The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations f...

A brief history is presented, outlining the development of rate theory during the past century. Starting from Arrhenius [Z. Phys. Chem. 4, 226 (1889)], we follow especially the formulation of transition state theory by Wigner [Z. Phys. Chem. Abt. B 19, 203 (1932)] and Eyring [J. Chem. Phys. 3, 107 (1935)]. Transition state theory (TST) made it possible to obtain quick estimates for reaction rat...

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.

A double nanohole in a metal film can optically trap nanoparticles such as polystyrene/silica spheres, encapsulated quantum dots and up-converting nanoparticles. Here we study the dynamics of trapped particles, showing a skewed distribution and low roll-off frequency that are indicative of Kramers-hopping at the nanoscale. Numerical simulations of trapped particles show a double-well potential ...

The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995)] using a procedure based on the method of reactive flux and the phase space distribution function. Their analysis is restricted to the high friction regime or diffusion-limite...

We continue the investigation on the applications of the Kramers equation to the numerical simulation of field theoretic models. In a previous paper we have described the theory and proposed various algorithms. Here, we compare the simplest of them with the Hybrid Monte Carlo algorithm studying the two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action with dynamical Wils...

We consider Kramers pairs of Majorana bound states under adiabatic time evolution. This is important for the prospects of using such bound states as parity qubits. We show that local adiabatic perturbations can cause a rotation in the space spanned by the Kramers pair. Hence, the quantum information is unprotected against local perturbations, in contrast to the case of single localized Majorana...