On Collins’s new viewpoint in physics [J. Math. Phys. 34, 3210–3221 (1993)]

Robert E. Collins

Eugene Paul Wigner

Jonathan M. Robbins

This Viewpoint relates to an article by J H Hannay (1985 J. Phys. A: Math. Gen. 18 221) and was published as part of a series of Viewpoints celebrating some of the most influential papers published in Journal of Physics A, which is celebrating its 50th anniversary.

Benoı̂t Collins, Ion Nechita

In this paper, we present applications of the calculus developed in Collins and Nechita [Comm. Math. Phys. 297 (2010) 345–370] and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to Gaussianization methods. Our main application is an in-depth study of the random matrix model introduced by Hayden and Winter [Comm. Math. Phys. 284 (2008) 263–280] and used recently by Brandao and Horodecki [Open Syst. Inf. Dyn. 17 (2010) 31–52] and Fukuda and King [J. Math. Phys. 51 (2010) 042201] to refine the Hastings counterexample to the additivity conjecture in quantum information theory. This model is exotic from the point of view of random matrix theory as its eigenvalues obey two different scalings simultaneously. We study its asymptotic behavior and obtain an asymptotic expansion for its von Neumann entropy.

Eugene Paul Wigner

Murray T. Batchelor

This Viewpoint relates to an article by den Nijs (1979 J. Phys. A: Math. Gen. 12 1857) and was published as part of a series of Viewpoints celebrating 50 of the most influential papers published in the J. Phys. series, which is celebrating its 50th anniversary. In this landmark paper Marcel den Nijs, at that time a graduate student supervised by Hubert Knops in Nijmegen, The Netherlands, proposed an exact formula for the thermal critical exponents of the two-dimensional q-state Potts model. The enduring influence of this paper is a measure of the importance of the Potts model and the value of exact results