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Turns out that this was my PhD thesis subject.

To put it simply two-level systems (TLS) are groups of atoms in a disordered solid that present two stable configurations, that is two physical states of similar potential energy separated by a small energy barrier. The barriers need to be small for it to be overcome by thermal fluctuation alone and thus for the TLS to resonate at a frequency close to the frequency of interest.

If you are interested by what exactly are these TLSs at the atomic level, have a look at this paper: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.97.014201


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