Equilibration problem for the generalized Langevin equation

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions necessary for equilibration for the case when the system potential is harmonic. We then give an example with a particular bath where we show that, even for parameter values where the harmonic case always equilibrates, with any finite amount of nonlinearity the system does not equilibrate for arbitrary initial conditions. We understand this as a consequence of the formation of nonlinear localized excitations similar to the discrete breather modes in nonlinear lattices.Comment: 5 pages, 2 figure

Electron Magnetic Resonance: The Modified Bloch Equation

We find a modified Bloch equation for the electronic magnetic moment when the magnetic moment explicitly contains a diamagnetic contribution (a magnetic field induced magnetic moment arising from the electronic orbital angular momentum) in addition to the intrinsic magnetic moment of the electron. The modified Bloch is coupled to equations of motion for the position and momentum operators. In the presence of static and time varying magnetic field components, the magnetic moment oscillates out of phase with the magnetic field and power is absorbed by virtue of the magnetic field induced magnetic moment, even in the absence of coupling to the environment. We explicitly work out the spectrum and absorption for the case of a $p$ state electron

Rotational dynamics and friction in double-walled carbon nanotubes

We report a study of the rotational dynamics in double-walled nanotubes using molecular dynamics simulations and a simple analytical model reproducing very well the observations. We show that the dynamic friction is linear in the angular velocity for a wide range of values. The molecular dynamics simulations show that for large enough systems the relaxation time takes a constant value depending only on the interlayer spacing and temperature. Moreover, the friction force increases linearly with contact area, and the relaxation time decreases with the temperature with a power law of exponent $-1.53 \pm 0.04$.Comment: submitted to PR

The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.Comment: 13 pages, 11 figure