45,600 research outputs found
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
We study analytically and numerically decoding properties of finite rate
hypergraph-product quantum LDPC codes obtained from random (3,4)-regular
Gallager codes, with a simple model of independent X and Z errors. Several
non-trival lower and upper bounds for the decodable region are constructed
analytically by analyzing the properties of the homological difference, equal
minus the logarithm of the maximum-likelihood decoding probability for a given
syndrome. Numerical results include an upper bound for the decodable region
from specific heat calculations in associated Ising models, and a minimum
weight decoding threshold of approximately 7%.Comment: 14 pages, 5 figure
Quantum Network Models and Classical Localization Problems
A review is given of quantum network models in class C which, on a suitable
2d lattice, describe the spin quantum Hall plateau transition. On a general
class of graphs, however, many observables of such models can be mapped to
those of a classical walk in a random environment, thus relating questions of
quantum and classical localization. In many cases it is possible to make
rigorous statements about the latter through the relation to associated
percolation problems, in both two and three dimensions.Comment: 23 pages. To appear in '50 years of Anderson Localization', E
Abrahams, ed. (World Scientific)
The HPx software for multicomponent reactive transport during variably-saturated flow: Recent developments and applications
Abstract
HPx is a multicomponent reactive transport model which uses HYDRUS as the flow and transport solver and PHREEQC-3 as the biogeochemical solver. Some recent adaptations have significantly increased the flexibility of the software for different environmental and engineering applications. This paper gives an overview of the most significant changes of HPx, such as coupling transport properties to geochemical state variables, gas diffusion, and transport in two and three dimensions. OpenMP allows for parallel computing using shared memory. Enhancements for scripting may eventually simplify input definitions and create possibilities for defining templates for generic (sub)problems. We included a discussion of root solute uptake and colloid-affected solute transport to show that most or all of the comprehensive features of HYDRUS can be extended with geochemical information. Finally, an example is used to demonstrate how HPx, and similar reactive transport models, can be helpful in implementing different factors relevant for soil organic matter dynamics in soils. HPx offers a unique framework to couple spatial-temporal variations in water contents, temperatures, and water fluxes, with dissolved organic matter and CO2 transport, as well as bioturbation processes
Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
Using a recent strategy to encode the space of flat connections on a
three-manifold with string-like defects into the space of flat connections on a
so-called 2d Heegaard surface, we propose a novel way to define gauge invariant
bases for (3+1)d lattice gauge theories and gauge models of topological phases.
In particular, this method reconstructs the spin network basis and yields a
novel dual spin network basis. While the spin network basis allows to interpret
states in terms of electric excitations, on top of a vacuum sharply peaked on a
vanishing electric field, the dual spin network basis describes magnetic (or
curvature) excitations, on top of a vacuum sharply peaked on a vanishing
magnetic field (or flat connection). This technique is also applicable for
manifolds with boundaries. We distinguish in particular a dual pair of boundary
conditions, namely of electric type and of magnetic type. This can be used to
consider a generalization of Ocneanu's tube algebra in order to reveal the
algebraic structure of the excitations associated with certain 3d manifolds.Comment: 45 page
Shape Animation with Combined Captured and Simulated Dynamics
We present a novel volumetric animation generation framework to create new
types of animations from raw 3D surface or point cloud sequence of captured
real performances. The framework considers as input time incoherent 3D
observations of a moving shape, and is thus particularly suitable for the
output of performance capture platforms. In our system, a suitable virtual
representation of the actor is built from real captures that allows seamless
combination and simulation with virtual external forces and objects, in which
the original captured actor can be reshaped, disassembled or reassembled from
user-specified virtual physics. Instead of using the dominant surface-based
geometric representation of the capture, which is less suitable for volumetric
effects, our pipeline exploits Centroidal Voronoi tessellation decompositions
as unified volumetric representation of the real captured actor, which we show
can be used seamlessly as a building block for all processing stages, from
capture and tracking to virtual physic simulation. The representation makes no
human specific assumption and can be used to capture and re-simulate the actor
with props or other moving scenery elements. We demonstrate the potential of
this pipeline for virtual reanimation of a real captured event with various
unprecedented volumetric visual effects, such as volumetric distortion,
erosion, morphing, gravity pull, or collisions
Renormalization of tensor-network states
We have discussed the tensor-network representation of classical statistical
or interacting quantum lattice models, and given a comprehensive introduction
to the numerical methods we recently proposed for studying the tensor-network
states/models in two dimensions. A second renormalization scheme is introduced
to take into account the environment contribution in the calculation of the
partition function of classical tensor network models or the expectation values
of quantum tensor network states. It improves significantly the accuracy of the
coarse grained tensor renormalization group method. In the study of the quantum
tensor-network states, we point out that the renormalization effect of the
environment can be efficiently and accurately described by the bond vector.
This, combined with the imaginary time evolution of the wavefunction, provides
an accurate projection method to determine the tensor-network wavfunction. It
reduces significantly the truncation error and enable a tensor-network state
with a large bond dimension, which is difficult to be accessed by other
methods, to be accurately determined.Comment: 18 pages 23 figures, minor changes, references adde
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