2,188 research outputs found
Gravitational radiations of generic isolated horizons and non-rotating dynamical horizons from asymptotic expansions
Instead of using a three dimensional analysis on quasi-local horizons, we
adopt a four dimensional asymptotic expansion analysis to study the next order
contributions from the nonlinearity of general relativity. From the similarity
between null infinity and horizons, the proper reference frames are chosen from
the compatible constant spinors for an observer to measure the energy-momentum
and flux near quasi-local horizons. In particular, we focus on the similarity
of Bondi-Sachs gravitational radiation for the quasi-local horizons and compare
our results to Ashtekar-Kirshnan flux formular. The quasi-local energy momentum
and flux of generic isolated horizons and non-rotating dynamical horizons are
discussed in this paper.Comment: PRD, 15 page
Domain wall space-times with a cosmological constant
We solve vacuum Einstein's field equations with the cosmological constant in
space-times admitting 3-parameter group of isometries with 2-dimensional
space-like orbits. The general exact solutions, which are represented in the
advanced and retarded null coordinates, have two arbitrary functions due to the
freedom of choosing null coordinates. In the thin-wall approximation, the
Israel's junction conditions yield one constraint equation on these two
functions in spherical, planar, and hyperbolic domain wall space-times with
reflection symmetry. The remain freedom of choosing coordinates are completely
fixed by requiring that when surface energy density of domain walls
vanishes, the metric solutions will return to some well-known solutions. It
leads us to find a planar domain wall solution, which is conformally flat, in
the de Sitter universe.Comment: 9 pages. no figur
The Expressivity of Classical and Quantum Neural Networks on Entanglement Entropy
Analytically continuing the von Neumann entropy from R\'enyi entropies is a
challenging task in quantum field theory. While the -th R\'enyi entropy can
be computed using the replica method in the path integral representation of
quantum field theory, the analytic continuation can only be achieved for some
simple systems on a case-by-case basis. In this work, we propose a general
framework to tackle this problem using classical and quantum neural networks
with supervised learning. We begin by studying several examples with known von
Neumann entropy, where the input data is generated by representing with a generating function. We adopt KerasTuner to determine the
optimal network architecture and hyperparameters with limited data. In
addition, we frame a similar problem in terms of quantum machine learning
models, where the expressivity of the quantum models for the entanglement
entropy as a partial Fourier series is established. Our proposed methods can
accurately predict the von Neumann and R\'enyi entropies numerically,
highlighting the potential of deep learning techniques for solving problems in
quantum information theory.Comment: 57 pages, 25 figure
Quantum Entanglement and Spectral Form Factor
We replace a Hamiltonian with a modular Hamiltonian in the spectral form
factor and the level spacing distribution function. This study establishes a
connection between quantities within Quantum Entanglement and Quantum Chaos. To
have a universal study for Quantum Entanglement, we consider the Gaussian
random 2-qubit model. The maximum violation of Bell's inequality demonstrates a
positive correlation with the entanglement entropy. Thus, the violation plays
an equivalent role as Quantum Entanglement. We first provide an analytical
estimation of the relation between quantum entanglement quantities and the dip
when a subregion only has one qubit. Our numerical result confirms the
analytical estimation. The occurring of the first dip shows a positive
correlation to entanglement entropy. The dynamics in a subregion is independent
of the initial state at a late time. It is one of the signaling conditions for
classical chaos. However, the simulation shows that the level spacing
distribution function is not in perfect agreement with random matrix theory at
a late time. In the end, we develop a technique within QFT to the spectral form
factor for its relation to an -sheet manifold. We apply the technology to a
single interval in CFT and the spherical entangling surface in
super Yang-Mills theory. The result is one for both cases, but
the R\'enyi entropy can depend on the R\'enyi index. For the case of CFT,
it indicates the difference between the continuum and discrete spectrum.Comment: 22 pages, 4 figures, minor changes, reference change
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