We study the dissipative, classical dynamics of a charged particle in the presence of a magnetic field. Two stochastic models are employed, and a comparative analysis is made, one based on diffusion processes and the other on jump processes. In the literature on collision-broadening of spectral lines, these processes go under the epithet of weak-collision model and Boltzmann-Lorentz model, respectively. We apply our model calculation to investigate the effect of magnetic field on the collision-broadened spectral lines, when the emitter carries an electrical charge. The spectral lines show narrowing as the magnetic field is increased, the narrowing being sharper in the Boltzmann-Lorentz model than in the weak collision model.

We study the quantum Brownian motion of a charged particle in the presence of a magnetic field. From the explicit solution of a quantum Langevin equation we calculate quantities such as the velocity correlation function and the mean-squared displacement. Our calculated expressions contain as special cases the motion of aclassical particle in a magnetic field and that of afree (but quantum) particle, in a dissipative environment.

Biswas and Soni [4] have surmised a semiclassical formula for Berry’s phase in terms of a generating function. We derive this formula apart from showing that it is not true in general and investigate its domain of validity. We also derive transformation formulae for Berry’s phase (Hannay’s angle) under general canonical transformations. A simpler proof for total angle invariance than hitherto available, is given.