13,332 research outputs found
The road toward a general relativistic metric inside the Earth and its effect on neutrino travel from CERN to GRAN-SASSO Laboratory
In a first attempt to describe the effect on neutrino travel inside the Earth
caused by general relativity in the case of a dense Earth, we have neglected
the Earth's rotation, the Earth's ellipticity and also the surface terrain
variation, nevertheless we have focused our attention on the density
description of the Earth interior provided by geophysic's models such as PREM.
Assuming a non rotating Earth, the general relativistic effect on neutrino
travelling from CERN to GRAN-SASSO happened to produce a delay of .Comment: 26 page
Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape
An estimate is derived for the volume fraction of a subset in the neighborhood
of the critical set
of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O),
where represents the unitary time evolution operator, {\rho} is the initial
density matrix of the ensemble, and O is an observable operator. This estimate
is based on the Hilbert-Schmidt geometry for the unitary group and a
first-order approximation of . An upper bound on these
near-critical volumes is conjectured and supported by numerical simulation,
leading to an asymptotic analysis as the dimension of the quantum system
rises in which the volume fractions of these "near-critical" sets decrease to
zero as increases. This result helps explain the apparent lack of influence
exerted by the many saddles of over the gradient flow.Comment: 27 pages, 1 figur
What surface maximizes entanglement entropy?
For a given quantum field theory, provided the area of the entangling surface
is fixed, what surface maximizes entanglement entropy? We analyze the answer to
this question in four and higher dimensions. Surprisingly, in four dimensions
the answer is related to a mathematical problem of finding surfaces which
minimize the Willmore (bending) energy and eventually to the Willmore
conjecture. We propose a generalization of the Willmore energy in higher
dimensions and analyze its minimizers in a general class of topologies
and make certain observations and conjectures which may have
some mathematical significance.Comment: 21 pages, 2 figures; V2: typos fixed, Refs. adde
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