Dynamics of Driven Dissipative Heisenberg Spins with Inertia

Abstract

This thesis is a study of the interplay between inertia, dissipation and driving on the dynamics of many-body systems in d-dimensions. The simplest example of a many-body spin system possessing inertial dynamics is the Heisenberg Model in which the spins precess in response to the local magnetic field. It is convenient to work with coarse grained magnetisation variables, while focussing the study at length scales much larger than any microscopic length(Typically of order lattice). By using the Hubbard-Stratonovich transformation the coarse graining is realised in a systematic way, and then the Landau-Ginzburg free-energy functional is obtained by taking a continuum limit. As in the single particle example the study arrives at equations of motion for the spin starting with a Heisenberg spin model interacting with a heat bath(consists of phonons or electrons) the resulting equations of motion have both inertia and dissipation and also thermal noise. The interplay between the inertia and dissipation is analysed by studying the ordering dynamics of this spin model as it approaches equilibrium following a quench from the high temperature phase. The effect of external driving on a Heisenberg magnet is studied in the presence of both dissipation and inertia. The last problem discusses the Heisenberg spins driven by an external thermal current generated by sandwiching the spin system between two different heat sources. In the last two problems the spin system is driven far from its equilibrium configuration.