Comment: 16 pages and 7 figure
Epicyclic orbital oscillations in Newton's and Einstein's dynamics
We apply Feynman's principle, ``The same equations have the same solutions'',
to Kepler's problem and show that Newton's dynamics in a properly curved 3-D
space is identical with that described by Einstein's theory in the 3-D optical
geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly,
Newton's formulae for Kepler's problem, in the case of nearly circular motion
in a static, spherically spherical gravitational potential accurately describe
strong field general relativistic effects, in particular vanishing of the
radial epicyclic frequency at the marginally stable orbit.Comment: 8 page
Adolescence and the next generation
Adolescent growth and social development shape the early development of offspring from preconception through to the post-partum period through distinct processes in males and females. At a time of great change in the forces shaping adolescence, including the timing of parenthood, investments in today\u27s adolescents, the largest cohort in human history, will yield great dividends for future generations
Non-locality of energy separating transformations for Dirac electrons in a magnetic field
We investigate a non-locality of Moss-Okninski transformation (MOT) used to
separate positive and negative energy states in the 3+1 Dirac equation for
relativistic electrons in the presence of a magnetic field. Properties of
functional kernels generated by the MOT are analyzed and kernel non-localities
are characterized by calculating their second moments parallel and
perpendicular to the magnetic field. Transformed functions are described and
investigated by computing their variances. It is shown that the non-locality of
the energy-separating transformation in the direction parallel to the magnetic
field is characterized by the Compton wavelength . In the
plane transverse to magnetic field the non-locality depends both on magnetic
radius and . The non-locality of MO
transformation for the 2+1 Dirac equation is also considered.Comment: 11 pages 3 figure
Block bond-order potential as a convergent moments-based method
The theory of a novel bond-order potential, which is based on the block
Lanczos algorithm, is presented within an orthogonal tight-binding
representation. The block scheme handles automatically the very different
character of sigma and pi bonds by introducing block elements, which produces
rapid convergence of the energies and forces within insulators, semiconductors,
metals, and molecules. The method gives the first convergent results for
vacancies in semiconductors using a moments-based method with a low number of
moments. Our use of the Lanczos basis simplifies the calculations of the band
energy and forces, which allows the application of the method to the molecular
dynamics simulations of large systems. As an illustration of this convergent
O(N) method we apply the block bond-order potential to the large scale
simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.
Atomic Scale Structure and Chemical Composition across Order-Disorder Interfaces
Through a combination of aberration-corrected high-resolution scanning transmission electron microscopy and three-dimensional atom probe tomography, the true atomic-scale structure and change in chemical composition across the complex order-disorder interface in a metallic alloy has been determined. The study reveals the presence of two interfacial widths, one corresponding to an order-disorder transition, and the other to the compositional transition across the interface, raising fundamental questions regarding the definition of the interfacial width in such systems
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