19,144 research outputs found
Entropy Bounds, Holographic Principle and Uncertainty Relation
A simple derivation of the bound on entropy is given and the holographic
principle is discussed. We estimate the number of quantum states inside space
region on the base of uncertainty relation. The result is compared with the
Bekenstein formula for entropy bound, which was initially derived from the
generalized second law of thermodynamics for black holes. The holographic
principle states that the entropy inside a region is bounded by the area of the
boundary of that region. This principle can be called the kinematical
holographic principle. We argue that it can be derived from the dynamical
holographic principle which states that the dynamics of a system in a region
should be described by a system which lives on the boundary of the region. This
last principle can be valid in general relativity because the ADM hamiltonian
reduces to the surface term.Comment: LaTeX, 8 pages, no figure
Scattering of twisted particles: extension to wave packets and orbital helicity
High-energy photons and other particles carrying non-zero orbital angular
momentum (OAM) emerge as a new tool in high-energy physics. Recently, it was
suggested to generate high-energy photons with non-zero OAM (twisted photons)
by the Compton backscattering of laser twisted photons on relativistic electron
beams. Twisted electrons in the intermediate energy range have also been
demostrated experimentally; twisted protons and other particles can in
principle be created in a similar way. Collisions of energetic twisted states
can offer a new look at particle properties and interactions. A theoretical
description of twisted particle scattering developed previously treated them as
pure Bessel states and ran into difficulty when describing the OAM of the final
twisted particle at non-zero scattering angles. Here we develop further this
formalism by incorporating two additional important features. First, we treat
the initial OAM state as a wave packet of a finite transverse size rather than
a pure Bessel state. This realistic assumption allows us to resolve the
existing controversy between two theoretical analyses for non-forward
scattering. Second, we describe the final twisted particle in terms of the
orbital helicity --- the OAM projection on its average direction of propagation
rather than on the fixed reaction axis. Using this formalism, we determine to
what extent the twisted state is transferred from the initial to final OAM
particle in a generic scattering kinematics. As a particular application, we
prove that in the Compton backscattering the orbital helicity of the final
photon stays close to the OAM projection of the initial photon.Comment: 18 pages, 4 figures; v2: expanded introduction and section 4.2 on
final orbital helicit
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