Response to ``Comment on `Frequency-domain stimulated and spontaneous light emission signals at molecular junctions''' J. Chem. Phys. 142, 137101 (2015)]

In a recent work [U. Harbola, B. K. Agrawalla, and S. Mukamel, J. Chem. Phys. 141, 074107 (2014)], we have presented a superoperator (Liouville space) diagrammatic formulation of spontaneous and stimulated optical signals from current-carrying molecular junctions. We computed the diagrams that contribute to the spontaneous light emission SLE (fluorescence and Raman) signal using a diagrammatic method which clearly distinguishes between the Raman and the fluorescence contributions. We pointed out some discrepancies with the work of Galperin, Ratner and Nitzan (GRN) [M. Galperin, M. A. Ratner and, A. Nitzan, J. Chem. Phys. 130, 144109 (2009)]. In their response [M. Galperin, M. A. Ratner and A. Nitzan, “Comment on‘ Frequency-domain stimulated and spontaneous light emission signals at molecular junctions’” [J. Chem. Phys. 141, 074107 (2014)], J. Chem. Phys. 142, 137101 (2015)] to our work, GRN have argued that there are no differences in the choice of Raman diagrams in both works. Here we reply to their points and show where the differences exist.

Spontaneous Lorentz violation: the case of infrared QED

It is by now clear that the infrared sector of quantum electrodynamics (QED) has an intriguingly complex structure. Based on earlier pioneering work on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the U(1) charge group of QED to the ``Sky'' group incorporating the well-known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality (Balachandran and Vaidya, Eur Phys J Plus 128:118, 2013). It was shown that the ``Sky'' group is generated by the algebra of angle-dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of the Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle-dependent fermion mass, modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content, and time dilation formulas for decays should also get corrections.

Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.