Photonic neural networks (PNNs) are promising to replace conventional deep learning hardware due their potentially higher energy efficiency and computational speed. Other than the fast progress on optical linear transformer, nonlinear activators much less mature. Usually, employ mapping from input amplitude output amplitude, which is limited by high threshold loss, or rely additional bias volta...

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here co...

The reversal time of the magnetization of single-domain ferromagnetic particles is estimated for mixed uniaxial and cubic anisotropy energies possessing nonparaboloidal saddles and well bottoms or either. The calculation generalizes the existing adaptation of the Kramers escape rate theory to fine ferromagnetic particles with nonaxially symmetric magnetocrystalline-Zeeman energies, originally b...

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissi...

We propose a scheme based on topological insulators to generate Kramers pairs of Majorana fermions or parafermions in the complete absence of magnetic fields. Our setup consists of two topological insulators whose edge states are brought close to an s-wave superconductor. The resulting proximity effect leads to an interplay between a nonlocal crossed Andreev pairing, which is dominant in the st...

We consider the braiding of Kramers pairs of Majorana bound states. We derive the most general transformation on the many-body ground state that is applied as the result of such a braiding process. The result is derived in the context of a toy model, but we will show that it has the most general form that is compatible with local and global conservation of electron parity. In accordance with ea...

The famous Kramers rate theory for diffusion-controlled reactions has been extended in numerous ways and successfully applied to many types of reactions. Its application to protein folding reactions has been of particular interest in recent years, as many researchers have performed experiments and simulations to test whether folding reactions are diffusion-controlled, whether the solvent is the...

The single ion magnetic properties of Co(ii) are affected by the details of the coordination geometry of the ion. Here we show that a geometry close to trigonal prismatic which arises when the ligand 6,6'-((1Z)-((piperazine-1,4-diylbis(propane-3,1-diyl))bis(azanylylidene))bis(methanylylidene))bis(2-methoxyphenol) coordinates to Co(ii) does indeed lead to enhanced single-ion behaviour as has pre...