The cosmological redshift is described by the intersection of two Hubble spheres, where a Hubble sphere is defined as a range over which spherical, quantum-waves interact, specifically R u = 1.9 × 10 26 m.

We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations. The C∗algebras associated with the discretized CCRs are the non-commutative spheres of Bratteli, Elliott, Evans and Kishimoto. 1991 Mathematics Subject Classification. Primary 46L40;...

Dynamically triangulated surface model is found to undergo a first-order crumpling transition between the smooth phase and a crumpled phase. Triangulated spheres are divided into compartmentalized domains, whose boundary bonds remain unflipped in the Monte Carlo simulations. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the su...

We show that for any co-amenable compact quantum group A = C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T → EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if a...

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or current fluctuations. The objects’ shape and composition enter only through their scattering...

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of all Podles̀ quantum spheres relative to an arbitary automorphism. Our calculations are based on a free resolution due to Masuda, Nakagami and Watanabe.

We describe the quantum subspaces of Banica-Goswami’s half-liberated real-spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.