No abstract

We consider the harmonic and anharmonic chains of oscillators with self-consistent stochastic reservoirs and derive an integral representation (à la Feynman-Kac) for the correlations, in particular, for the heat flow. For the harmonic chain, we give a new proof that its thermal conductivity is finite in the steady state. Based on this integral representation for the correlations and a perturbative analysis, the approach is quite general and can be extended to more intricate systems.

We investigate the Lagrangian mechanism of the kinematic "fluctuation" magnetic dynamo in turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely many field lines to each space point, with the resultant magnetic field at that point given by the average over all the individual line vectors. As a consequence of the roughness of the advecting velocity, this remains true even in the limit of zero resistivity. We show that the presence of dynamo effect requires sufficient angular correlation of the passive line-vectors that arrive simultaneously at the same space point. We demonstrate this in detail for the Kazantsev-Kraichnan model of kinematic dynamo with a Gaussian advecting velocity that is spatially rough and white-noise in time. In the regime where dynamo action fails, we also obtain the precise rate of decay of the magnetic energy. These exact results for the model are obtained by a generalization of the "slow-mode expansion" of Bernard, Gawȩdzki and Kupiainen to non-Hermitian evolution. Much of our analysis applies also to magnetohydrodynamic turbulence.

In this paper we show how the equations of motion of a superfield, which makes its appearance in a path-integral approach to classical mechanics, can be derived without the need of the least-action principle

We consider the analytical investigation of the heat current in the steady state of the quantum harmonic chain of oscillators with alternate masses and self-consistent reservoirs. We analyze the thermal conductivity kappa and obtain interesting properties: in the high temperature regime, where quantum and classical descriptions coincide, kappa does not change with temperature, but it is quite sensitive to the difference between the alternate masses; and contrasting with this behavior, in the low temperature regime, kappa becomes an explicit function of the temperature, but its dependence on the masses difference disappears. Our results reinforce the message that quantum effects cannot be neglected in the study of heat conduction in low temperatures.