Dissipative dynamics of classical and quantum systems

Abstract

We have calculated the dynamic structure factor for tethered surfaces in the concentrated and semi-dilute regimes. We also calculated the concentration dependence of the diffusion constant and the coefficient of form birefringence in these regimes. We have made an assumption of how the end-to-end distance must scale as a function of the linear size L of the membrane to calculate the above-mentioned quantities. These results should be easily verifiable by neutron and light scattering experiments. In this chapter, we have used the formalism developed in references [1], [2], and [4] to calculate the dissipative dynamics of a charged spinless particle in the presence of a magnetic field. Firstly, we have obtained the position autocorrelation function in the presence of a magnetic field and shown that it is qualitatively the same as that of a free particle, provided there is dissipation. Secondly, we have calculated the time-averaged induced orbital magnetic moment of the electron and found it to be smaller than the Landau diamagnetic moment of an electron without dissipation. With dissipation switched off, we do recover the normal Landau result. We now apply the above-mentioned formalism to analyze qualitatively two specific situations: 1. A Rydberg atom in a damped cavity, and 2. A deep impurity level in a semiconductor. Firstly, we describe the possible application of our results to a Rydberg atom in a damped cavity.