Quantum theory of structured monochromatic light

Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom that the photons inherit from the classical wave solutions are orthogonal. To test this critical assumption, we quantize the beam-like solutions of the vector Helmholtz equation from first principles to delineate its elementary quantum mechanical degrees of freedom. We show that although the beam-photon operators do not in general satisfy the canonical commutation relations, implying that the photon states they create are not orthogonal, the states are nevertheless bona fide eigenstates of the number and Hamiltonian operators. The explicit representation for the photon operators presented in this work forms a natural basis to study light-matter interactions and quantum information processing at the single photon level

Pausing the Game: Esports Developers’ Copyright Claims to Prevent or Restrict Tournament Play

Unlike traditional sports, esports are-—at their core—-video games, which must be designed and programmed by a game company. These video game developers are the copyright owners of the esports titles they create, which, in turn, results in continued developer control even after a player has purchased or downloaded the game. Because there is no relevant court precedent that is directly applicable to the world of esports, game developers unimpededly exert their copyright authority in order to restrict third-party tournaments that utilize their games, and in some cases, prevent those events from occurring altogether. This use of copyright authority is an overly broad construction of copyright law that deprives gaming communities of valuable events and fails to protect one of the most important interests of the copyright holder: consumer trust. This Note argues that control over third-party tournaments does not fall within the rights guaranteed to copyright owners by the Copyright Act of 1976. While esports developers should maintain some level of control over their titles, the right to conduct tournaments for their games is one that should not be held exclusively. This Note proposes a compulsory licensing scheme for esports titles as a superior alternative to the current approach. After publishing its game, a developer would register its title with a licensing collective, which could grant conditional licenses to any third party that wishes to organize tournaments using that game. This scheme sufficiently balances the interests of both video-game developers and third-party tournament organizers

Climbing the Anki Mountain, One (Review) Step at a Time: A Written and Video-Based Guide on Using Anki in Medical School to Enhance Knowledge Acquisition and Retention

https://digitalcommons.unmc.edu/emet_posters/1030/thumbnail.jp

An index theorem for Wiener--Hopf operators

We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this C$^*$-algebra is known to be isomorphic to the reduced C$^*$-algebra of a certain restricted action groupoid. In a previous paper, we have determined a composition series of this C$^*$-algebra, and compute the $K$-theory homomorphisms induced by the `symbol' maps given by the subquotients of the composition series in terms of the analytical index of a continuous family of Fredholm operators. In this paper, we obtain a topological expression for these index maps in terms of geometric-topological data naturally associated to the underlying convex cone. The resulting index formula is expressed in the framework of Kasparov's bivariant $KK$-theory. Our proof relies heavily on groupoid methods.Comment: 46 pages, 1 figure; last version prior to publication, journal reference adde