3,231 research outputs found
Orthonormal bases of extreme quantumness
Spin anticoherent states acquired recently a lot of attention as the most "quantum" states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this work, we introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy. In this way, we identify the most coherent and most quantum states, which lead to orthogonal measurements of extreme quantumness. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. Results obtained lead to maximally (minimally) entangled bases in the dimensional symmetric subspace of the dimensional space of states of multipartite systems composed of qubits. Some bases found are iso-coherent as they consist of all states of the same degree of spin-coherence
Apartment classes of integral symplectic groups
In this note we present an alternative proof of a theorem of Gunnells, which
states that the Steinberg module of is a
cyclic -module, generated by integral
apartment classes.Comment: 16 pages. Comments welcome
On Chevalley group schemes over function fields: quotients of the Bruhat-Tits building by -arithmetic subgroups
Let be a reductive Chevalley group scheme (defined over
). Let be a smooth, projective, geometrically
integral curve over a field . Let be a closed point on
. Let be the ring of functions that are regular outside
. The fraction field of has a discrete valuation
associated to . In this
work, we study the action of the group of -points of
on the Bruhat-Tits building
in order to describe the
structure of the orbit space . We obtain
that this orbit space is the ``gluing'' of a closed connected CW-complex with
some sector chambers. The latter are parametrized by a set depending on the
Picard group of and on the rank of
. Moreover, we observe that any rational sector face whose tip is a
special vertex contains a subsector face that embeds into this orbit space. We
deduce, from this description, a writing of as a free product
with amalgamation. We also obtain a counting of the -conjugacy classes
of maximal unipotent subgroups contained in a finite index subgroup , together with a description of these maximal
unipotent subgroups.Comment: Comments are welcom
Modeling horizon absorption in spinning binary black holes using effective worldline theory
The mass and spin of black holes (BHs) in binary systems may change due to
the infall of gravitational-wave (GW) energy down the horizons. For spinning
BHs, this effect enters at 2.5 post-Newtonian (PN) order relative to the
leading-order energy flux at infinity. There is currently a discrepancy in the
literature in the expressions of these horizon fluxes in the test-body limit at
4PN order (relative 1.5PN order). Here, we model the horizon absorption as
tidal heating in an effective worldline theory of a spinning particle equipped
with tidally-induced quadrupole and octupole moments. We match the tidal
response to analytic solutions of the Teukolsky equation in a scattering
scenario, and obtain general formulae for the evolution of mass and spin. We
then specialize to the case of aligned-spin--quasi-circular binaries, obtaining
the corresponding contributions to the GW phasing through 4PN order.
Importantly, we find that the number of GW cycles due to horizon fluxes with
masses observed by LIGO-Virgo-KAGRA detectors is about 2-3 orders of magnitude
smaller than the other contributions to the phasing at the same PN order.
Furthermore, in the test-body limit, we find full agreement with results
obtained earlier from BH perturbation theory, with a small mass in an
equatorial circular orbit treated as a source perturbing the Kerr metric. Thus,
we weigh in on one side of the previous discrepancy.Comment: 29 Pages, 1 figure, 2 table
Commensurations of and its Torelli subgroup
For , the abstract commensurators of both and
its Torelli subgroup are isomorphic to
itself.Comment: 29 pages, 5 figure
Simulation of incompressible viscous flow using finite element method
This study focused on simulating incompressible viscous flow using the finite element method. This study used velocity and pressure as unknowns known as primitive variable formulations. Simulation of incompressible fluid flow poses numerical challenges due to the presence of nonlinear convective terms in Navier-Stokes equations and the incompressible nature of the fluid. If the connection between velocities and pressure is not discretized correctly, the stable and convergent velocities might be gained, but the obtained pressure will be oscillatory. To avoid these difficulties, continuous quadratic and additional cubic bubble functions will be used for the velocity field and linear functions for the pressure field. This kind of discretization satisfies the Ladyzhenskaya-Babuška-Brezzi (LBB) stability condition. Two cases of different Reynolds numbers were used to test the formulation's effectiveness. In the case of Reynolds number 0.12, no vortices were formed, suggesting that the flow is primarily governed by fluid friction, and fluid inertia has minimal effect. In the case of Reynolds number 120, the vortex formation, which is known as Von Kármán vortex street, appeared. These results concluded that the formulation using the finite element method is correct
RecolorNeRF: Layer Decomposed Radiance Fields for Efficient Color Editing of 3D Scenes
Radiance fields have gradually become a main representation of media.
Although its appearance editing has been studied, how to achieve
view-consistent recoloring in an efficient manner is still under explored. We
present RecolorNeRF, a novel user-friendly color editing approach for the
neural radiance fields. Our key idea is to decompose the scene into a set of
pure-colored layers, forming a palette. By this means, color manipulation can
be conducted by altering the color components of the palette directly. To
support efficient palette-based editing, the color of each layer needs to be as
representative as possible. In the end, the problem is formulated as an
optimization problem, where the layers and their blending weights are jointly
optimized with the NeRF itself. Extensive experiments show that our
jointly-optimized layer decomposition can be used against multiple backbones
and produce photo-realistic recolored novel-view renderings. We demonstrate
that RecolorNeRF outperforms baseline methods both quantitatively and
qualitatively for color editing even in complex real-world scenes.Comment: To appear in ACM Multimedia 2023. Project website is accessible at
https://sites.google.com/view/recolorner
FLARE: Fast Learning of Animatable and Relightable Mesh Avatars
Our goal is to efficiently learn personalized animatable 3D head avatars from
videos that are geometrically accurate, realistic, relightable, and compatible
with current rendering systems. While 3D meshes enable efficient processing and
are highly portable, they lack realism in terms of shape and appearance. Neural
representations, on the other hand, are realistic but lack compatibility and
are slow to train and render. Our key insight is that it is possible to
efficiently learn high-fidelity 3D mesh representations via differentiable
rendering by exploiting highly-optimized methods from traditional computer
graphics and approximating some of the components with neural networks. To that
end, we introduce FLARE, a technique that enables the creation of animatable
and relightable mesh avatars from a single monocular video. First, we learn a
canonical geometry using a mesh representation, enabling efficient
differentiable rasterization and straightforward animation via learned
blendshapes and linear blend skinning weights. Second, we follow
physically-based rendering and factor observed colors into intrinsic albedo,
roughness, and a neural representation of the illumination, allowing the
learned avatars to be relit in novel scenes. Since our input videos are
captured on a single device with a narrow field of view, modeling the
surrounding environment light is non-trivial. Based on the split-sum
approximation for modeling specular reflections, we address this by
approximating the pre-filtered environment map with a multi-layer perceptron
(MLP) modulated by the surface roughness, eliminating the need to explicitly
model the light. We demonstrate that our mesh-based avatar formulation,
combined with learned deformation, material, and lighting MLPs, produces
avatars with high-quality geometry and appearance, while also being efficient
to train and render compared to existing approaches.Comment: 15 pages, Accepted: ACM Transactions on Graphics (Proceedings of
SIGGRAPH Asia), 202
- …