Quantum manifolds

Valentin Lychagin

Metin Celalettin, Horace King

The 'Celalettin-Field Quantum Observation Tunnel' (Celalettin Tunnel) is a quantum observation technique. It is within a pneumatic manifold of Euclidean space where the randomness of particle Orbital Angular Momentum (OAM) is mitigated via electric polarization. It is described by the Celalettin Tunnel Conjecture. The presence of an electric field affects the nuclear spin of the particles within the pneumatic manifold. The manifold, namely the IC-Manifold, or Invizicloud© is unique as its axioms are a combination of classical and quantum non-logical parameters. The IC-Manifold has a variable density and exists only according to 'Celalettin's two rules of quantum interaction':1. Quantum interaction causes quantum observation during fundamental particle interactions with orbital angular momentum electric polarized atoms within the IC-Manifold causing depolarization. 2. The photoelectric effect is not limited to solids but can occur in an IC-Manifold.

Hoshang Heydari

In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We also investigate entangled multipartite states based on moment map and Delzant's construction of toric manifolds and algebraic toric varieties.

Jan Naudts

Michael Hartley Freedman, Matthew B. Hastings

Jakub Bělín, Tomáš Tyc, S. A. R. Horsley

Abstract We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.