  A theoretical analysis based on a numerical solution of the coupled
time-dependent Ginzburg-Landau and heat dissipation equations shows a strong
dependence of the critical currents on the applied magnetic field in a
mesoscopic square with attached contacts. In agreement with experiment we found
hysteresis which are caused by a strong heat dissipation in the sample at
currents close to the depairing Ginzburg-Landau current and/or the dynamics of
the superconducting condensate. The theoretically obtained nonmonotonous
dependence of the switching current (from superconducting to the resistive
state) on the applied magnetic field, arising from the changes in the
vorticity, agrees quantitatively with the experimental data. Our results show
that heat dissipation leads to an increase of the hysteresis in the
current-voltage characteristic and hence masks the actual dynamics of the
superconducting condensate.
