  We present a classical analog of the quantum metric tensor, which is defined
for classical integrable systems that undergo an adiabatic evolution governed
by slowly varying parameters. This classical metric measures the distance, on
the parameter space, between two infinitesimally different points in phase
space, whereas the quantum metric tensor measures the distance between two
infinitesimally different quantum states. We discuss the properties of this
metric and calculate its components, exactly in the cases of the generalized
harmonic oscillator, the generalized harmonic oscillator with a linear term,
and perturbatively for the quartic anharmonic oscillator. Finally, we propose
alternative expressions for the quantum metric tensor and Berry's connection in
terms of quantum operators.
