相关论文: Volume as an index of a subalgebra
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…
Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt, the aim in this paper…
The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…
Volume of metric balls relates to rate-distortion theory and packing bounds on codes. In this paper, the volume of balls in complex Grassmann manifolds is evaluated for an arbitrary radius. The ball is defined as a set of hyperplanes of a…
If there exists a completely bounded projection of B(H) onto a von Neumann algebra M on H, then M is injective. If there exists a bounded projection and M is properly infinite, the same conclusion holds.
The first terms of the small volume asymptotic expansion for the splitting of Neumann boundary condition Laplacian eigenvalues due to a grounded inclusion of size {\epsilon} are derived. An explicit formula to compute the first term from…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
We take a first step towards developing a new language to describe causal structure, event horizons, and quantum extremal surfaces (QES) for the bulk description of holographic systems beyond the standard Einstein gravity regime. By…
We argue that the Leutheusser-Liu procedure of isolating a von Neumann algebra in the $N = \infty$ limit of string theories, leads to the algebra of relativistic fermion fields on a half line for the $c = 1$ string theory. This is a Type…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
We study a simple version of the AdS/CFT (anti-de Sitter spacetime/Conformal Field Theory) correspondence, where operators have integer conformal dimensions. In this model, bulk causality follows from boundary analyticity, even in…
Accretion is thought to primarily contribute to the mass accumulation history of supermassive black holes throughout cosmic time. While this may be true at high redshifts, at lower redshifts and for the most massive black holes mergers…
The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a…
We compute the topologically twisted index for general $\mathcal{N} = 2$ supersymmetric field theories on $\mathbb{H}_2\times S^1$. We also discuss asymptotically $AdS_4$ magnetically charged black holes with hyperbolic horizon, in…
We provide a deep Boltzmann machine (DBM) for the AdS/CFT correspondence. Under the philosophy that the bulk spacetime is a neural network, we give a dictionary between those, and obtain a restricted DBM as a discretized bulk scalar field…
The explanation of black hole entropy as statistical entropy is one of the big successes of string theory. In this article we review recent progress in this subject, focussing on understanding quantum effects on black hole entropy.…
A ``large'' AdS black hole can attain equilibrium with its own Hawking radiation, and in that condition it is thought to be dual to a strongly coupled field theory, also at equilibrium. But the interior of the black hole is by no means…
We investigate the bulk reconstruction of AdS black hole spacetime emergent from quantum entanglement within a machine learning framework. Utilizing neural ordinary differential equations alongside Monte-Carlo integration, we develop a…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…
Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix…