  We study mesoscopic resonant tunneling as well as multichannel Kondo problems
by mapping them to a first-quantized quantum mechanical model of a particle
moving in a multi-dimensional periodic potential with Ohmic dissipation. From a
renormalization group analysis, we obtain phase diagrams of the quantum
Brownian motion model with various lattice symmetries. For a symmorphic
lattice, there are two phases at T=0: a localized phase in which the particle
is trapped in a potential minimum, and a free phase in which the particle is
unaffected by the periodic potential. For a non-symmorphic lattice, however,
there may be an additional intermediate phase in which the particle is neither
localized nor completely free. The fixed point governing the intermediate phase
is shown to be identical to the well-known multichannel Kondo fixed point in
the Toulouse limit as well as the resonance fixed point of a quantum dot model
and a double-barrier Luttinger liquid model. The mapping allows us to compute
the fixed-poing mobility $\mu^*$ of the quantum Brownian motion model exactly,
using known conformal-field-theory results of the Kondo problem. From the
mobility, we find that the peak value of the conductance resonance of a
spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the
resonance line shape is predicted.
