Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schr\"odinger chain in the regime of homogeneous chaos

We study the discrete nonlinear Schr\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density $\rho$ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, $D(\rho)=D_0\rho^2$. An explicit expression for $D_0$ is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.Comment: 24 pages, 13 figure

Theory of electron spin resonance in bulk topological insulators Bi2Se3, Bi2Te3 and Sb2Te3

We report a theoretical study of electron spin resonance in bulk topological insulators, such as Bi2Se3, Bi2Te3 and Sb2Te3. Using the effective four-band model, we find the electron energy spectrum in a static magnetic field and determine the response to electric and magnetic dipole perturbations, represented by oscillating electric and magnetic fields perpendicular to the static field. We determine the associated selection rules and calculate the absorption spectra. This enables us to separate the effective orbital and spin degrees of freedom and to determine the effective g-factors for electrons and holes.Comment: 10 pages, 4 figure

Effect of inelastic collisions on multiphonon Raman scattering in graphene

We calculate the probabilities of two- and four-phonon Raman scattering in graphene and show how the relative intensities of the overtone peaks encode information about relative rates of different inelastic processes electrons are subject to. If the most important processes are electron-phonon and electron-electron scattering, the rate of the latter can be deduced from the Raman spectra

Effect of disorder on coherent quantum phase slips in Josephson junction chains

We study coherent quantum phase-slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total QPS amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains