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

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/*N*^{2}. 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 *E*_{3 }. 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.

This work is licensed under a Creative Commons Attribution 3.0 Unported License. Images: 1. E Sadurní and E Rivera-Mociños 2015 *J. Phys. A: Math. Theor.* **48** 405301 2. Jean Desbois 2015 *J. Phys. A: Math. Theor.* **48** 425001 3. Michael Canagasabey *et al* 2015 *J. Phys. A: Math. Theor.* **48** 415402 4. A Marchesiello *et al* 2015 *J. Phys. A: Math. Theor.* **48** 395206 copyright IOP Publishing Ltd 2015

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Categories: Journal of Physics A: Mathematical and Theoretical

Tags: Computational physics, Mathematical physics, Particle physics, Quantum field theory, Quantum mechanics, Statistical physics