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Register a new userRelationship between two-level systems and quasi-localized normal modes in glasses
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Tunnelling Two-Level Systems (TLS) dominate the physics of glasses at low temperatures. Yet TLS are extremely rare and it is extremely difficult to directly observe them $it{in , silico}$. It is thus crucial to develop simple structural predictors that can provide markers for determining if a TLS is present in a given glass region. It has been speculated that Quasi-Localized vibrational Modes (QLM) are closely related to TLS, and that one can extract information about TLS from QLM. In this work we address this possibility. In particular, we investigate the degree to which a linear or non-linear vibrational mode analysis can predict the location of TLS independently found by energy landscape exploration. We find that even though there is a notable spatial correlation between QLM and TLS, in general TLS are strongly non-linear and their global properties cannot be predicted by a simple normal mode analysis.
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The existence of a constant density of two-level systems (TLS) was proposed as the basis of some intriguing universal aspects of glasses at ultra-low temperatures. Here we ask whether their existence is necessary for explaining the universal density of states quasi-localized modes (QLM) in glasses at ultra-low temperatures. A careful examination of the QLM that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as $omega^3$ and the other as $omega^4$. The properties of the glassy energy landscape that is responsible for the two types of modes is examined here, explaining the analytic feature responsible for the creations of (at least) two families of QLMs. Although adjacent wells certainly exist in the complex energy landscape of glasses, doubt is cast on the relevance of TLS for the universal density of QLMs.
We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply-peaked quasi-extended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q-factors of resonators.
We study the relation between quasi-normal modes (QNMs) and transmission resonances (TRs) in one-dimensional (1D) disordered systems. We show for the first time that while each maximum in the transmission coefficient is always related to a QNM, the reverse statement is not necessarily correct. There exists an intermediate state, at which only a part of the QNMs are localized and these QNMs provide a resonant transmission. The rest of the solutions of the eigenvalue problem (denoted as strange quasi-modes) are never found in regular open cavities and resonators, and arise exclusively due to random scatterings. Although these strange QNMs belong to a discrete spectrum, they are not localized and not associated with any anomalies in the transmission. The ratio of the number of the normal QNMs to the total number of QNMs is independent of the type of disorder, and slightly deviates from the constant $sqrt{2/5}$ in rather large ranges of the strength of a single scattering and the length of the random sample.
We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at low temperatures (1 K and below). We study an ensemble of TLSs coupled to phonons. By integrating out the phonons within the framework of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive analytically the explicit form of the interactions among TLSs, and of the dissipation terms. We find that the unitary dynamics of the system shows clear signatures of Many-Body Localization physics. We study numerically the time behavior of the concurrence, which measures pairwise entanglement also in non-isolated systems, and show that it presents a power-law decay both in the absence and in the presence of dissipation, if the latter is not too large. These features can be ascribed to the strong, long-tailed disorder characterizing the distributions of the model parameters. Our findings show that assuming ergodicity when discussing TLS physics might not be justified for all kinds of experiments on low-temperature glasses.
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
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