3,100 research outputs found
Inducing Effect on the Percolation Transition in Complex Networks
Percolation theory concerns the emergence of connected clusters that
percolate through a networked system. Previous studies ignored the effect that
a node outside the percolating cluster may actively induce its inside
neighbours to exit the percolating cluster. Here we study this inducing effect
on the classical site percolation and K-core percolation, showing that the
inducing effect always causes a discontinuous percolation transition. We
precisely predict the percolation threshold and core size for uncorrelated
random networks with arbitrary degree distributions. For low-dimensional
lattices the percolation threshold fluctuates considerably over realizations,
yet we can still predict the core size once the percolation occurs. The core
sizes of real-world networks can also be well predicted using degree
distribution as the only input. Our work therefore provides a theoretical
framework for quantitatively understanding discontinuous breakdown phenomena in
various complex systems.Comment: Main text and appendices. Title has been change
Thermodynamics of Taub-NUT-AdS Spactimes
We apply the generalised Komar method proposed in [arxiv:2208.05494] to
Taub-NUT-AdS spacetime in the theory of Einstein gravity plus a cosmological
constant. Based on a generalised closed 2-form, we derive the total mass and
NUT charge of the Taub-NUT-AdS spacetime. Together with other thermodynamic
quantities calculated through standard method, we conform the first law and
Smarr relation. Then, we consider charged AdS NUTy spacetimes in
Einstein-Maxwell theory with a cosmological constant, and show that the
generalised Komar method works, too. We obtain all the thermodynamic
quantities, and the first law and Smarr relation are checked to be satisfied
automatically.Comment: 14 pages, no figur
Differentiable Programming Tensor Networks
Differentiable programming is a fresh programming paradigm which composes
parameterized algorithmic components and trains them using automatic
differentiation (AD). The concept emerges from deep learning but is not only
limited to training neural networks. We present theory and practice of
programming tensor network algorithms in a fully differentiable way. By
formulating the tensor network algorithm as a computation graph, one can
compute higher order derivatives of the program accurately and efficiently
using AD. We present essential techniques to differentiate through the tensor
networks contractions, including stable AD for tensor decomposition and
efficient backpropagation through fixed point iterations. As a demonstration,
we compute the specific heat of the Ising model directly by taking the second
order derivative of the free energy obtained in the tensor renormalization
group calculation. Next, we perform gradient based variational optimization of
infinite projected entangled pair states for quantum antiferromagnetic
Heisenberg model and obtain start-of-the-art variational energy and
magnetization with moderate efforts. Differentiable programming removes
laborious human efforts in deriving and implementing analytical gradients for
tensor network programs, which opens the door to more innovations in tensor
network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted
for publication in PRX. Source code available at
https://github.com/wangleiphy/tensorgra
Smarr Integral Formula of D-dimensional Stationary Spacetimes in Einstein-\AE ther-Maxwell Theroy
Using the Wald formalism, we investigate the thermodynamics of charged black
holes in D-dimensional stationary spacetimes with or without rotations in
Einstein-\ae ther-Maxwell theory. In particular, assuming the existence of a
scaling symmetry of the action, we obtain the Smarr integral formula, which can
be applied to both Killing and universal horizons. When restricted to
4-dimensional spherically symmetric spacetimes, previous results obtained by a
different method are re-derived.Comment: No figures and tables. Phys. Let. B782 (2018) 723-72
The puzzle of anomalously large isospin violations in
The BES-III Collaboration recently report the observation of anomalously
large isospin violations in , where the in the invariant mass
spectrum appears to be much narrower ( 10 MeV) than the peak width
(50 MeV) measured in other processes. We show that a mechanism, named as
triangle singularity (TS), can produce a narrow enhancement between the charged
and neutral thresholds, i.e., . It can also
lead to different invariant mass spectra for
and , which can possibly explain the long-standing puzzle
about the need for two close states and in
and , respectively. The TS could be a key to our
understanding of the nature of and advance our knowledge
about the mixing between and .Comment: 4 pages and 7 eps figures; Journal-matched versio
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