8,713 research outputs found
Zero area singularities in general relativity and inverse mean curvature flow
First we restate the definition of a Zero Area Singularity, recently
introduced by H. Bray. We then consider several definitions of mass for these
singularities. We use the Inverse Mean Curvature Flow to prove some new results
about the mass of a singularity, the ADM mass of the manifold, and the capacity
of the singularity.Comment: 13 page
Variational quantum Monte Carlo simulations with tensor-network states
We show that the formalism of tensor-network states, such as the matrix
product states (MPS), can be used as a basis for variational quantum Monte
Carlo simulations. Using a stochastic optimization method, we demonstrate the
potential of this approach by explicit MPS calculations for the transverse
Ising chain with up to N=256 spins at criticality, using periodic boundary
conditions and D*D matrices with D up to 48. The computational cost of our
scheme formally scales as ND^3, whereas standard MPS approaches and the related
density matrix renromalization group method scale as ND^5 and ND^6,
respectively, for periodic systems.Comment: 4+ pages, 2 figures. v2: improved data, comparisons with exact
results, to appear in Phys Rev Let
Superlubricity - a new perspective on an established paradigm
Superlubricity is a frictionless tribological state sometimes occurring in
nanoscale material junctions. It is often associated with incommensurate
surface lattice structures appearing at the interface. Here, by using the
recently introduced registry index concept which quantifies the registry
mismatch in layered materials, we prove the existence of a direct relation
between interlayer commensurability and wearless friction in layered materials.
We show that our simple and intuitive model is able to capture, down to fine
details, the experimentally measured frictional behavior of a hexagonal
graphene flake sliding on-top of the surface of graphite. We further predict
that superlubricity is expected to occur in hexagonal boron nitride as well
with tribological characteristics very similar to those observed for the
graphitic system. The success of our method in predicting experimental results
along with its exceptional computational efficiency opens the way for modeling
large-scale material interfaces way beyond the reach of standard simulation
techniques.Comment: 18 pages, 7 figure
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