  We study the dissipative dynamics of a charged oscillator in a magnetic field
by coupling (a la Caldeira and Leggett) it to a heat bath consisting of
non-interacting harmonic oscillators. We derive here the auto-correlation
functions of the position and momentum and study its behavior at various
limiting situations. The equilibrium (steady state) dispersions of position and
momentum are obtained from their respective autocorrelation functions. We
analyse the equilibrium position and momentum dispersions at low and high
temperatures for both low and high magnetic field strengths. We obtain the
classical diffusive behavior (at long times) as well as the equilibrium
momentum dispersion of the free quantum charged particle in a magnetic field,
in the limit of vanishing oscillator potential {\omega}_0 . We establish the
relations between the reduced partition function and the equilibrium
dispersions of the dissipative and confined cyclotron problem.
