pinecone/core-2020-05-10-deduplication huggingface dataset:
Obtaining gauge invariant actions via symplectic embedding formalism

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.Comment: 20 pages. Two-column format. Final version to appear in Annalen der
  Physik. arXiv admin note: substantial text overlap with arXiv:1001.2254,
  arXiv:hep-th/010908
Discretized Thermal Green's Functions

We present a spectral weight conserving formalism for Fermionic thermal
Green's functions that are discretized in imaginary time and thus periodic in
imaginary ("Matsubara") frequency. The formalism requires a generalization of
the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free
energy. A conformal transformation is used to analytically continue the
periodized Matsubara Green's function to the continuous real axis in a way that
conserves the discontinuity at t=0 of the corresponding real-time Green's
function. For given discretization the method allows numerical Green's function
calculations of very high precision and it appears to give a well controlled
convergent approximation as we decrease the discretization interval. The ideas
are tested on Dynamical Mean Field Theory calculations of the paramagnetic
Hubbard model
On the quantum statistics of bound states within the Rutherford model of
  matter

The quantum statistical treatment of the Rutherford model, considering matter
as a system of point charges (electrons and nuclei) is analyzed. First, in the
historical context, the solutions of different fundamental problems, such as
the divergence of the partition function, elaborated by Herzfeld, Planck,
Brillouin and Rompe - most of the relevant papers published in the Annalen der
Physik, are discussed. Beyond this, the modern state of art is presented and
new results are given which explain, why bound states according to a discrete
part of the spectra occur only in a valley in the temperature-density plane.
Based on the actual state of the quantum statistics of Coulomb systems, virial
expansions within the canonical ensemble and the grand ensemble and
combinations are derived. The following transitions along isotherms are
studied: (i) the formation of bound states occurring by increasing the density
from low to moderate values, (ii) the disappearance of bound state effects at
higher densities due to medium effects. Within the physical picture we
calculate isotherms of pressure for Hydrogen in a broad density region and show
that in the region between $20\, 000$ K and $100\, 000$ K and particle
densities below $10^{22}$ cm$^{-3}$ the cross-over from full to partial
ionization may be well described by the contributions of extended ring diagrams
and ladder diagrams.Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with
  arXiv:1110.196
Model of a relativistic oscillator in a generalized Schr\"odinger
  picture

In a generalized Schr\"odinger picture, we consider the motion of a
relativistic particle in an external field (like in the case of a harmonic
oscillator). In this picture the analogs of the Schr\"odinger operators of the
particle are independent of both the time and the space coordinates. These
operators induce operators which are related to Killing vectors of the Anti de
Sitter (AdS) space. We also consider the nonrelativistic limit.Comment: 16 pages, physical discussion extended to three dimensional problem
  (spin=0
Conformal transformations in metric-affine gravity and ghosts

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 of 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 the conformal factor are avoided thanks to the independence of connection from the metric
Teleparallel gauge theory of gravity

In this work a tetrad theory of gravity, invariant under conformal
transformations, is investigated. The action of the theory is similar to the
action of Maxwell's electromagnetism. The role of the electromagnetic gauge
potential is played by the trace of the torsion tensor of the Weitzenb\"ock
spacetime. It is shown that all static, spherically symmetric space-times, are
solutions of the vacuum field equations. However, by fixing the gauge in the
linearized form of the vacuum field equations, the usual Newtonian limit for
the gravitational field is obtained.Comment: 10 pages, no figures, 5 references adde
Multiple Dark Matter as a self-regulating mechanism for dark sector
  interactions

(Abridged) Present cosmological constraints and the absence of a direct
detection and identification of any dark matter particle candidate leave room
to the possibility that the dark sector of the Universe be actually more
complex than it is normally assumed. In particular, more than one new
fundamental particle could be responsible for the observed dark matter density
in the Universe, and possible new interactions between dark energy and dark
matter might characterize the dark sector. In the present work, we investigate
the possibility that two dark matter particles exist in nature, with identical
physical properties except for the sign of their coupling constant to dark
energy. Extending previous works on similar scenarios, we study the evolution
of the background cosmology as well as the growth of linear density
perturbations for a wide range of parameters of such model. Interestingly, our
results show how the simple assumption that dark matter particles carry a
"charge" with respect to their interaction with the dark energy field allows
for new long-range scalar forces of gravitational strength in the dark sector
without conflicting with present observations both at the background and linear
levels. Our scenario does not introduce new parameters with respect to the case
of a single dark matter species for which such strong dark interactions have
been already ruled out.Comment: 18 pages, 1 table, 9 figures. Invited paper for the special issue of
  Annalen der Physik on "Dark Matter" (Ed. Matthias Bartelmann and Volker
  Springel
An array of surface-enhanced Raman scattering substrates based on plasmonic lenses

Cataloged from PDF version of article.An array of ring-shaped holes is prepared from silver thin films using electron beam lithography. The optimal conditions for high performance as a surface-enhanced Raman scattering (SERS) substrate are investigated. Either the diameter of the hole (0.5, 1.0, 2.0, 3.0 and 4.0 mu m) or the slit width (200, 300, 400, 500 and 600 nm) is varied. 4-Aminothiophenol (ATP) adsorbed on the structures as a self-assembled monolayer (SAM) is used as probe to evaluate the SERS performance of the generated structures. It is found that there is an optimal configuration for ring-shaped holes with a 3.0-mu m diameter and 200-nm slit width. The SERS activity on this optimal lens configuration is found to be 13 times greater than that of the activity on the silver thin film. An array of these structures at this optimal configuration can easily be constructed and used in a range of SERS-based sensing applications
Problem of Time in Quantum Gravity

The Problem of Time occurs because the `time' of GR and of ordinary Quantum
Theory are mutually incompatible notions. This is problematic in trying to
replace these two branches of physics with a single framework in situations in
which the conditions of both apply, e.g. in black holes or in the very early
universe. Emphasis in this Review is on the Problem of Time being multi-faceted
and on the nature of each of the eight principal facets. Namely, the Frozen
Formalism Problem, Configurational Relationalism Problem (formerly Sandwich
Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly
Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time,
Problem of Beables (alias Problem of Observables) and Spacetime
Reconstruction/Replacement Problem. Strategizing in this Review is not just
centred about the Frozen Formalism Problem facet, but rather about each of the
eight facets. Particular emphasis is placed upon A) relationalism as an
underpinning of the facets and as a selector of particular strategies
(especially a modification of Barbour relationalism, though also with some
consideration of Rovelli relationalism). B) Classifying approaches by the full
ordering in which they embrace constrain, quantize, find time/history and find
observables, rather than only by partial orderings such as "Dirac-quantize". C)
Foliation (in)dependence and Spacetime Reconstruction for a wide range of
physical theories, strategizing centred about the Problem of Beables, the
Patching Approach to the Global Problem of Time, and the role of the
question-types considered in physics. D) The Halliwell- and
Gambini-Porto-Pullin-type combined Strategies in the context of semiclassical
quantum cosmology.Comment: Invited Review: 26 pages including 2 Figures. This v2 has a number of
  minor improvements and correction
A square-torsion modification of Einstein-Cartan theory

In the present paper we consider a theory of gravity in which not only
curvature but also torsion is explicitly present in the Lagrangian, both with
their own coupling constant. In particular, we discuss the couplings to Dirac
fields and spin fluids: in the case of Dirac fields, we discuss how in our
approach, the Dirac self-interactions depend on the coupling constant as a
parameter that may even make these non-linearities manifest at subatomic
scales, showing different applications according to the value of the parameter
we have assigned; in the case of spin fluids, we discuss FLRW cosmological
models arising from the proposed theory.Comment: 21 page
A short walk through quantum optomechanics

This paper gives an brief review of the basic physics of quantum
optomechanics and provides an overview of some of its recent developments and
current areas of focus. It first outlines the basic theory of cavity
optomechanical cooling and gives a brief status report of the experimental
state-of-the-art. It then turns to the deep quantum regime of operation of
optomechanical oscillators and cover selected aspects of quantum state
preparation, control and characterization, including mechanical squeezing and
pulsed optomechanics. This is followed by a discussion of the "bottom-up"
approach that exploits ultracold atomic samples instead of nanoscale systems.
It concludes with an outlook that concentrates largely on the functionalization
of quantum optomechanical systems and their promise in metrology applications
Observational effects from quantum cosmology

The status of quantum cosmologies as testable models of the early universe is
assessed in the context of inflation. While traditional Wheeler-DeWitt
quantization is unable to produce sizable effects in the cosmic microwave
background, the more recent loop quantum cosmology can generate potentially
detectable departures from the standard cosmic spectrum. Thus, present
observations constrain the parameter space of the model, which could be made
falsifiable by near-future experiments.Comment: 16 pages, 3 figures. Invited review article also containing original
  material. v2: new section on holonomy corrections, introduction extended,
  references added, typos corrected; v3: includes corrections of eqs. (3), (62)
  and (64c) of the erratu
State of the art in the determination of the fine structure constant:
  test of Quantum Electrodynamics and determination of h/mu

The fine structure constant $\alpha$ has a particular status in physics. Its
precise determination is required to test the quantum electrodynamics (QED)
theory. The constant $\alpha$ is also a keystone for the determination of other
fundamental physical constants, especially the ones involved in the framework
of the future International System of units. This paper presents Paris
experiment, where the fine structure constant is determined by measuring the
recoil velocity of a rubidium atom when it absorbs a photon. The impact of the
recent improvement of QED calculations of the electron moment anomaly and the
recent measurement of the cesium atom recoil at Berkeley will be discussed. The
opportunity to provide a precise value of the ratio $h/m_{\mathrm{u}}$ between
the Planck constant and the atomic mass constant will be investigated
Full characterization of the quantum linear-zigzag transition in atomic
  chains

A string of repulsively interacting particles exhibits a phase transition to
a zigzag structure, by reducing the transverse trap potential or the
interparticle distance. The transition is driven by transverse, short
wavelength vibrational modes. Based on the emergent symmetry Z_2 it has been
argued that this instability is a quantum phase transition, which can be mapped
to an Ising model in transverse field. We perform an extensive Density Matrix
Renormalization Group analysis of the behaviour at criticality and evaluate the
critical exponents and the central charge with high precision. We thus provide
strong numerical evidence confirming that the quantum linear-zigzag transition
belongs to the critical Ising model universality class. These results show that
structural instabilities of one-dimensional interacting atomic arrays can
simulate quantum critical phenomena typical of ferromagnetic systems.Comment: 5 pages, 4 figure
Quantum simulations of localization effects with dipolar interactions

Quantum information processing often uses systems with dipolar interactions.
We use a nuclear spin-based quantum simulator, to study the spreading of
information in such a dipolar-coupled system and how perturbations to the
dipolar couplings limit the spreading, leading to localization. In [Phys. Rev.
Lett. 104, 230403 (2010)], we found that the system reaches a dynamic
equilibrium size, which decreases with the square of the perturbation strength.
Here, we study the impact of a disordered Hamiltonian with dipolar 1/r^3
interactions. We show that the expansion of the coherence length of the cluster
size of the spins becomes frozen in the presence of large disorder, reminiscent
of Anderson localization of non-interacting waves in a disordered potential.Comment: 10 pages, 12 figure
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of
  Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many
areas of physics. In condensed matter physics, Abelian U(1) lattice gauge
theories arise in the description of certain quantum spin liquids. In quantum
information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In
particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge
theory of the strong interactions between quarks and gluons, is
non-perturbatively regularized on a lattice. Quantum link models extend the
concept of lattice gauge theories beyond the Wilson formulation, and are well
suited for both digital and analog quantum simulation using ultracold atomic
gases in optical lattices. Since quantum simulators do not suffer from the
notorious sign problem, they open the door to studies of the real-time
evolution of strongly coupled quantum systems, which are impossible with
classical simulation methods. A plethora of interesting lattice gauge theories
suggests itself for quantum simulation, which should allow us to address very
challenging problems, ranging from confinement and deconfinement, or chiral
symmetry breaking and its restoration at finite baryon density, to color
superconductivity and the real-time evolution of heavy-ion collisions, first in
simpler model gauge theories and ultimately in QCD.Comment: 27 pages, 6 figures, invited contribution to the "Annalen der Physik"
  topical issue "Quantum Simulation", guest editors: R. Blatt, I. Bloch, J. I.
  Cirac, and P. Zolle
Simulating quantum magnets with symmetric top molecules

We establish a correspondence between the electric dipole matrix elements of
a polyatomic symmetric top molecule in a state with nonzero projection of the
total angular momentum on the symmetry axis of the molecule and the magnetic
dipole matrix elements of a magnetic dipole associated with an elemental spin
$F$. It is shown that this correspondence makes it possible to perform quantum
simulation of the single-particle spectrum and the dipole-dipole interactions
of magnetic dipoles in a static external magnetic field $\bf{B}$ with symmetric
top molecules subject to a static external electric field
$\bf{E}_{\mathrm{DC}}$. We further show that no such correspondence exists for
$^1\Sigma$ molecules in static fields, such as the alkali metal dimers. The
effective spin angular momentum of the simulated magnetic dipole corresponds to
the rotational angular momentum of the symmetric top molecule, and so quantum
simulation of arbitrarily large integer spins is possible. Further, taking the
molecule CH$_3$F as an example, we show that the characteristic dipole-dipole
interaction energies of the simulated magnetic dipole are a factor of 620, 600,
and 310 larger than for the highly magnetic atoms Chromium, Erbium, and
Dysprosium, respectively. We present several applications of our correspondence
for many-body physics, including long-range and anisotropic spin models with
arbitrary integer spin $S$ using symmetric top molecules in optical lattices,
quantum simulation of molecular magnets, and spontaneous demagnetization of
Bose-Einstein condensates due to dipole-dipole interactions. Our results are
expected to be relevant as cold symmetric top molecules reach quantum
degeneracy through Stark deceleration and opto-electrical cooling.Comment: 28 pages, 3 figures, submitted to the special issue of Annalen der
  Physik on "Quantum Simulation"; v2: revised in response to referees' comment
Quantum simulations of the early universe

A procedure is described whereby a linearly coupled spinor Bose condensate
can be used as a physically accessible quantum simulator of the early universe.
In particular, an experiment to generate an analog of an unstable vacuum in a
relativistic scalar field theory is proposed. This is related to quantum
theories of the inflationary phase of the early universe. There is an unstable
vacuum sector whose dynamics correspond to the quantum sine-Gordon equations in
one, two or three space dimensions. Numerical simulations of the expected
behavior are reported using a truncated Wigner phase-space method, giving
evidence for the dynamical formation of complex spatial clusters. Preliminary
results showing the dependence on coupling strength, condensate size and
dimensionality are obtained.Comment: 10 pages, 7 figure
On non-equilibrium photon distributions in the Casimir effect

The electromagnetic field in a typical geometry of the Casimir effect is
described in the Schwinger-Keldysh formalism. The main result is the photon
distribution function (Keldysh Green function) in any stationary state of the
field. A two-plate geometry with a sliding interface in local equilibrium is
studied in detail, and full agreement with the results of Rytov fluctuation
electrodynamics is found. As an illustration, plots are shown for a spectrum of
the energy density between the plates.Comment: 16 pages, 4 figures, added Appendi
Superconductivity, diamagnetism, and the mean inner potential of solids

The mean inner potential of a solid is known to be proportional to its
diamagnetic susceptibility. Superconductors exhibit giant diamagnetism. What
does this say about the connection between superconductivity and mean inner
potential? Nothing, according to the conventional theory of superconductivity.
Instead, we propose that a deep connection exists between the mean inner
potential, diamagnetism, and superconductivity: that they are all intimately
linked to the fundamental charge asymmetry of matter. We discuss how this
physics can be probed experimentally and what the implications of different
experimental findings would be for the understanding of superconductivity.Comment: Small changes in response to referee's comments. To be published in
  Annalen der Physi
Two-dimensional electronic spectroscopy for the quantum-optics
  enthusiast

Recent interest in the role of quantum mechanics in the primary events of
photosynthetic energy transfer has led to a convergence of nonlinear optical
spectroscopy and quantum optics on the topic of energy-transfer dynamics in
pigment-protein complexes. The convergence of these two communities has
unveiled a mismatch between the background and terminology of the respective
fields. To make connections, we provide a pedagogical guide to understanding
the basics of two-dimensional electronic spectra aimed at researchers with a
background in quantum optics.Comment: Pedagogical guide; 20 pages, 6 figures; comments welcome
Nodal theorems for the Dirac equation in d >= 1 dimensions

A single particle obeys the Dirac equation in $d \ge 1$ spatial dimensions
and is bound by an attractive central monotone potential that vanishes at
infinity. In one dimension, the potential is even, and monotone for $x\ge 0.$
The asymptotic behavior of the wave functions near the origin and at infinity
are discussed. Nodal theorems are proven for the cases $d=1$ and $d > 1$, which
specify the relationship between the numbers of nodes $n_1$ and $n_2$ in the
upper and lower components of the Dirac spinor. For $d=1$, $n_2 = n_1 + 1,$
whereas for $d >1,$ $n_2 = n_1 +1$ if $k_d > 0,$ and $n_2 = n_1$ if $k_d < 0,$
where $k_d = \tau(j + \frac{d-2}{2}),$ and $\tau = \pm 1.$ This work
generalizes the classic results of Rose and Newton in 1951 for the case $d=3.$
Specific examples are presented with graphs, including Dirac spinor orbits
$(\psi_1(r), \psi_2(r)), r \ge 0.$Comment: 10 pages, 10 figure