We present a novel view of the standard model of tunneling two level systems (TLS) to explain the puzzling universal value of a quantity, $C\sim 3\times 10^{-4}$, that characterizes phonon scattering in glasses below 1 K as reflected in thermal conductivity, ultrasonic attenuation, internal friction, and the change in sound velocity. Physical considerations lead to a broad distribution of phonon-TLS couplings that (1) exponentially renormalize tunneling matrix elements, and (2) reduce the TLS density of states through TLS-TLS interactions. We find good agreement between theory and experiment for a variety of individual glasses.
Scalable Physics-Inspired Transformers for Spin Glasses
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（基础与前沿科学研究院，电子科技大学）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（物理科学与技术学院，北京邮电大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（理论物理研究所，中国科学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州先进研究院，UCAS）；School of Physics, University of Electronic Science and Technology of China（物理学院，电子科技大学）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（量子物理与光量子信息重点实验室，教育部，电子科技大学）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（四川省非经典信息科学基础学科研究中心，电子科技大学）
