pinecone/core-2020-05-10-deduplication huggingface dataset:
The self-energy of the uniform electron gas in the second order of
  exchange

The on-shell self-energy of the homogeneous electron gas in second order of
exchange, $\Sigma_{2{\rm x}}= {\rm Re} \Sigma_{2{\rm x}}(k_{\rm F},k_{\rm
F}^2/2)$, is given by a certain integral. This integral is treated here in a
similar way as Onsager, Mittag, and Stephen [Ann. Physik (Leipzig) {\bf 18}, 71
(1966)] have obtained their famous analytical expression $e_{2{\rm x}}={1/6}\ln
2- 3\frac{\zeta(3)}{(2\pi)^2}$ (in atomic units) for the correlation energy in
second order of exchange. Here it is shown that the result for the
corresponding on-shell self-energy is $\Sigma_{2{\rm x}}=e_{2{\rm x}}$. The
off-shell self-energy $\Sigma_{2{\rm x}}(k,\omega)$ correctly yields $2e_{2{\rm
x}}$ (the potential component of $e_{2{\rm x}}$) through the Galitskii-Migdal
formula. The quantities $e_{2{\rm x}}$ and $\Sigma_{2{\rm x}}$ appear in the
high-density limit of the Hugenholtz-van Hove (Luttinger-Ward) theorem.Comment: 12 pages, 2 figure
Dynamical Adjustment of Propagators in Renormalization Group Flows

A class of continuous renormalization group flows with a dynamical adjustment
of the propagator is introduced and studied theoretically for fermionic and
bosonic quantum field theories. The adjustment allows to include self--energy
effects nontrivially in the denominator of the propagator and to adapt the
scale decomposition to a moving singularity, and hence to define flows of Fermi
surfaces in a natural way. These flows require no counterterms, but the
counterterms used in earlier treatments can be constructed using them. The
influence of propagator adjustment on the strong--coupling behaviour of flows
is examined for a simple example, and some conclusions about the strong
coupling behaviour of renormalization group flows are drawn.Comment: LaTeX, 54 pages, 3 postscript figure
From RHIC to LHC: A relativistic diffusion approach

We investigate the energy dependence of stopping and hadron production in
high-energy heavy-ion collisions based on a three-sources Relativistic
Diffusion Model. The transport coefficients are extrapolated from Au + Au and
Cu + Cu at RHIC energies (sqrt{s_NN)=19.6 - 200 GeV) to Pb + Pb at LHC energies
sqrt{s_NN)= 5.52 TeV. Rapidity distributions for net protons, and
pseudorapidity spectra for produced charged particles in central collisions are
compared to data at RHIC energies, and discussed for several extrapolations to
LHC energies.Comment: 17 pages, 8 figure
Spin in fractional quantum Hall systems

A system at filling factor 2/3 could be a candidate for a quantum Hall
ferromagnet at integer filling factor of composite fermions. Using exact
diagonalization with electrons on a torus we study the transition from the
singlet ground state to the polarized ground state at this filling and look for
signatures of quantum Hall ferromagnetism. Differences between the fractional
and corresponding integer systems are emphasised. Most interestingly, we find
around the transition a low excited half-polarized state which might become the
ground state in the thermodynamical limit. We study its structure and compare
it to the singlet and polarized ground states. A new interpretation of the
singlet state is suggested and comparison of the filling factors 2/3 and 2/5 is
presented. Adding magnetic inhomogeneities into the system we investigate the
stability of all the three involved states and the tendency to build up domains
like in conventional ferromagnets.Comment: 97 pages, 69 figures, submitted to Annalen der Physi
Introducing Relativity in Global Navigation Satellite Systems

Today, the Global Navigation Satellite Systems, used as global positioning
systems, are the GPS and the GLONASS. They are based on a Newtonian model and
hence they are only operative when several relativistic effects are taken into
account. The most important relativistic effects (to order 1/c^2) are: the
Einstein gravitational blue shift effect of the satellite clock frequency
(Equivalence Principle of General Relativity) and the Doppler red shift of
second order, due to the motion of the satellite (Special Relativity).
  On the other hand, in a few years the Galileo system will be built, copying
the GPS system unless an alternative project is designed. In this work, it will
be also shown that the SYPOR project, using fully relativistic concepts, is an
alternative to a mere copy of the GPS system. According to this project, the
Galileo system would be exact and there would be no need for relativistic
corrections.Comment: 24 pages, RevTeX 4, based on a talk given in "International School:
  Relativistic Coordinates, Reference and Positioning Systems", Salamanca
  (Spain), January 21-25, 2005; final version with an extended section on the
  SYPOR project, accepted in Annalen der Physik (Leipzig
Two interacting spins in external fields. Four-level systems

In the present article, we consider the so-called two-spin equation that
describes four-level quantum systems. Recently, these systems attract attention
due to their relation to the problem of quantum computation. We study general
properties of the two-spin equation and show that the problem for certain
external backgrounds can be identified with the problem of one spin in an
appropriate background. This allows one to generate a number of exact solutions
for two-spin equations on the basis of already known exact solutions of the
one-spin equation. Besides, we present some exact solutions for the two-spin
equation with an external background different for each spin but having the
same direction. We study the eigenvalue problem for a time-independent spin
interaction and a time-independent external background. A possible analogue of
the Rabi problem for the two-spin equation is defined. We present its exact
solution and demonstrate the existence of magnetic resonances in two specific
frequencies, one of them coinciding with the Rabi frequency, and the other
depending on the rotating field magnitude. The resonance that corresponds to
the second frequency is suppressed with respect to the first one.Comment: 14 page
Exact Solution of the Klein-Gordon Equation for the PT-Symmetric
  Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method

The one-dimensional Klein-Gordon (KG) equation has been solved for the
PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov(NU}
method which is based on solving the second-order linear differential equations
by reduction to a generalized equation of hypergeometric type is used to obtain
exact energy eigenvalues and corresponding eigenfunctions. We have also
investigated the positive and negative exact bound states of the s-states for
different types of complex generalized WS potentials.Comment: 29 pages, 8 figure
The Einstein-Elko system -- Can dark matter drive inflation?

Recently, a spin one half matter field with mass dimension one was
discovered, called Elko spinors. The present work shows how to introduce these
fields into a curved spacetime by the standard covariantisation scheme. After
formulating the coupled Einstein-Elko field equations, the spacetime is assumed
to be homogeneous and isotropic in order to simplify the resulting field
equations. Analytical ghost Elko solutions are constructed which have vanishing
energy-momentum tensor without and with cosmological constant. The cosmological
Elko theory is finally related to the standard scalar field theory with self
interaction that gives rise to inflation and it is pointed out that the Elko
spinors are not only prime dark matter candidates but also prime candidates for
inflation.Comment: 24 page
Near field in quantum electrodynamics: Green functions, Lorentz
  condition, "nonlocality in the small", frustrated total reflection

Investigation of near field of QED requires the refuse from an averaging of
the Lorentz condition that smooths out some field peculiarities. Instead of it
Schwinger decomposition of the 4-potential with the Bogoliubov method of
interaction switching in time and in space regions is considered. At such
approach near field is describable by the part of covariant Green function of
QED, the fast-damping Schwinger function formed by longitudinal and scalar
components of A&#956; none restricted by light cone. This description reveals
possibility of superluminal phenomena within the near field zone as a
"nonlocality in the small". Some specification of Bogoliubov method allows, as
examples, descriptions of near fields of point-like charge and at FTIR
phenomena. Precisely such possibilities of nonlocal interactions are revealed
in the common QED expressions for the Van-der-Waals and Casimir interactions
and in the F\"{o}rster law.
  Key words: Lorentz condition, near field, propagators, superluminal, FTIR.
  PACS: 03.30.+p, 12.20.-m, 13.40.-f, 68.37.Uv.Comment: 21 page
Synergetic Analysis of the Haeussler-von der Malsburg Equations for
  Manifolds of Arbitrary Geometry

We generalize a model of Haeussler and von der Malsburg which describes the
self-organized generation of retinotopic projections between two
one-dimensional discrete cell arrays on the basis of cooperative and
competitive interactions of the individual synaptic contacts. Our generalized
model is independent of the special geometry of the cell arrays and describes
the temporal evolution of the connection weights between cells on different
manifolds. By linearizing the equations of evolution around the stationary
uniform state we determine the critical global growth rate for synapses onto
the tectum where an instability arises. Within a nonlinear analysis we use then
the methods of synergetics to adiabatically eliminate the stable modes near the
instability. The resulting order parameter equations describe the emergence of
retinotopic projections from initially undifferentiated mappings independent of
dimension and geometry.Comment: Dedicated to Hermann Haken on the occasion of his 80th birthda
Solutions of the Haeussler-von der Malsburg Equations in Manifolds with
  Constant Curvatures

We apply generic order parameter equations for the emergence of retinotopy
between manifolds of different geometry to one- and two-dimensional Euclidean
and spherical manifolds. To this end we elaborate both a linear and a nonlinear
synergetic analysis which results in order parameter equations for the dynamics
of connection weights between two cell sheets. Our results for strings are
analogous to those for discrete linear chains obtained previously by Haeussler
and von der Malsburg. The case of planes turns out to be more involved as the
two dimensions do not decouple in a trivial way. However, superimposing two
modes under suitable conditions provides a state with a pronounced retinotopic
character. In the case of spherical manifolds we show that the order parameter
equations provide stable stationary solutions which correspond to retinotopic
modes. A further analysis of higher modes furnishes proof that our model
describes the emergence of a perfect one-to-one retinotopy between two spheres.Comment: Dedicated to Hermann Haken on the occasion of his 80th birthda
A New Look at the Quantum Mechanics of the Harmonic Oscillator

Classically the Harmonic Oscillator (HO) is the generic example for the use
of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic
transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally
{(q,p)} has the structure of the plane R^2, but {(phi,I)} that of the punctured
plane R^2 -(0,0). This implies qualitative differences for the QM of the two
phase spaces: The quantizing group for the plane R^2 consists of the (centrally
extended) translations generated by {q,p,1}, but the corresponding group for
{(phi,I)} is SO(1,2) = Sp(2,R)/Z_2, (Sp(2,R): symplectic group of the plane),
with Lie algebra basis {h_0 = I, h_1 = I cos phi, h_2 = - I sin phi}. In the QM
for the (phi,I)-model the three h_j correspond to self-adjoint generators K_j,
j=0,1,2, of irreducible unitary representations (positive discrete series) for
SO(1,2) or one of its infinitely many covering groups, the Bargmann index k > 0
of which determines the ground state energy E (k, n=0) = hbar omega k of the
(phi,I)-Hamiltonian H(K). For an m-fold covering the lowest possible value is
k=1/m, which can be made arbitrarily small! The operators Q and P, now
expressed as functions of the K_j, keep their usual properties, but the richer
structure of the K_j quantum model of the HO is ``erased'' when passing to the
simpler Q,P model! The (phi,I)-variant of the HO implies many experimental
tests: Mulliken-type experiments for isotopic diatomic molecules, experiments
with harmonic traps for atoms, ions and BE-condensates, with the (Landau)
levels of charged particles in magnetic fields, with the propagation of light
in vacuum, passing through electric or magnetic fields. Finally it leads to a
new theoretical estimate for the quantum vacuum energy of fields and its
relation to the cosmological constant.Comment: 100 pages (Latex); v2: abstract simplified, remarks and references
  adde
Semiclassical expansion of quantum characteristics for many-body
  potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the
Wigner function and the star-product operation. Quantum characteristics, which
appear in the Heisenberg picture as the Weyl's symbols of operators of
canonical coordinates and momenta, can be used to solve the evolution equations
for symbols of other operators acting in the Hilbert space. To any fixed order
in the Planck's constant, many-body potential scattering problem simplifies to
a statistical-mechanical problem of computing an ensemble of quantum
characteristics and their derivatives with respect to the initial canonical
coordinates and momenta. The reduction to a system of ordinary differential
equations pertains rigorously at any fixed order in $\hbar$. We present
semiclassical expansion of quantum characteristics for many-body scattering
problem and provide tools for calculation of average values of time-dependent
physical observables and cross sections. The method of quantum characteristics
admits the consistent incorporation of specific quantum effects, such as
non-locality and coherence in propagation of particles, into the semiclassical
transport models. We formulate the principle of stationary action for quantum
Hamilton's equations and give quantum-mechanical extensions of the Liouville
theorem on the conservation of phase-space volume and the Poincar\'e theorem on
the conservation of $2p$ forms. The lowest order quantum corrections to the
Kepler periodic orbits are constructed. These corrections show the resonance
behavior.Comment: 24 pages REVTeX, 3 eps figures, replaced with extended version,
  accepted for publication to Annalen der Physi
A case study of the Hirsch index for 26 non-prominent physicists

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.Comment: 13 pages, 3 figures, updated after extensive language editing, no
  other changes to first versio
Mapping electron delocalization by charge transport spectroscopy in an
  artificial molecule

In this letter we present an experimental realization of the quantum
mechanics textbook example of two interacting electronic quantum states that
hybridize forming a molecular state. In our particular realization, the quantum
states themselves are fabricated as quantum dots in a molecule, a carbon
nanotube.
  For sufficient quantum-mechanical interaction (tunnel coupling) between the
two quantum states, the molecular wavefunction is a superposition of the two
isolated (dot) wavefunctions. As a result, the electron becomes delocalized and
a covalent bond forms.
  In this work, we show that electrical transport can be used as a sensitive
probe to measure the relative weight of the two components in the superposition
state as a function of the gate-voltages.
  For the field of carbon nanotube double quantum dots, the findings represent
an additional step towards the engineering of quantum states
Shot noise in non-adiabatically driven nanoscale conductors

We investigate the noise properties of pump currents through molecular wires
and coupled quantum dots. As a model we employ a two level system that is
connected to electron reservoirs and is non-adiabatically driven. Concerning
the electron-electron interaction, we focus on two limits: non-interacting
electrons and strong Coulomb repulsion. While the former case is treated within
a Floquet scattering formalism, we derive for the latter case a master equation
formalism for the computation of the current and the zero-frequency noise. For
a pump operated close to internal resonances, the differences between the
non-interacting and the strongly interacting limit turn out to be surprisingly
small.Comment: 17 pages, 2 figure
Josephson junctions as detectors for non-Gaussian noise

Non-Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on-chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non-zero third cumulant is presented, together with numerical simulations when the noise source is a tunnel junction with Poisson noise. Comparison between experiment and theory is discussed
Nonlocal Lagrangians for Accelerated Systems

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.Comment: 11 pages, no figures; v2: 20 pages; expanded version accepted for
  publication in Ann. Phys. (Leipzig); v3: several typos corrected to match the
  published versio
Analytical solution of a Hubbard model extended by nearest neighbour
  Coulomb and exchange interaction on a triangle and tetrahedron

The Hubbard model extended by either nearest-neighbour Coulomb correlation
and/or nearest neighbour Heisenberg exchange is solved analytically for a
triangle and tetrahedron. All eigenvalues and eigenvectors are given as
functions of the model parameters in a closed form. The groundstate crossings
and degeneracies are discussed both for the canonical and grand-canonical
energy levels. The grand canonical potential and the electron occupation of the
related cluster gases were calculated for arbitrary values (attractive and
repulsive) of the three interaction constants. In the pure Hubbard model we
found various steps in the electron occupation higher than one. It is shown
that the various degeneracies of the grand-canonical energy levels are
partially lifted by an antiferromagnetic exchange interaction, whereas a
moderate ferromagnetic exchange modifies only slightly the results of the pure
Hubbard model. A repulsive nn Coulomb correlation lifts these degeneracies
completely. The relation of the cluster gas results to extended systems is
discussed.Comment: 115 pages, 20 figures. If you do not intend to work with the
  eigenvalues and eigenvectors do NOT print the appendices (92 pages), instead
  print pages 1-11 (article) and 103-115 (figures
Revival-collapse phenomenon in the quadrature squeezing of the
  multiphoton Jaynes-Cummings model with the binomial states

In this paper we study the interaction between two-level atom and quantized
single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom
are initially prepared in the binomial state and the excited atomic state,
respectively. For this system we prove that the revival-collapse phenomenon
exhibited in the atomic inversion of the standard JCM can be numerically
(naturally) manifested in the evolution of the squeezing factor of the
three-photon (standard) JCM provided that the initial photon-number
distribution of the radiation has a smooth envelope.Comment: 14 pages, 4 figures, Comments are most welcom
Interacting bosons in an optical lattice

Several models of a strongly interacting Bose gas in an optical lattice are
studied within the functional-integral approach. The one-dimensional Bose gas
is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator
of a three-dimensional Bose gas are described in mean-field approximation, and
the corresponding phase diagrams are evaluated. Other characteristic
quantities, like the spectrum of quasiparticle excitations and the static
structure factor, are obtained from Gaussian fluctuations around the mean-field
solutions. We discuss the role of quantum and thermal fluctuations, and
determine the behavior of physical quantities in terms of density and
temperature of the Bose gas. In particular, we study the dilute limit, where
the mean-field equation becomes the Gross-Pitaevskii equation. This allows us
to extend the Gross-Pitaevskii equation to the dense regime by introducing
renormalized parameters in the latter.Comment: 58 pages, 14 figure
Universal tunneling time for all fields

Tunneling is an important physical process. The observation that particles
surmount a high mountain in spite of the fact that they don't have the
necessary energy cannot be explained by classical physics. However, this so
called tunneling became allowed by quantum mechanics. Experimental tunneling
studies with different photonic barriers from microwave frequencies up to
ultraviolet frequencies pointed towards a universal tunneling time
(Haibel,Esposito). Experiments and calculations have shown that the tunneling
time of opaque photonic barriers (optical mirrors, e.g.) equals approximately
the reciprocal frequency of the corresponding electromagnetic wave. The
tunneling process is described by virtual photons. Virtual particles like
photons or electrons are not observable. However, from the theoretical point of
view, they represent necessary intermediate states between observable real
states. In the case of tunneling there is a virtual particle between the
incident and the transmitted particle. Tunneling modes have a purely imaginary
wave number. They represent solutions of the Schroedinger equation and of the
classical Helmholtz equation. Recent experimental and theoretical data of
electron and sound tunneling confirmed the conjecture that the tunneling
process is characterized by a universal tunneling time independent of the kind
of field. Tunneling proceeds at a time of the order of the reciprocal frequency
of the wave.Comment: 7 pages latex, 3 figure