Latest highlights from JPhysA: mathematical and theoretical

By Rebecca McCutcheon on October 23, 2015

A selection of the latest papers to be designated IOP Select for their novelty, significance and potential impact on future research.

$jpa519177f2_lr fractal$ Fractal position spectrum for a class of oscillators

E Sadurní and E Rivera-Mociños from The Institute for Physics at the Autonomous University of Puebla show that the position operator in a class of f-deformed oscillators has a fractal spectrum. This image shows the numerical spectrum of an off-diagonal ergodic operator with periodic boundary conditions.

Algebraic area enclosed by random walks on a lattice

In this work Jean Desbois from Paris-Sud University computes the moments〈A^2k〉of the algebraic area enclosed by a (closed or open) random walk on a lattice and also the characteristic function〈e^iRA〉 at order 1/N². The work begins with an algebraic area, A, enclosed by a random walk [OB] on a lattice. The walk is closed by adding the straight line [BO] (see figure).

Fusion rules for the logarithmic N = 1 superconformal minimal models: I. The Neveu–Schwarz sector

Michael Canagasabey et al explore some of the representation-theoretic aspects of the Neveu–Schwarz algebra that pertain to logarithmic conformal field theory. The figure shows examples of the structures of Neveu–Schwarz Fock modules.

Three-dimensional superintegrable systems in a static electromagnetic field

A Marchesiello et al’s paper details a systematic study of integrable and superintegrable systems in the presence of a magnetic field in three-dimensional Euclidean space E₃. The systems presented are exactly solvable, both in classical and quantum mechanics. The image shows an example of a classic trajectory given in terms of elliptic functions.