  We experimentally study the various manifestations of ohmic losses in a
two-dimensional microwave chaotic cavity and exhibit two different
contributions to the resonance widths. We show that the parts of these widths,
which vary from mode to mode, are associated to ohmic losses located at the
boundary of the cavity. We also describe how this non-proportional damping is
responsible for the complex character of wavefunctions (corresponding to a
spatially non-uniform phase), which is ubiquitous in open or dissipative wave
systems. We experimentally demonstrate that the non-proportional widths are
related to a single parameter, which measures the amount of complexity of
wavefunctions, and provide theoretical arguments in favor of this relation.
