4,181 research outputs found
Coulomb field of an accelerated charge: physical and mathematical aspects
The Maxwell field equations relative to a uniformly accelerated frame, and
the variational principle from which they are obtained, are formulated in terms
of the technique of geometrical gauge invariant potentials. They refer to the
transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge
invariant "2+2" decomposition is used to see how the Coulomb field of a charge,
static in an accelerated frame, has properties that suggest features of
electromagnetism which are different from those in an inertial frame. In
particular, (1) an illustrative calculation shows that the Larmor radiation
reaction equals the electrostatic attraction between the accelerated charge and
the charge induced on the surface whose history is the event horizon, and (2) a
spectral decomposition of the Coulomb potential in the accelerated frame
suggests the possibility that the distortive effects of this charge on the
Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at
http://www.math.ohio-state.edu/~gerlac
On the analysis of island shape evolution from diffuse x-ray scattering of organic thin films and the implications for growth
Understanding the growth of organic semi-conducting molecules with shape
anisotropy is of high relevance to the processing of optoelectronic devices.
This work provides insight into the growth of thin films of the prototypical
rodlike organic semiconductor diindenoperylene on a microscopic level, by
analyzing in detail the film morphology. We model our data, which were obtained
by high-resolution grazing incidence small angle x-ray scattering (GISAXS),
using a theoretical description from small angle scattering theory derived for
simple liquids. Based on form factor calculations for different object types we
determine how the island shapes change in the respective layers. Atomic force
microscopy measurements approve our findings.Comment: 11 pages, 7 figures, accepted by Phys. Rev.
Covariant Perturbations of Schwarzschild Black Holes
We present a new covariant and gauge-invariant perturbation formalism for
dealing with spacetimes having spherical symmetry (or some preferred spatial
direction) in the background, and apply it to the case of gravitational wave
propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach
is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit
vector in addition to the timelike congruence, and decomposing all covariant
quantities with respect to this. The background Schwarzschild solution is
discussed and a covariant characterisation is given. We give the full
first-order system of linearised 1+1+2 covariant equations, and we show how, by
introducing (time and spherical) harmonic functions, these may be reduced to a
system of first-order ordinary differential equations and algebraic constraints
for the 1+1+2 variables which may be solved straightforwardly. We show how both
the odd and even parity perturbations may be unified by the discovery of a
covariant, frame- and gauge-invariant, transverse-traceless tensor describing
gravitational waves, which satisfies a covariant wave equation equivalent to
the Regge-Wheeler equation for both even and odd parity perturbations. We show
how the Zerilli equation may be derived from this tensor, and derive a similar
transverse traceless tensor equivalent to this equation. The so-called
`special' quasinormal modes with purely imaginary frequency emerge naturally.
The significance of the degrees of freedom in the choice of the two frame
vectors is discussed, and we demonstrate that, for a certain frame choice, the
underlying dynamics is governed purely by the Regge-Wheeler tensor. The two
transverse-traceless Weyl tensors which carry the curvature of gravitational
waves are discussed.Comment: 23 pages, 1 figure, Revtex 4. Submitted to Classical and Quantum
Gravity. Revised version is significantly streamlined with an important error
corrected which simplifies the presentatio
Employing electro-mechanical analogies for co-resonantly coupled cantilever sensors
Understanding the behaviour of mechanical systems can be facilitated and
improved by employing electro-mechanical analogies. These analogies enable
the use of network analysis tools as well as purely analytical treatment of
the mechanical system translated into an electric circuit. Recently, we
developed a novel kind of sensor set-up based on two coupled cantilever beams
with matched resonance frequencies (co-resonant coupling) and possible
applications in magnetic force microscopy and cantilever
magnetometry. In order to analyse the sensor's behaviour in detail,
we describe it as an electric circuit model. Starting from a simplified
coupled harmonic oscillator model with neglected damping, we gradually
increase the complexity of the system by adding damping and interaction
elements. For each stage, various features of the coupled system are
discussed and compared to measured data obtained with a co-resonant sensor.
Furthermore, we show that the circuit model can be used to derive sensor
parameters which are essential for the evaluation of measured data. Finally,
the much more complex circuit representation of a bending beam is discussed,
revealing that the simplified circuit model of a coupled harmonic oscillator
is a very good representation of the sensor system
A sediment agglutination on females of the free-living marine nematodeDesmodora schulzi
The Stern-Gerlach Experiment Revisited
The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment
of quantum physics providing evidence for several fundamental properties of
quantum systems. Based on today's knowledge we illustrate the different
benchmark results of the SGE for the development of modern quantum physics and
chemistry.
The SGE provided the first direct experimental evidence for angular momentum
quantization in the quantum world and thus also for the existence of
directional quantization of all angular momenta in the process of measurement.
It measured for the first time a ground state property of an atom, it produced
for the first time a `spin-polarized' atomic beam, it almost revealed the
electron spin. The SGE was the first fully successful molecular beam experiment
with high momentum-resolution by beam measurements in vacuum. This technique
provided a new kinematic microscope with which inner atomic or nuclear
properties could be investigated.
The original SGE is described together with early attempts by Einstein,
Ehrenfest, Heisenberg, and others to understand directional quantization in the
SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are
presented. The first realization of these proposals by Stern, Phipps, Frisch
and Segr\`e is described. The set-up suggested by Einstein can be considered an
anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which
the directional quantization process and possible interference effects of the
two different spin states are investigated.
In full agreement with the results of the new quantum theory directional
quantization appears as a general and universal feature of quantum
measurements. One experimental example for such directional quantization in
scattering processes is shown. Last not least, the early history of the
`almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig
Variational study of the Holstein polaron
The paper deals with the ground and the first excited state of the polaron in
the one dimensional Holstein model. Various variational methods are used to
investigate both the weak coupling and strong coupling case, as well as the
crossover regime between them. Two of the methods, which are presented here for
the first time, introduce interesting elements to the understanding of the
nature of the polaron. Reliable numerical evidence is found that, in the strong
coupling regime, the ground and the first excited state of the self-trapped
polaron are well described within the adiabatic limit. The lattice vibration
modes associated with the self-trapped polarons are analyzed in detail, and the
frequency softening of the vibration mode at the central site of the small
polaron is estimated. It is shown that the first excited state of the system in
the strong coupling regime corresponds to the excitation of the soft phonon
mode within the polaron. In the crossover regime, the ground and the first
excited state of the system can be approximated by the anticrossing of the
self-trapped and the delocalized polaron state. In this way, the connection
between the behavior of the ground and the first excited state is qualitatively
explained.Comment: 11 pages, 4 figures, PRB 65, 14430
Fundamental Constants and the Problem of Time
We point out that for a large class of parametrized theories, there is a
constant in the constrained Hamiltonian which drops out of the classical
equations of motion in configuration space. Examples include the mass of a
relativistic particle in free fall, the tension of the Nambu string, and
Newton's constant for the case of pure gravity uncoupled to matter or other
fields. In the general case, the classically irrelevant constant is
proportional to the ratio of the kinetic and potential terms in the
Hamiltonian. It is shown that this ratio can be reinterpreted as an {\it
unconstrained} Hamiltonian, which generates the usual classical equations of
motion. At the quantum level, this immediately suggests a resolution of the
"problem of time" in quantum gravity. We then make contact with a recently
proposed transfer matrix formulation of quantum gravity and discuss the
semiclassical limit. In this formulation, it is argued that a physical state
can obey a (generalized) Poincar\'e algebra of constraints, and still be an
approximate eigenstate of 3-geometry. Solutions of the quantum evolution
equations for certain minisuperspace examples are presented. An implication of
our proposal is the existence of a small, inherent uncertainty in the
phenomenological value of Planck's constant.Comment: 46 pages + 5 figures, LaTex, NBI-HE-94-3
Charge density wave and quantum fluctuations in a molecular crystal
We consider an electron-phonon system in two and three dimensions on square,
hexagonal and cubic lattices. The model is a modification of the standard
Holstein model where the optical branch is appropriately curved in order to
have a reflection positive Hamiltonian. Using infrared bounds together with a
recent result on the coexistence of long-range order for electron and phonon
fields, we prove that, at sufficiently low temperatures and sufficiently strong
electron-phonon coupling, there is a Peierls instability towards a period two
charge-density wave at half-filling. Our results take into account the quantum
fluctuations of the elastic field in a rigorous way and are therefore
independent of any adiabatic approximation. The strong coupling and low
temperature regime found here is independent of the strength of the quantum
fluctuations of the elastic field.Comment: 15 pages, 1 figur
Gravitational Collapse of a Radiating Shell
We study the collapse of a self-gravitating and radiating shell. Matter
constituting the shell is quantized and the construction is viewed as a
semiclassical model of possible black hole formation. It is shown that the
shell internal degrees of freedom are excited by the quantum non-adiabaticity
of the collapse and, consequently, on coupling them to a massless scalar field,
the collapsing matter emits a burst of coherent (thermal) radiation.Comment: LaTeX, 34 pages, 21 EPS figures include
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