1,180 research outputs found
Moment-Based Order-Independent Transparency
Compositing transparent surfaces rendered in an arbitrary order requires techniques for order-independent transparency. Each surface color needs to be multiplied by the appropriate transmittance to the eye to incorporate occlusion. Building upon moment shadow mapping, we present a moment-based method for compact storage and fast reconstruction of this depth-dependent function per pixel. We work with the logarithm of the transmittance such that the function may be accumulated additively rather than multiplicatively. Then an additive rendering pass for all transparent surfaces yields moments. Moment-based reconstruction algorithms provide approximations to the original function, which are used for compositing in a second additive pass. We utilize existing algorithms with four or six power moments and develop new algorithms using eight power moments or up to four trigonometric moments. The resulting techniques are completely order-independent, work well for participating media as well as transparent surfaces and come in many variants providing different tradeoffs. We also utilize the same approach for the closely related problem of computing shadows for transparent surfaces
Quantum Space-time and Classical Gravity
A method has been recently proposed for defining an arbitrary number of
differential calculi over a given noncommutative associative algebra. As an
example a version of quantized space-time is considered here. It is found that
there is a natural differential calculus using which the space-time is
necessarily flat Minkowski space-time. Perturbations of this calculus are shown
to give rise to non-trivial gravitational fields.Comment: 21 pages LaTe
Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice
Topological states of matter, as quantum Hall systems or topological
insulators, cannot be distinguished from ordinary matter by local measurements
in the bulk of the material. Instead, global measurements are required,
revealing topological invariants as the Chern number. At the heart of
topological materials are topologically protected edge states that occur at the
intersection between regions of different topological order. Ultracold atomic
gases in optical lattices are promising new platforms for topological states of
matter, though the observation of edge states has so far been restricted in
these systems to the state space imposed by the internal atomic structure. Here
we report on the observation of an edge state between two topological distinct
phases of an atomic physics system in real space using optical microscopy. An
interface between two spatial regions of different topological order is
realized in a one-dimensional optical lattice of spatially chirped amplitude.
To reach this, a magnetic field gradient causes a spatial variation of the
Raman detuning in an atomic rubidium three- level system and a corresponding
spatial variation of the coupling between momentum eigenstates. This novel
experimental technique realizes a cold atom system described by a Dirac
equation with an inhomogeneous mass term closely related to the SSH-model. The
observed edge state is characterized by measuring the overlap to various
initial states, revealing that this topological state has singlet nature in
contrast to the other system eigenstates, which occur pairwise. We also
determine the size of the energy gap to the adjacent eigenstate doublet. Our
findings hold prospects for the spectroscopy of surface states in topological
matter and for the quantum simulation of interacting Dirac systems
Fuzzy Space-Time
A review is made of recent efforts to define linear connections and their
corresponding curvature within the context of noncommutative geometry. As an
application it is suggested that it is possible to identify the gravitational
field as a phenomenological manifestation of space-time commutation relations
and to thereby clarify its role as an ultraviolet regularizer.Comment: 17 pages LaTe
Fine structure and optical pumping of spins in individual semiconductor quantum dots
We review spin properties of semiconductor quantum dots and their effect on
optical spectra. Photoluminescence and other types of spectroscopy are used to
probe neutral and charged excitons in individual quantum dots with high
spectral and spatial resolution. Spectral fine structure and polarization
reveal how quantum dot spins interact with each other and with their
environment. By taking advantage of the selectivity of optical selection rules
and spin relaxation, optical spin pumping of the ground state electron and
nuclear spins is achieved. Through such mechanisms, light can be used to
process spins for use as a carrier of information
- …