To investigate the possible contribution to the thermal transport from the interactions between the tunneling systems in glasses, we have performed measurements on a glass sample composed of a capillary array to suppress the propagation of the thermal phonons, which are generally believed to be solely responsible for the heat transport in glasses. The measurement is performed down to 16 mK using our recently developed contact-free technique, which employs optical heating and a SQUID-based magnetization thermometers. The preliminary results show that the thermal conductivity of such a sample first follows the expected cubic temperature dependence and then, at temperatures below 50 mK, gradually starts to have a much smaller temperature exponent as temperature goes down, indicating either the onset of a new transport mechanism or the propagation of phonons over the pores of the capillary array.
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