20,509 research outputs found
Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
In addition to simple scale invariance, a universe dominated by dark energy
naturally gives rise to correlation functions possessing full conformal
invariance. This is due to the mathematical isomorphism between the conformal
group of certain 3 dimensional slices of de Sitter space and the de Sitter
isometry group SO(4,1). In the standard homogeneous isotropic cosmological
model in which primordial density perturbations are generated during a long
vacuum energy dominated de Sitter phase, the embedding of flat spatial sections
in de Sitter space induces a conformal invariant perturbation spectrum and
definite prediction for the shape of the non-Gaussian CMB bispectrum. In the
case in which the density fluctuations are generated instead on the de Sitter
horizon, conformal invariance of the horizon embedding implies a different but
also quite definite prediction for the angular correlations of CMB
non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic
to the symmetries of de Sitter space and in that sense, independent of specific
model assumptions. Each is different from the predictions of single field slow
roll inflation models which rely on the breaking of de Sitter invariance. We
propose a quantum origin for the CMB fluctuations in the scalar gravitational
sector from the conformal anomaly that could give rise to these
non-Gaussianities without a slow roll inflaton field, and argue that conformal
invariance also leads to the expectation for the relation n_S-1=n_T between the
spectral indices of the scalar and tensor power spectrum. Confirmation of this
prediction or detection of non-Gaussian correlations in the CMB of one of the
bispectral shape functions predicted by conformal invariance can be used both
to establish the physical origins of primordial density fluctuations and
distinguish between different dynamical models of cosmological vacuum dark
energy.Comment: 73 pages, 9 figures. Final Version published in JCAP. New Section 4
added on linearized scalar gravitational potentials; New Section 8 added on
gravitational wave tensor perturbations and relation of spectral indices n_T
= n_S -1; Table of Contents added; Eqs. (3.14) and (3.15) added to clarify
relationship of bispectrum plotted to CMB measurements; Some other minor
modification
On Nonrigid Shape Similarity and Correspondence
An important operation in geometry processing is finding the correspondences
between pairs of shapes. The Gromov-Hausdorff distance, a measure of
dissimilarity between metric spaces, has been found to be highly useful for
nonrigid shape comparison. Here, we explore the applicability of related shape
similarity measures to the problem of shape correspondence, adopting spectral
type distances. We propose to evaluate the spectral kernel distance, the
spectral embedding distance and the novel spectral quasi-conformal distance,
comparing the manifolds from different viewpoints. By matching the shapes in
the spectral domain, important attributes of surface structure are being
aligned. For the purpose of testing our ideas, we introduce a fully automatic
framework for finding intrinsic correspondence between two shapes. The proposed
method achieves state-of-the-art results on the Princeton isometric shape
matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks
On localization and position operators in Moebius-covariant theories
Some years ago it was shown that, in some cases, a notion of locality can
arise from the group of symmetry enjoyed by the theory, thus in an intrinsic
way. In particular, when Moebius covariance is present, it is possible to
associate some particular transformations to the Tomita Takesaki modular
operator and conjugation of a specific interval of an abstract circle. In this
context we propose a way to define an operator representing the coordinate
conjugated with the modular transformations. Remarkably this coordinate turns
out to be compatible with the abstract notion of locality. Finally a concrete
example concerning a quantum particle on a line is also given.Comment: 19 pages, UTM 705, version to appear in RM
On a Zero Curvature Representation for Bosonic Strings and -Branes
It is shown that a zero curvature representation for -- dimensional --
brane equations of motion originates naturally in the geometric (Lund- Regge-
Omnes) approach. To study the possibility to use this zero curvature
representation for investigation of nonlinear equations of -- branes, the
simplest case of -- dimensional string () is considered. The connection
is found between the gauge (world--sheet Lorentz) invariance of the
string theory with a nontrivial dependence on a spectral parameter of the Lax
matrices associated with the nonlinear equations describing the embedding of a
string world sheet into flat -- dimensional space -- time. Namely, the
spectral parameter can be identified with a parameter of constant
gauge transformations, after the deformation of the Lax matrices has been
performed.Comment: 14 pages. LATEX. Revised version. Submitted to Phys. Lett. B. The
arrangement of the material is changed. Some additional references are
include
Topology by dissipation
Topological states of fermionic matter can be induced by means of a suitably
engineered dissipative dynamics. Dissipation then does not occur as a
perturbation, but rather as the main resource for many-body dynamics, providing
a targeted cooling into a topological phase starting from an arbitrary initial
state. We explore the concept of topological order in this setting, developing
and applying a general theoretical framework based on the system density matrix
which replaces the wave function appropriate for the discussion of Hamiltonian
ground-state physics. We identify key analogies and differences to the more
conventional Hamiltonian scenario. Differences mainly arise from the fact that
the properties of the spectrum and of the state of the system are not as
tightly related as in a Hamiltonian context. We provide a symmetry-based
topological classification of bulk steady states and identify the classes that
are achievable by means of quasi-local dissipative processes driving into
superfluid paired states. We also explore the fate of the bulk-edge
correspondence in the dissipative setting, and demonstrate the emergence of
Majorana edge modes. We illustrate our findings in one- and two-dimensional
models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure
Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
We study the bulk-edge correspondence in topological insulators by taking
Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant
in this model is Z2 invariant modulo the spectral flow of a single-parameter
family of 1+1-dimensional Dirac operators with a global boundary condition
induced by the Kramers degeneracy of the system. This spectral flow is defined
as an integer which counts the difference between the number of eigenvalues of
the Dirac operator family that flow from negative to non-negative and the
number of eigenvalues that flow from non-negative to negative. Since the bulk
states of the insulator are completely gapped and the ground state is assumed
being no more degenerate except the Kramers, they do not contribute to the
spectral flow and only edge states contribute to. The parity of the number of
the Kramers pairs of gapless edge states is exactly the same as that of the
spectral flow. This reveals the origin of the edge-bulk correspondence, i.e.,
why the edge states can be used to characterize the topological insulators.
Furthermore, the spectral flow is related to the reduced eta-invariant and thus
counts both the discrete ground state degeneracy and the continuous gapless
excitations, which distinguishes the topological insulator from the
conventional band insulator even if the edge states open a gap due to a strong
interaction between edge modes. We emphasize that these results are also valid
even for a weak disordered and/or weak interacting system. The higher spectral
flow to categorize the higher-dimensional topological insulators are expected.Comment: 9 page, accepted for publication in Nucl Phys
Results on the symmetries of integrable fermionic models on chains
We investigate integrable fermionic models within the scheme of the graded
Quantum Inverse Scattering Method, and prove that any symmetry imposed on the
solution of the Yang-Baxter Equation reflects on the constants of motion of the
model; generalizations with respect to known results are discussed. This
theorem is shown to be very effective when combined with the Polynomial
\Rc-matrix Technique (PRT): we apply both of them to the study of the
extended Hubbard models, for which we find all the subcases enjoying several
kinds of (super)symmetries. In particular, we derive a geometrical construction
expressing any -invariant model as a linear combination of EKS and
U-supersymmetric models. Furtherly, we use the PRT to obtain 32 integrable
-invariant models. By joint use of the Sutherland's Species technique
and -pairs construction we propose a general method to derive their
physical features, and we provide some explicit results.Comment: 25 pages, 2 figure
Visualizing the geometry of state space in plane Couette flow
Motivated by recent experimental and numerical studies of coherent structures
in wall-bounded shear flows, we initiate a systematic exploration of the
hierarchy of unstable invariant solutions of the Navier-Stokes equations. We
construct a dynamical, 10^5-dimensional state-space representation of plane
Couette flow at Re = 400 in a small, periodic cell and offer a new method of
visualizing invariant manifolds embedded in such high dimensions. We compute a
new equilibrium solution of plane Couette flow and the leading eigenvalues and
eigenfunctions of known equilibria at this Reynolds number and cell size. What
emerges from global continuations of their unstable manifolds is a surprisingly
elegant dynamical-systems visualization of moderate-Reynolds turbulence. The
invariant manifolds tessellate the region of state space explored by
transiently turbulent dynamics with a rigid web of continuous and discrete
symmetry-induced heteroclinic connections.Comment: 32 pages, 13 figures submitted to Journal of Fluid Mechanic
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