Letters are outstanding short papers reporting new and timely developments in mathematical and theoretical physics. They are concise, innovative and high quality. Here are some of our recent highlights:
Self-avoiding walks subject to a force (Open Access)
Professor Esaias J Janse van Rensburg from York University, Toronto and Stuart G Whittington from Toronto University, Canada prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. More specifically they show the force dependence of the free energy is identical when the force is applied at the last vertex or at the top (confining) plane, and discuss the relevance of this result to numerical results and to a recent result about convergence rates when the walk is being pushed towards the surface.
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. In this Letter Dorje Brody from Brunel University, London shows, that in contrast, PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics.
Read our past interview with Brody here: Quantum mechanics meets mathematical finance
Michel Bauer, Denis Bernard and Antoine Tilloy from CEA Saclay and ENS, France use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. They found using a time proportional to the effect of measurements on the system provided a better parametrization of the evolution in the limit of infinitely strong continuous measurements and illustrated the benefits of this approach.
They believe the same ideas could be used in the discrete case of iterated weak measurement and in higher dimensions, though specific examples of interest are still to be worked out. Eventually, the method proposed could be general enough to have applications to the analysis of other SDEs in the strong noise limit, e.g. in population dynamics and turbulence.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License. Image 1 – E J Janse van Rensburg and S G Whittington 2016 J. Phys. A: Math. Theor. 49 11LT01 Image 2 – Adapted from Michel Bauer et al 2016 J. Phys. A: Math. Theor. 49 10LT01