3,277 research outputs found

### The generalization of the Regge-Wheeler equation for self-gravitating matter fields

It is shown that the dynamical evolution of perturbations on a static
spacetime is governed by a standard pulsation equation for the extrinsic
curvature tensor. The centerpiece of the pulsation equation is a wave operator
whose spatial part is manifestly self-adjoint. In contrast to metric
formulations, the curvature-based approach to gravitational perturbation theory
generalizes in a natural way to self-gravitating matter fields. For a certain
relevant subspace of perturbations the pulsation operator is symmetric with
respect to a positive inner product and therefore allows spectral theory to be
applied. In particular, this is the case for odd-parity perturbations of
spherically symmetric background configurations. As an example, the pulsation
equations for self-gravitating, non-Abelian gauge fields are explicitly shown
to be symmetric in the gravitational, the Yang Mills, and the off-diagonal
sector.Comment: 4 pages, revtex, no figure

### 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

### On the exciton binding energy in a quantum well

We consider a model describing the one-dimensional confinement of an exciton
in a symmetrical, rectangular quantum-well structure and derive upper and lower
bounds for the binding energy $E_b$ of the exciton. Based on these bounds, we
study the dependence of $E_b$ on the width of the confining potential with a
higher accuracy than previous reports. For an infinitely deep potential the
binding energy varies as expected from $1 Ry$ at large widths to $4 Ry$ at
small widths. For a finite potential, but without consideration of a mass
mismatch or a dielectric mismatch, we substantiate earlier results that the
binding energy approaches the value $1 Ry$ for both small and large widths,
having a characteristic peak for some intermediate size of the slab. Taking the
mismatch into account, this result will in general no longer be true. For the
specific case of a $Ga_{1-x}Al_{x}As/GaAs/Ga_{1-x}Al_{x}As$ quantum-well
structure, however, and in contrast to previous findings, the peak structure is
shown to survive.Comment: 32 pages, ReVTeX, including 9 figure

### Money in monetary policy design: monetary cross-checking in the New-Keynesian model

In the New-Keynesian model, optimal interest rate policy under uncertainty is formulated without reference to monetary aggregates as long as certain standard assumptions on the distributions of unobservables are satisfied. The model has been criticized for failing to explain common trends in money growth and inflation, and that therefore money should be used as a cross-check in policy formulation (see Lucas (2007)). We show that the New-Keynesian model can explain such trends if one allows for the possibility of persistent central bank misperceptions. Such misperceptions motivate the search for policies that include additional robustness checks. In earlier work, we proposed an interest rate rule that is near-optimal in normal times but includes a cross-check with monetary information. In case of unusual monetary trends, interest rates are adjusted. In this paper, we show in detail how to derive the appropriate magnitude of the interest rate adjustment following a significant cross-check with monetary information, when the New-Keynesian model is the central bank’s preferred model. The cross-check is shown to be effective in offsetting persistent deviations of inflation due to central bank misperceptions. Keywords: Monetary Policy, New-Keynesian Model, Money, Quantity Theory, European Central Bank, Policy Under Uncertaint

### Disorder-Induced Resistive Anomaly Near Ferromagnetic Phase Transitions

We show that the resistivity rho(T) of disordered ferromagnets near, and
above, the Curie temperature T_c generically exhibits a stronger anomaly than
the scaling-based Fisher-Langer prediction. Treating transport beyond the
Boltzmann description, we find that within mean-field theory, d\rho/dT exhibits
a |T-T_c|^{-1/2} singularity near T_c. Our results, being solely due to
impurities, are relevant to ferromagnets with low T_c, such as SrRuO3 or
diluted magnetic semiconductors, whose mobility near T_c is limited by
disorder.Comment: 5 pages, 3 figures; V2: with a few clarifications, as publishe

### Observing Brownian motion in vibration-fluidized granular matter

At the beginning of last century, Gerlach and Lehrer observed the rotational
Brownian motion of a very fine wire immersed in an equilibrium environment, a
gas. This simple experiment eventually permitted the full development of one of
the most important ideas of equilibrium statistical mechanics: the very
complicated many-particle problem of a large number of molecules colliding with
the wire, can be represented by two macroscopic parameters only, namely
viscosity and the temperature. Can this idea, mathematically developed in the
so-called Langevin model and the fluctuation-dissipation theorem be used to
describe systems that are far from equilibrium? Here we address the question
and reproduce the Gerlach and Lehrer experiment in an archetype non-equilibrium
system, by immersing a sensitive torsion oscillator in a granular system of
millimetre-size grains, fluidized by strong external vibrations. The
vibro-fluidized granular medium is a driven environment, with continuous
injection and dissipation of energy, and the immersed oscillator can be seen as
analogous to an elastically bound Brownian particle. We show, by measuring the
noise and the susceptibility, that the experiment can be treated, in first
approximation, with the same formalism as in the equilibrium case, giving
experimental access to a ''granular viscosity'' and an ''effective
temperature'', however anisotropic and inhomogeneous, and yielding the
surprising result that the vibro-fluidized granular matter behaves as a
''thermal'' bath satisfying a fluctuation-dissipation relation

### Mean parameter model for the Pekar-Fr\"{o}hlich polaron in a multilayered heterostructure

The polaron energy and the effective mass are calculated for an electron
confined in a finite quantum well constructed of $GaAs/Al_x Ga_{1-x} As$
layers. To simplify the study we suggest a model in which parameters of a
medium are averaged over the ground-state wave function. The rectangular and
the Rosen-Morse potential are used as examples.
To describe the confined electron properties explicitly to the second order
of perturbations in powers of the electron-phonon coupling constant we use the
exact energy-dependent Green function for the Rosen-Morse confining potential.
In the case of the rectangular potential, the sum over all intermediate virtual
states is calculated. The comparison is made with the often used leading term
approximation when only the ground-state is taken into account as a virtual
state. It is shown that the results are quite different, so the incorporation
of all virtual states and especially those of the continuous spectrum is
essential.
Our model reproduces the correct three-dimensional asymptotics at both small
and large widths. We obtained a rather monotonous behavior of the polaron
energy as a function of the confining potential width and found a peak of the
effective mass. The comparison is made with theoretical results by other
authors. We found that our model gives practically the same (or very close)
results as the explicit calculations for potential widths $L \geq 10 \AA$.Comment: 12 pages, LaTeX, including 5 PS-figures, subm. to Phys. Rev. B, new
data are discusse

### The astrometric Gaia-FUN-SSO observation campaign of 99 942 Apophis

Astrometric observations performed by the Gaia Follow-Up Network for Solar
System Objects (Gaia-FUN-SSO) play a key role in ensuring that moving objects
first detected by ESA's Gaia mission remain recoverable after their discovery.
An observation campaign on the potentially hazardous asteroid (99 942) Apophis
was conducted during the asteroid's latest period of visibility, from
12/21/2012 to 5/2/2013, to test the coordination and evaluate the overall
performance of the Gaia-FUN-SSO . The 2732 high quality astrometric
observations acquired during the Gaia-FUN-SSO campaign were reduced with the
Platform for Reduction of Astronomical Images Automatically (PRAIA), using the
USNO CCD Astrograph Catalogue 4 (UCAC4) as a reference. The astrometric
reduction process and the precision of the newly obtained measurements are
discussed. We compare the residuals of astrometric observations that we
obtained using this reduction process to data sets that were individually
reduced by observers and accepted by the Minor Planet Center. We obtained 2103
previously unpublished astrometric positions and provide these to the
scientific community. Using these data we show that our reduction of this
astrometric campaign with a reliable stellar catalog substantially improves the
quality of the astrometric results. We present evidence that the new data will
help to reduce the orbit uncertainty of Apophis during its close approach in
2029. We show that uncertainties due to geolocations of observing stations, as
well as rounding of astrometric data can introduce an unnecessary degradation
in the quality of the resulting astrometric positions. Finally, we discuss the
impact of our campaign reduction on the recovery process of newly discovered
asteroids.Comment: Accepted for publication in A&

### Coupled surface polaritons and the Casimir force

The Casimir force between metallic plates made of realistic materials is
evaluated for distances in the nanometer range. A spectrum over real
frequencies is introduced and shows narrow peaks due to surface resonances
(plasmon polaritons or phonon polaritons) that are coupled across the vacuum
gap. We demonstrate that the Casimir force originates from the attraction
(repulsion) due to the corresponding symmetric (antisymmetric) eigenmodes,
respectively. This picture is used to derive a simple analytical estimate of
the Casimir force at short distances. We recover the result known for Drude
metals without absorption and compute the correction for weakly absorbing
materials.Comment: revised version submitted to Phys. Rev. A, 06 November 200

### 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

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