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We have calculated the temperature profiles for phonon heat transport in asuspended membrane with a radially symmetric heat source in the two extremecases of either fully ballistic or fully diffusive transport. Theoreticalresults confirm that it is possible to distinguish these two transportmechanisms from the radial temperature profiles alone. Models are also comparedto experimental data measured with 40 nm thick, free standing silicon nitridemembranes below 1 K by using tunnel junction (SINIS) thermometers. The measuredtemperature profile is qualitatively in agreement with the ballistic model.

Temperature Profile for Ballistic and Diffusive Phonon Transport in a Suspended Membrane with a Radial Symmetric Heat Source