6,690 research outputs found
Busemann functions and barrier functions
We show that Busemann functions on a smooth, non-compact, complete,
boundaryless, connected Riemannian manifold are viscosity solutions with
respect to the Hamilton-Jacobi equation determined by the Riemannian metric and
consequently they are locally semi-concave with linear modulus. We also
analysis the structure of singularity sets of Busemann functions. Moreover we
study barrier functions, which are analogues to Mather's barrier functions in
Mather theory, and provide some fundamental properties. Based on barrier
functions, we could define some relations on the set of lines and thus classify
them. We also discuss some initial relations with the ideal boundary of the
Riemannian manifold.Comment: comments are welcome
Robust control of long distance entanglement in disordered spin chains
We derive temporally shaped control pulses for the creation of long-distance
entanglement in disordered spin chains. Our approach is based on a
time-dependent target functional and a time-local control strategy that permits
to ensure that the description of the chain in terms of matrix product states
is always valid. With this approach, we demonstrate that long-distance
entanglement can be created even for substantially disordered interaction
landscapes.Comment: Published versio
GeV Scale Asymmetric Dark Matter from Mirror Universe: Direct Detection and LHC Signatures
Mirror universe is a fundamental way to restore parity symmetry in weak
interactions. It naturally provides the lightest mirror nucleon as a unique
GeV-scale asymmetric dark matter particle candidate. We conjecture that the
mirror parity is respected by the fundamental interaction Lagrangian, and its
possible soft breaking arises only from non-interaction terms in the
gauge-singlet sector. We realize the spontaneous mirror parity violation by
minimizing the vacuum Higgs potential, and derive the corresponding Higgs
spectrum. We demonstrate that the common origin of CP violation in the visible
and mirror neutrino seesaws can generate the right amount of matter and mirror
dark matter via leptogenesis. We analyze the direct detections of GeV-scale
mirror dark matter by TEXONO and CDEX experiments. We further study the
predicted distinctive Higgs signatures at the LHC.Comment: 16pp. Plenary talk presented by HJH at the International Symposium on
Cosmology and Particle Astrophysics (CosPA2011). To appear in the conference
proceedings of IJMP. Minor refinement
Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
We present a new variational method, based on the matrix product operator
(MPO) ansatz, for finding the steady state of dissipative quantum chains
governed by master equations of the Lindblad form. Instead of requiring an
accurate representation of the system evolution until the stationary state is
attained, the algorithm directly targets the final state, thus allowing for a
faster convergence when the steady state is a MPO with small bond dimension.
Our numerical simulations for several dissipative spin models over a wide range
of parameters illustrate the performance of the method and show that indeed the
stationary state is often well described by a MPO of very moderate dimensions.Comment: Accepted versio
Quantum Electroweak Symmetry Breaking Through Loop Quadratic Contributions
Based on two postulations that (i) the Higgs boson has a large bare mass GeV at the characteristic energy scale which defines
the standard model (SM) in the ultraviolet region, and (ii) quadratic
contributions of Feynman loop diagrams in quantum field theories are physically
meaningful, we show that the SM electroweak symmetry breaking is induced by the
quadratic contributions from loop effects. As the quadratic running of Higgs
mass parameter leads to an additive renormalization, which distinguishes from
the logarithmic running with a multiplicative renormalization, the symmetry
breaking occurs once the sliding energy scale moves from down to a
transition scale at which the additive renormalized Higgs
mass parameter gets to change the sign. With the input of
current experimental data, this symmetry breaking energy scale is found to be
GeV, which provides another basic energy scale for the
SM besides . Studying such a symmetry breaking mechanism could play an
important role in understanding both the hierarchy problem and naturalness
problem. It also provides a possible way to explore the experimental
implications of the quadratic contributions as lies within the
probing reach of the LHC and the future Great Collider.Comment: 10 pages, 2 figures, published versio
Visibility computation through image generalization
This dissertation introduces the image generalization paradigm for computing visibility. The paradigm is based on the observation that an image is a powerful tool for computing visibility. An image can be rendered efficiently with the support of graphics hardware and each of the millions of pixels in the image reports a visible geometric primitive. However, the visibility solution computed by a conventional image is far from complete. A conventional image has a uniform sampling rate which can miss visible geometric primitives with a small screen footprint. A conventional image can only find geometric primitives to which there is direct line of sight from the center of projection (i.e. the eye) of the image; therefore, a conventional image cannot compute the set of geometric primitives that become visible as the viewpoint translates, or as time changes in a dynamic dataset. Finally, like any sample-based representation, a conventional image can only confirm that a geometric primitive is visible, but it cannot confirm that a geometric primitive is hidden, as that would require an infinite number of samples to confirm that the primitive is hidden at all of its points. ^ The image generalization paradigm overcomes the visibility computation limitations of conventional images. The paradigm has three elements. (1) Sampling pattern generalization entails adding sampling locations to the image plane where needed to find visible geometric primitives with a small footprint. (2) Visibility sample generalization entails replacing the conventional scalar visibility sample with a higher dimensional sample that records all geometric primitives visible at a sampling location as the viewpoint translates or as time changes in a dynamic dataset; the higher-dimensional visibility sample is computed exactly, by solving visibility event equations, and not through sampling. Another form of visibility sample generalization is to enhance a sample with its trajectory as the geometric primitive it samples moves in a dynamic dataset. (3) Ray geometry generalization redefines a camera ray as the set of 3D points that project at a given image location; this generalization supports rays that are not straight lines, and enables designing cameras with non-linear rays that circumvent occluders to gather samples not visible from a reference viewpoint. ^ The image generalization paradigm has been used to develop visibility algorithms for a variety of datasets, of visibility parameter domains, and of performance-accuracy tradeoff requirements. These include an aggressive from-point visibility algorithm that guarantees finding all geometric primitives with a visible fragment, no matter how small primitive\u27s image footprint, an efficient and robust exact from-point visibility algorithm that iterates between a sample-based and a continuous visibility analysis of the image plane to quickly converge to the exact solution, a from-rectangle visibility algorithm that uses 2D visibility samples to compute a visible set that is exact under viewpoint translation, a flexible pinhole camera that enables local modulations of the sampling rate over the image plane according to an input importance map, an animated depth image that not only stores color and depth per pixel but also a compact representation of pixel sample trajectories, and a curved ray camera that integrates seamlessly multiple viewpoints into a multiperspective image without the viewpoint transition distortion artifacts of prior art methods
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