1,167 research outputs found

### Einstein's Equations in the Presence of Signature Change

We discuss Einstein's field equations in the presence of signature change
using variational methods, obtaining a generalization of the Lanczos equation
relating the distributional term in the stress tensor to the discontinuity of
the extrinsic curvature. In particular, there is no distributional term in the
stress tensor, and hence no surface layer, precisely when the extrinsic
curvature is continuous, in agreement with the standard result for constant
signature.Comment: REVTeX, 8 pages; to appear in JM

### Doped high-Tc cuprate superconductors elucidated in the light of zeros and poles of electronic Green's function

We study electronic structure of hole- and electron-doped Mott insulators in
the two-dimensional Hubbard model to reach a unified picture for the normal
state of cuprate high-Tc superconductors. By using a cluster extension of the
dynamical mean-field theory, we demonstrate that structure of coexisting zeros
and poles of the single-particle Green's function holds the key to understand
Mott physics in the underdoped region. We show evidence for the emergence of
non-Fermi-liquid phase caused by the topological quantum phase transition of
Fermi surface by analyzing low-energy charge dynamics. The spectra calculated
in a wide range of energy and momentum reproduce various anomalous properties
observed in experiments for the high-Tc cuprates. Our results reveal that the
pseudogap in hole-doped cuprates has a d-wave-like structure only below the
Fermi level, while it retains non-d-wave structure with a fully opened gap
above the Fermi energy even in the nodal direction due to a zero surface
extending over the entire Brillouin zone. In addition to the non-d-wave
pseudogap, the present comprehensive identifications of the spectral asymmetry
as to the Fermi energy, the Fermi arc, and the back-bending behavior of the
dispersion, waterfall, and low-energy kink, in agreement with the experimental
anomalies of the cuprates, do not support that these originate from (the
precursors of) symmetry breakings such as the preformed pairing and the
d-density wave fluctuations, but support that they are direct consequences of
the proximity to the Mott insulator. Several possible experiments are further
proposed to prove or disprove our zero mechanism.Comment: 17 pages, 15 figure

### Double Time Window Targeting Technique: Real time DMRG dynamics in the PPP model

We present a generalized adaptive time-dependent density matrix
renormalization group (DMRG) scheme, called the {\it double time window
targeting} (DTWT) technique, which gives accurate results with nominal
computational resources, within reasonable computational time. This procedure
originates from the amalgamation of the features of pace keeping DMRG
algorithm, first proposed by Luo {\it et. al}, [Phys.Rev. Lett. {\bf 91},
049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and
White [Phys. Rev. B {\bf 72}, 020404 (2005)]. Using the DTWT technique, we
study the phenomena of spin-charge separation in conjugated polymers (materials
for molecular electronics and spintronics), which have long-range
electron-electron interactions and belong to the class of strongly correlated
low-dimensional many-body systems. The issue of real time dynamics within the
Pariser-Parr-Pople (PPP) model which includes long-range electron correlations
has not been addressed in the literature so far. The present study on PPP
chains has revealed that, (i) long-range electron correlations enable both the
charge and spin degree of freedom of the electron, to propagate faster in the
PPP model compared to Hubbard model, (ii) for standard parameters of the PPP
model as applied to conjugated polymers, the charge velocity is almost twice
that of the spin velocity and, (iii) the simplistic interpretation of
long-range correlations by merely renormalizing the {\it U} value of the
Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP
model.Comment: Final (published) version; 39 pages, 13 figures, 1 table; 2 new
references adde

### Exact diagonalization results for resonant inelastic x-ray scattering spectra of one-dimensional Mott insulators

We examine the momentum-dependent excitation spectra of indirect as well as
direct resonant inelastic x-ray scattering (RIXS) processes in half-filled
(extended) Hubbard rings. We determine the fundamental features of the
groundstate RIXS response and discuss the experimental conditions that can
allow for the low-energy part of these features to be distinguished in
one-dimensional copper-oxide materials, focusing particularly on the different
magnetic excitations occurring in indirect and direct RIXS processes. We study
the dependence of spin and charge excitations on the choice of and detuning
from resonance. Moreover, final state excitation weights are calculated as a
function of the core-hole potential strength and lifetime. We show that these
results can be used to determine material characteristics, such as the
core-hole properties, from RIXS measurements.Comment: 7 pages, 4 figures; v2: references added, published versio

### (1+1)-dimensional separation of variables

In this paper we explore general conditions which guarantee that the geodesic
flow on a 2-dimensional manifold with indefinite signature is locally
separable. This is equivalent to showing that a 2-dimensional natural
Hamiltonian system on the hyperbolic plane possesses a second integral of
motion which is a quadratic polynomial in the momenta associated with a
2nd-rank Killing tensor. We examine the possibility that the integral is
preserved by the Hamiltonian flow on a given energy hypersurface only (weak
integrability) and derive the additional requirement necessary to have
conservation at arbitrary values of the Hamiltonian (strong integrability).
Using null coordinates, we show that the leading-order coefficients of the
invariant are arbitrary functions of one variable in the case of weak
integrability. These functions are quadratic polynomials in the coordinates in
the case of strong integrability. We show that for $(1+1)$-dimensional systems
there are three possible types of conformal Killing tensors, and therefore,
three distinct separability structures in contrast to the single standard
Hamilton-Jacobi type separation in the positive definite case. One of the new
separability structures is the complex/harmonic type which is characterized by
complex separation variables. The other new type is the linear/null separation
which occurs when the conformal Killing tensor has a null eigenvector.Comment: To appear on Journal of Mathematical Physic

### A duality relation for fluid spacetime

We consider the electromagnetic resolution of gravitational field. We show
that under the duality transformation, in which active and passive electric
parts of the Riemann curvature are interchanged, a fluid spacetime in comoving
coordinates remains invariant in its character with density and pressure
transforming, while energy flux and anisotropic pressure remaining unaltered.
Further if fluid admits a barotropic equation of state, $p = (\gamma - 1) \rho$
where $1 \leq \gamma \leq 2$, which will transform to $p = (\frac{2 \gamma}{3
\gamma - 2} - 1) \rho$. Clearly the stiff fluid and dust are dual to each-other
while $\rho + 3 p =0$, will go to flat spacetime. However the n $(\rho - 3 p =
0)$ and the deSitter $(\rho + p = 0$) universes ar e self-dual.Comment: 5 pages, LaTeX version, Accepted in Classical Quantum Gravity as a
Lette

### Low ordered magnetic moment by off-diagonal frustration in undoped parent compounds to iron-based high-Tc superconductors

A Heisenberg model over the square lattice recently introduced by Si and
Abrahams to describe local-moment magnetism in the new class of Fe-As high-Tc
superconductors is analyzed in the classical limit and on a small cluster by
exact diagonalization. In the case of spin-1 iron atoms, large enough
Heisenberg exchange interactions between neighboring spin-1/2 moments on
different iron 3d orbitals that frustrate true magnetic order lead to hidden
magnetic order that violates Hund's rule. It accounts for the low ordered
magnetic moment observed by elastic neutron diffraction in an undoped parent
compound to Fe-As superconductors. We predict that low-energy spin-wave
excitations exist at wavenumbers corresponding to either hidden Neel or hidden
ferromagnetic order.Comment: 7 pages, 6 figures, version published in Physical Review Letter

### Evolution of Thick Walls in Curved Spacetimes

We generalize our previous thick shell formalism to incorporate any
codimension-1 thick wall with a peculiar velocity and proper thickness bounded
by arbitrary spacetimes. Within this new formulation we obtain the equation of
motion of a spherically symmetric dust thick shell immersed in vacuum as well
as in Friedmann-Robertson-Walker spacetimes.Comment: 8 pages, 1 figur

### Exact diagonalization study of the tunable edge magnetism in graphene

The tunable magnetism at graphene edges with lengths of up to 48 unit cells
is analyzed by an exact diagonalization technique. For this we use a
generalized interacting one-dimensional model which can be tuned continuously
from a limit describing graphene zigzag edge states with a ferromagnetic phase,
to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism.
This analysis sheds light onto the question why the edge states have a
ferromagnetic ground state, while a usual one-dimensional metal does not.
Essentially we find that there are two important features of edge states: (a)
umklapp processes are completely forbidden for edge states; this allows a
spin-polarized ground state. (b) the strong momentum dependence of the
effective interaction vertex for edge states gives rise to a regime of partial
spin-polarization and a second order phase transition between a standard
paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.Comment: 11 pages, 8 figure

### The Degrees of Freedom of Partial Least Squares Regression

The derivation of statistical properties for Partial Least Squares regression
can be a challenging task. The reason is that the construction of latent
components from the predictor variables also depends on the response variable.
While this typically leads to good performance and interpretable models in
practice, it makes the statistical analysis more involved. In this work, we
study the intrinsic complexity of Partial Least Squares Regression. Our
contribution is an unbiased estimate of its Degrees of Freedom. It is defined
as the trace of the first derivative of the fitted values, seen as a function
of the response. We establish two equivalent representations that rely on the
close connection of Partial Least Squares to matrix decompositions and Krylov
subspace techniques. We show that the Degrees of Freedom depend on the
collinearity of the predictor variables: The lower the collinearity is, the
higher the Degrees of Freedom are. In particular, they are typically higher
than the naive approach that defines the Degrees of Freedom as the number of
components. Further, we illustrate how the Degrees of Freedom approach can be
used for the comparison of different regression methods. In the experimental
section, we show that our Degrees of Freedom estimate in combination with
information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio

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