  Usually one finds that dissipation tends to make a quantum system more
classical in nature. In this paper we study the effect of momentum dissipation
on a quantum system. The momentum of the particle is coupled bilinearly to the
momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we
find that the position and momentum variances for momentum coupling are
respectively identical to momentum and position variances for spatial friction.
This implies that momentum coupling leads to an increase in the fluctuations in
position as the temperature is lowered, exactly the opposite of the classical
like localization of the oscillator, found with spatial friction. For a
parabolic barrier, momentum coupling causes an {\it increase} in the unstable
normal mode barrier frequency, as compared to the lowering of the barrier
frequency in the presence of purely spatial coupling. This increase in the
frequency leads to an enhancement of the thermal tunneling flux, which below
the crossover temperature becomes exponentially large. The crossover
temperature between tunneling and thermal activation {\it increases} with
momentum friction so that quantum effects in the escape are relevant at higher
temperatures.
