# Annalen der Physik

Published by Wiley-VCH Verlag

Online ISSN: 1521-3889

Published by Wiley-VCH Verlag

Online ISSN: 1521-3889

Publications

Article

We present a new plasmonic device architecture based on ultrasmooth metallic surfaces with buried plasmonic nanostructures. Using template-stripping techniques, ultrathin gold films with less than 5 Ã… surface roughness are optically coupled to an arbitrary arrangement of buried metallic gratings, rings, and nanodots. As a prototypical example, we present linear plasmonic gratings buried under an ultrasmooth 20 nm thick gold surface for biosensing. The optical illumination and collection are completely decoupled from the microfluidic delivery of liquid samples due to the backside, reflection-mode geometry. This allows for sensing with opaque or highly scattering liquids. With the buried nanostructure design, we maintain high sensitivity and decoupled backside (reflective) optical access as with traditional prism-based surface plasmon resonance (SPR) sensors. In addition, we also gain the benefits offered by nanoplasmonic sensors such as spectral tunability and high-resolution, wide-field SPR imaging with normal-incidence epi-illumination that is simple to construct and align. Beyond sensing, our buried plasmonic nanostructures with ultrasmooth metallic surfaces can benefit nanophotonic waveguides, surface-enhanced spectroscopy, nanolithography, and optical trapping.

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Article

In my reply I present a re-analysis of the data of the Smithsonian Astrophysical Observatory (SAO). For this, a new data reduction method is introduced, allowing a drastic lowering of data scatter, so that the time series of the reduced data clearly shows the â‰ˆ 1 % variation of the terrestric solar irradiance in parallel with solar activity. The implications are discussed. In his reply the author present a re-analysis of the data of the Smithsonian Astrophysical Observatory (SAO). For this, a new data reduction method is introduced, allowing a drastic lowering of data scatter, so that the time series of the reduced data clearly shows the â‰ˆ 1 % variation of the terrestric solar irradiance in parallel with solar activity. The implications are discussed.

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Article

An analysis of ground-based observations of solar irradiance was recently published in this journal, reporting an apparent increase of solar irradiance on the ground of the order of 1% between solar minima and maxima [1]. Since the corresponding variations in total solar irradiance on top of the atmosphere are accurately determined from satellite observations to be of the order of 0.1% only [2], the one order of magnitude stronger effect in the terrestrial insolation data was interpreted as evidence for cosmic-ray induced aerosol formation in the atmosphere. In my opinion, however, this result does not reflect reality. Using the energy budget of Earth's surface, I show that changes of ground-based insolation with the solar cycle of the order of 1% between solar minima and maxima would result in large surface air temperature variations which are inconsistent with the instrumental record. It would appear that the strong variations of terrestrial irradiance found by [1] are due to the uncorrected effects of volcanic or local aerosols and seasonal variations. Taking these effects into account, I find a variation of terrestrial insolation with solar activity which is of the same order as the one measured from space, bringing the surface energy budget into agreement with the solar signal detected in temperature data.

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Article

This study demonstrates the proof-of-principle of rapid surface modification of plasmonic nanostructured materials with oligonucleotides using low power microwave heating. Due to their interesting optical and electronic properties, silver nanoparticle films (SNFs, 2 nm thick) deposited onto glass slides were used as the model plasmonic nanostructured materials. Rapid surface modification of SNFs with oligonucleotides was carried out using two strategies (1) Strategy 1: for ss-oligonucleotides, surface hybridization and (2) Strategy 2: for ds-oligonucleotides, solution hybridization), where the samples were exposed to 10, 15, 30 and 60 seconds microwave heating. To assess the efficacy of our new rapid surface modification technique, identical experiments carried out without the microwave heating (i.e., conventional method), which requires 24 hours for the completion of the identical steps. It was found that SNFs can be modified with ss- and ds-oligonucleotides in 10 seconds, which typically requires several hours of incubation time for the chemisorption of thiol groups on to the planar metal surface using conventional techniques.

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Article

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated at finite temperatures. We present results for the stationary current for the case of a piecewise linear potential, especially for potentials being close to the case with inversion symmetry. The aim is to study the stationary current as a function of the potential. Depending on the form of the potential, the current changes sign once or even twice as a function of the correlation time of the potential fluctuations. To explain these current reversals, several mechanisms are proposed. Finally, we discuss to what extent the model is useful to understand the motion of biomolecular motors.

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Article

In 1912, Otto Sackur and Hugo Tetrode independently put forward an equation
for the absolute entropy of a monoatomic ideal gas and published it in "Annalen
der Physik." The grand achievement in the derivation of this equation was the
discretization of phase space for massive particles, expressed as \delta q
\delta p = h, where q and p are conjugate variables and h is Planck's constant.
Due to the dependence of the absolute entropy on Planck's constant, Sackur and
Tetrode were able to devise a test of their equation by applying it to the
monoatomic vapor of mercury; from the satisfactory numerical comparison of h
obtained from thermodynamic data on mercury with Planck's value from black-body
radiation, they inferred the correctness of their equation. In this review we
highlight this almost forgotten episode of physics, discuss the arguments
leading to the derivation of the Sackur--Tetrode equation and outline the
method how this equation was tested with thermodynamic data.

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Article

Using Raman spectroscopy and transport measurements we investigate thin epitaxial films of Y{1-x}(Pr,Ca)xBa2Cu3O{6+y}. We explore the electronic Raman responses obtained after subtraction of phononic excitations, and the 2Delta peaks that form out of the electronic background below Tc. We find that the energy of the B1g 2Delta peak increases monotonically with decreasing doping until the peaks become unresolvable. In contrast, the peaks in A1g symmetry follow Tc being resolvable in the Pr-doped films. The B2g responses are weak and a 2Delta peak is only detected at the highest doping level. As a consequence of strong electron-phonon coupling, the B1g phonon at 340 cm^-1 exhibits a pronounced Fano-type line shape. We use a phenomenological model to describe the line shape that takes into account real and imaginary part of the electronic response. It allows us to obtain the self-energy corrections and the mass- enhancement factor lambda as a measure of the coupling. In the normal state we find lambda=0.015 around optimal doping and decreasing values with decreasing doping. The electron-phonon coupling increases strongly below T_c in overdoped samples in which the B1g 2Delta peaks appear in the vicinity of the phonon. Self-energy effects observed in the superconducting state can only partly be assigned to the redistributing electronic response. Anomalies with respect to frequency, linewidth, and intensity remain. They appear at increasing tempera- tures with decreasing doping and we provide evidence that they are connected to the presence of the pseudogap. We supplement our study by a comparison with single crystal data and investigate the influence of site-substitutional disorder on the electronic response and the electron-phonon interaction. Comment: 46 pages including 20 figures, accepted for publication in Annalen der Physik to appear August 1999. Figures and PDF-document are available under http://www.physnet.uni-hamburg.de/home/vms/bock/annalen.htm

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Article

We review the work and life of Otto Stern who developed the molecular beam
technique and with its aid laid the foundations of experimental atomic physics.
Among the key results of his research are: the experimental determination of
the Maxwell-Boltzmann distribution of molecular velocities (1920), experimental
demonstration of space quantization of angular momentum (1922), diffraction of
matter waves comprised of atoms and molecules by crystals (1931) and the
determination of the magnetic dipole moments of the proton and deuteron (1933).

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Article

Anderson localization of Bogoliubov excitations is studied for disordered
lattice Bose gases in planar quasi-one-dimensional geometries. The inverse
localization length is computed as function of energy by a numerical
transfer-matrix scheme, for strips of different widths. These results are
described accurately by analytical formulas based on a weak-disorder expansion
of backscattering mean free paths.

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Article

We review recent advances in the field of full counting statistics (FCS) of charge transfer through impurities imbedded into strongly correlated one-dimensional metallic systems, modelled by Tomonaga-Luttinger liquids (TLLs). We concentrate on the exact analytic solutions for the cumulant generating function (CGF), which became available recently and apply these methods in order to obtain the FCS of a non-trivial contact between two crossed TLL.

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Article

We discuss the generalization of Doubly Special Relativity to a curved de Sitter background. The model has three fundamental observer-independent scales, the velocity of light c, the de Sitter radius Î±, and the Planck energy Îº, and can be realized through a nonlinear action of the de Sitter group on a noncommutative position space. We consider different choices of coordinates on the de Sitter hyperboloid that, although equivalent, may be more suitable for treating different problems. Also the momentum space can be described as a hyperboloid embedded in a five-dimensional space, but in this case different choices of coordinates lead to inequivalent models. We investigate the kinematics and the Hamiltonian dynamics of some specific models and describe some of their phenomenological consequences. Finally, we show that it is possible to construct a model exhibiting a duality for the interchange of positions and momenta together with the interchange of Î± and Îº.

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Article

The h index was introduced by Hirsch to quantify an individual's scientific research output. It has been widely used in different fields to show the relevance of the research work of prominent scientists. I have worked out 26 practical cases of physicists which are not so prominent. Therefore this case study should be more relevant to discuss various features of the Hirsch index which are interesting or disturbing or both for the more average situation. In particular, I investigate quantitatively some pitfalls in the evaluation and the influence of self-citations.

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Article

We develop a quasiclassical method based on the path integral formalism, to study the influence of disorder on magnetooscillations of the density of states and conductivity. The treatment is appropriate for electron systems in the presence of a random potential with large correlation length or a random magnetic field, which are characterisitic features of various 2D electronic systems presently studied in experiment. In particular, we study the system of composite fermions in the fractional quantum Hall effect device, which are coupled to the Chern--Simons field and subject to a long--range random potential.

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Article

The negative magnetoresistance due to weak localization is investigated in the two-dimensional metallic state of Si-MOS structures for high conductance values between 35 and 120 e^2/h. The extracted phase coherence time is equal to the momentum relaxation time at 10 K but nearly 100 times longer at the lowest temperature. Nevertheless, only weak logarithmic corrections to the conductivity are present in the investigated temperature and concentration range thus proving the absence of strong quantum effects due to electron-electron interaction. From saturation effects of the phase coherence time a lower boundary for spin-orbit scattering of about 200 ps is estimated. Comment: 4 pages, 3 figures, Conf. on "Localization: Disorder and Interaction in Transport Phenomena" July 29 - August 2, 1999, Hamburg, Germany

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Article

The article provides full-analytic gravitational wave (GW) forms for
eccentric nonspinning compact binaries of arbitrary mass ratio in the time
Fourier domain. The semi-analytical property of recent descriptions, i.e. the
demand of inverting the higher-order Kepler equation numerically but keeping
all other computations analytic, is avoided for the first time. The article is
a completion of a previous one (Tessmer and Sch\"afer, Phys. Rev. D 82, 124064
(2010)) to second post-Newtonian (2PN) order in the harmonic GW amplitude and
conservative orbital dynamics. A fully analytical inversion formula of the
Kepler equation in harmonic coordinates is provided, as well as the analytic
time Fourier expansion of trigonometric functions of the eccentric anomaly in
terms of sines and cosines of the mean anomaly. Tail terms are not considered.

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Article

We present a generating functional producing quark wave functions of all Fock states in the octet, decuplet and antidecuplet baryons in the mean field approximation, both in the rest and infinite momentum frames. In particular, for the usual octet and decuplet baryons we get the SU(6)-symmetric wave functions for their 3-quark component but with specific corrections from relativism and from additional quark-antiquark pairs. For the exotic antidecuplet baryons we obtain the 5-quark wave function. Comment: 20 p., 6 figs

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Article

We investigate the dynamics of electrons in the vicinity of the Anderson transition in $d=3$ dimensions. Using the exact eigenstates from a numerical diagonalization, a number of quantities related to the critical behavior of the diffusion function are obtained. The relation $\eta = d-D_{2}$ between the correlation dimension $D_{2}$ of the multifractal eigenstates and the exponent $\eta$ which enters into correlation functions is verified. Numerically, we have $\eta\approx 1.3$. Implications of critical dynamics for experiments are predicted. We investigate the long-time behavior of the motion of a wave packet. Furthermore, electron-electron and electron-phonon scattering rates are calculated. For the latter, we predict a change of the temperature dependence for low $T$ due to $\eta$. The electron-electron scattering rate is found to be linear in $T$ and depends on the dimensionless conductance at the critical point.

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Article

We construct a simple U(1) hidden sector model of metastable dark matter that
could explain excess 511 keV gamma rays from the galactic center as observed by
INTEGRAL, through inelastic scattering of dark matter followed by its decay.
Although the model is highly constrained, it naturally accommodates dark matter
with mass and cross section in the range suggested by the CoGeNT and CRESST
experiments. The dark gauge boson that mediates the interactions with standard
model matter has a mass of several hundred MeV, and might be discovered by
heavy photon detection experiments, including APEX, MAMI and HPS.

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Article

We present a novel approach for designing new hard magnets by forming stacks of existing binary magnets to enhance the magneto crystalline anisotropy. This is followed by an attempt at reducing the amount of expensive metal in these stacks by replacing it with cheaper metal with similar ionic radius. This strategy is explored using examples of FePt, MnAl and MnGa. In this study a few promising materials are suggested as good candidates for hard magnets: stacked binary FePt2MnGa2 in structure where each magnetic layer is separated by two non-magnetic layers, FePtMnGa and FePtMnAl in hexagonally distorted Heusler structures and FePt0.5Ti0.5MnAl.

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Article

We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so-called GW and dynamical mean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable. The authors propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so-called GW and dynamical mean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable.

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Article

Acceleration-induced nonlocality and the corresponding Lorentz-invariant
nonlocal field equations of accelerated systems in Minkowski spacetime are
discussed. Under physically reasonable conditions, the nonlocal equation of
motion of the field can be derived from a variational principle of stationary
action involving a nonlocal Lagrangian that is simply obtained by composing the
local inertial Lagrangian with the nonlocal transformation of the field to the
accelerated system. The implications of this approach for the electromagnetic
and Dirac fields are briefly discussed.

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Article

The nonlocal electrodynamics of accelerated systems is discussed in connection with the development of Lorentz-invariant nonlocal field equations. Nonlocal Maxwell's equations are presented explicitly for certain linearly accelerated systems. In general, the field equations remain nonlocal even after accelerated motion has ceased. Comment: LaTeX file, 23 pages, no figures, accepted for publication in Annalen der Physik

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Article

We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an otherwise identical momentarily comoving inertial observer. We find that consistency can be achieved only in a rather limited neighborhood around the observer with linear dimensions that are negligibly small compared to the characteristic acceleration length of the observer. Comment: LaTeX file (annalen.cls), 4 figures, 17 pages, accepted for publication in Annalen der Physik

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Article

It has been shown that an improved estimation of quantum vacuum energy can yield not only acceptable but also experimentally sensible results. The very idea consists in a straightforward extraction of gravitationally interacting part of the full quantum vacuum energy by means of gauge transformations. The implementation of the idea has been performed in the formalism of effective action, in the language of Schwinger's proper time and the Seeley--DeWitt heat kernel expansion, in the background of the Friedmann--Robertson--Walker geometry.

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Article

Based on the generalized principle of relativity and the ensuing symmetry, we
have shown that there are only two possible types of transformations between
uniformly accelerated systems. The first allowable type of transformation holds
if and only if the Clock Hypothesis is true. If the Clock Hypothesis is not
true, the transformation is of Lorentz-type and implies the existence of a
universal maximal acceleration $a_m$.
We present an extension of relativistic dynamics for which all admissible
solutions will have have a speed bounded by the speed of light $c$ and the
acceleration bounded by $a_m$. An additional Doppler type shift for an
accelerated source is predicted. The formulas for such shift are the same as
for the usual Doppler shift with $v/c$ replaced by $a/a_m$.
The W. K\"{u}ndig experiment of measurement of the transverse Doppler shift
in an accelerated system was also exposed to a longtitudal shift due to the
acceleration. This experiment, as reanalyzed by Kholmetskii et al, shows that
the Clock Hypothesis is not valid. Based on the results of this experiment, we
predict that the value of the maximal acceleration $a_m$ is of the order
$10^{19}m/s^2$. Moreover, our analysis provides a way to measure experimentally
the maximal acceleration with existing technology.

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Article

The paper is devoted to an explanation of the accelerated rate of expansion
of the Universe. Usually the acceleration of the Universe, which is described
by FRW metric, is due to dark energy. It is shown that this effect may be
considered as a manifestation of torsion tensor for a flat Universe in the
realm of Teleparallel gravity. An observer with radial field velocity obey
Hubble's Law. As a consequence it is established that this is radial
acceleration in a flat Universe. In Eq. (\ref{24}) the acceleration is written
in terms of the deceleration parameter, the Hubble's constant and the proper
distance. This may be interpreted as an acceleration of the Universe.

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Article

The purpose of this paper is to explain clearly why nonlocality must be an
essential part of the theory of relativity. In the standard local version of
this theory, Lorentz invariance is extended to accelerated observers by
assuming that they are pointwise inertial. This locality postulate is exact
when dealing with phenomena involving classical point particles and rays of
radiation, but breaks down for electromagnetic fields, as field properties in
general cannot be measured instantaneously. The problem is corrected in
nonlocal relativity by supplementing the locality postulate with a certain
average over the past world line of the observer.

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Article

Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal coordinate system constructed along its worldline, the particles in the swarm that move along the radial direction and are ultrarelativistic (that is, they have speeds above c/sqrt(2)) decelerate toward this terminal speed. On the other hand, the swarm particles that are ultrarelativistic and move in directions normal to the radial (jet) directions accelerate to almost the speed of light by the gravitational tidal force of the mass M. The implications of these effects as well as the influence of the higher-order terms on the tidal acceleration mechanism are investigated. The observational evidence in support of these general relativistic effects is briefly discussed.

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Article

The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. We show that only kinetic memory is acceptable, since dynamic memory leads to divergences for nonuniform accelerated motion. Comment: LaTeX file, 6 PS figures, 34 pages

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Article

The concept of gauge invariance is one of the most subtle and useful concepts
in modern theoretical physics. It is one of the Standard Model cornerstones.
The main benefit due to the gauge invariance is that it can permit the
comprehension of difficult systems in physics with an arbitrary choice of a
reference frame at every instant of time. It is the objective of this work to
show a path of obtaining gauge invariant theories from non-invariant ones. Both
are named also as first- and second-class theories respectively, obeying
Dirac's formalism. Namely, it is very important to understand why it is always
desirable to have a bridge between gauge invariant and non-invariant theories.
Once established, this kind of mapping between first-class (gauge invariant)
and second-class systems, in Dirac's formalism can be considered as a sort of
equivalence. This work describe this kind of equivalence obtaining a gauge
invariant theory starting with a non-invariant one using the symplectic
embedding formalism developed by some of us some years back. To illustrate the
procedure it was analyzed both Abelian and non-Abelian theories. It was
demonstrated that this method is more convenient than others. For example, it
was shown exactly that this embedding method used here does not require any
special modification to handle with non-Abelian systems.

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Article

In the context of the exact factorization of the electron-nuclear wave
function, the coupling between electrons and nuclei beyond the adiabatic regime
is encoded (i) in the time-dependent vector and scalar potentials and (ii) in
the electron-nuclear coupling operator. The former appear in the
Schroedinger-like equation that drives the evolution of the nuclear degrees of
freedom, whereas the latter is responsible for inducing non-adiabatic effects
in the electronic evolution equation. As we have devoted previous studies to
the analysis of the vector and scalar potentials, in this paper we focus on the
properties of the electron-nuclear coupling operator, with the aim of
describing a numerical procedure to approximate it within a semiclassical
treatment of the nuclear dynamics.

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Article

Variational wave functions are very useful for describing the panoply of
ground states found in interacting many-electron systems. Some particular trial
states are "adiabatically" linked to a reference state, from which they borrow
the essential properties. A prominent example is the Gutzwiller ansatz, where
one starts with the filled Fermi sea. A simple soluble example, the anisotropic
XY chain, illustrates the adiabatic continuity of this class of wave functions.
To describe symmetry breaking, one has to modify the reference state
accordingly. Alternatively, a quantum phase transition can be described by a
pair of variational wave functions, starting at weak and strong coupling,
respectively.

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Article

We develop a resource efficient method by which the ground-state of an
arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state
of a (k-1)-local optimization Hamiltonian. This result is important because
adiabatic quantum algorithms are often most easily formulated using many-body
interactions but experimentally available interactions are generally 2-body. In
this context, the efficiency of a reduction gadget is measured by the number of
ancilla qubits required as well as the amount of control precision needed to
implement the resulting Hamiltonian. First, we optimize methods of applying
these gadgets to obtain 2-local Hamiltonians using the least possible number of
ancilla qubits. Next, we show a novel reduction gadget which minimizes control
precision and a heuristic which uses this gadget to compile 3-local problems
with a significant reduction in control precision. Finally, we present numerics
which indicate a substantial decrease in the resources required to implement
randomly generated, 3-body optimization Hamiltonians when compared to other
methods in the literature.

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Article

Conformal transformations play a widespread role in gravity theories in
regard to their cosmological and other implications. In the pure metric theory
of gravity, conformal transformations change the frame to a new one wherein one
obtains a conformal-invariant scalar-tensor theory such that the scalar field,
deriving from the conformal factor, is a ghost.
In this work, conformal transformations and ghosts will be analyzed in the
framework of the metric-affine theory of gravity. Within this framework, metric
and connection are independent variables, and hence, transform independently
under conformal transformations. It will be shown that, if affine connection is
invariant under conformal transformations then the scalar field under concern
is a non-ghost, non-dynamical field. It is an auxiliary field at the classical
level, and might develop a kinetic term at the quantum level.
Alternatively, if connection transforms additively with a structure similar
to yet more general than that of the Levi-Civita connection, the resulting
action describes the gravitational dynamics correctly, and more importantly,
the scalar field becomes a dynamical non-ghost field. The equations of motion,
for generic geometrical and matter-sector variables, do not reduce connection
to the Levi-Civita connection, and hence, independence of connection from
metric is maintained. Therefore, metric-affine gravity provides an arena in
which ghosts arising from conformal factor are avoided thanks to the
independence of connection from the metric.

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Article

Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter). We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the metric-affine formalism. The result is that the extra curvature and torsion degrees of freedom can be dealt under the standard of an effective scalar field of fully geometric origin. The initial value problem for such theories is also discussed. Comment: 10 pages, Grassmann Meeting 2009, Annalen der Physik

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Article

The quantum algebra of observables postulated in hep-th/9805057 is constructed up to degree five. All independent relations of degree four are given; they involve three as yet undetermined parameters. Definitions and symbols are used as introduced in the above-mentioned article. Comment: 5 pages, no figures, addendum to hep-th/9805057

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Article

A relevant part of the quantum algebra of observables for the closed bosonic strings moving in 1+3-dimensional Minkowski space is presented in the form of generating relations involving still one, as yet undetermined, real free parameter. Comment: 34 pages, Latex2e, no figures; one miscount (and its consequences) corrected on page 30, line seven from below

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Chapter

We have studied the competition between fission and evaporation as fragmentation channels of excited doubly charged Sodium clusters. We have used an Extended Thomas-Fermi method and the jellium model. A preliminary account of the influence of shell effects is also given.

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Article

The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_{n}^{(\mu,\nu)}(x), where \mu>-1, \nu>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2} molecules are also calculated and compared with the previous models and experiments. Comment: 18 pages

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Article

By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many-particle states differing in electron number and spin if the electron density is away from half-filling. The grand partition sum is calculated and the specific heat, the suszeptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. Furthermore, for both the grand canonical and the canonical ensemble the so called crossing points of the suszeptibility are calculated. They confirm the universal value predicted by Vollhardt [1]. Comment: 42 pages, including 9 tables and 22 figures, RevTeX 3.1

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Article

The solvability of The Dirac equation is studied for the exponential-type
potentials with the pseudospin symmetry by using the parametric generalization
of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the
corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse
potentials are obtained within the framework of an approximation to the
spin-orbit coupling term, so the solutions are given for any value of the
spin-orbit quantum number $\kappa=0$, or $\kappa \neq 0$.

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Article

We have calculated wave functions and matrix elements of the dipole operator in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we have considered two cases. First, we have studied the fluctuations as an external Aharonov-Bohm flux is varied. Second, we have considered the influence of incipient localization. In both cases, the statistical properties of the eigenfunctions are non-trivial, in that the joint probability distribution function of eigenvalues and eigenvectors does no longer factorize. We report on detailed comparisons with analytical results, obtained within the non-linear sigma model and/or the semiclassical approach. Comment: 5 pages, 4 figures, to appear in Proceedings PILS'98 in Ann. Physik Leibzig 1998

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