The “glass transition” as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse

Nussinov, Zohar; Weingartner, Nicholas B.; Nogueira, Flavio S.

doi:10.1142/9789813271340_0006

Cited by 3 publications

(4 citation statements)

References 71 publications

(89 reference statements)

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“…Such a general combination of eigenstates does not imply experimentally discernible equilibrium solid (crystalline) order. Sharp Bragg peaks need not appear in states formed by superposing eigenstates that, individually, display order [21,132]. This absence of ordering reflects the possible lack of clear structure when, e.g., randomly superposing different Fourier modes with each Fourier mode displaying its defining periodic order.…”

Section: Captures Viable Contributions From Any "Phase Transition Energymentioning

confidence: 99%

Macroscopic length correlations in non-equilibrium systems and their possible realizations

Nussinov

2020

Nuclear Physics B

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We consider general systems that start from and/or end in thermodynamic equilibrium while experiencing a finite rate of change of their energy density or of other intensive quantities q at intermediate times. We demonstrate that at these times, during which the global intensive quantities q vary at a finite rate, the associated covariance, the connected pair correlator Gij = qiqj − qi qj , between any two (far separated) sites i and j in a macroscopic system may, on average, become finite. Such non-vanishing connected correlations between distant sites are general and may also appear in quantum and classical theories that only have local interactions. If in an initial equilibrium state, the intensive quantities q are static then a minimal time scale tmin may need to be exceeded in order for an external drive to create a finite expectation value of dq/dt; concomitantly, in such driven systems, a finite average of Gij over all site pairs can appear at times t > tmin. For systems of linear scale L with a maximal (Lieb-Robinson or other) speed v, this minimal time tmin = O(L/v). Once the global mean q no longer changes, the average of Gij over all site pairs i and j may tend to zero. However, when the equilibration times are significant (e.g., as in a glass that is not in true thermodynamic equilibrium yet in which the energy density (or temperature) reaches a final steady state value), these long range correlations may persist also long after q ceases to change. We explore viable experimental implications of our findings and speculate on their potential realization in glasses (where a prediction of a theory based on the effect that we describe here suggests a universal collapse of the viscosity that agrees with all published viscosity measurements over sixteen decades) and non-Fermi liquids. We derive uncertainty relation based inequalities that connect the heat capacity to the dynamics in general open thermal systems. These rigorous inequalities suggest the shortest possible fluctuation times scales in open equilibrated systems at a temperature T are typically "Planckian" (i.e., O( /(kBT ))). We briefly comment on parallels between quantum measurements, unitary quantum evolution, and thermalization and on how Gaussian distributions of intensive quantities may generically emerge at long times after the system is no longer driven.

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Section: Captures Viable Contributions From Any "Phase Transition Energymentioning

confidence: 99%

Macroscopic length correlations in non-equilibrium systems and their possible realizations

Nussinov

2020

Nuclear Physics B

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“…Physically, the distribution may be not only a function of the activation energy alone but also of the temperature. Indeed, in a similar spirit on a different problem (that of supercooled liquids below the melting (or liquidus) temperature ), a particular theory [23][24][25][26] reproduces all experimentally measured data of supercooled liquids over 16 decades of viscosity with a single-parameter scale free temperature dependent normal distribution of effective equilibrium relaxation rates. In what follows, we will test the applicability of Eq.…”

Section: Introductionmentioning

confidence: 77%

“…Beyond its historical roots in chemical reaction rates, the Arrhenius equation has seen widespread use in other (at times, interrelated) arenas including (i) semiconductor physics (e.g., where it enables a determination of the number of thermally activated electrons in the conduction and valence bands) [10] aiding theoretical design and enabling a basic understanding of diodes, transistors, solar cells, and principles of semiconductor devices, (ii) metallurgy (e.g., creep rate and the number of vacancies/interstitial sites in a crystal), e.g., [11][12][13][14], (iii) the analysis of data from dynamical probes such as those of dielectric response, NMR and NQR in a host of systems, e.g., [15][16][17][18][19], (iv) relaxation rates associated with particles of fixed structural "softness" (an analogue of elastic defect density in amorphous systems whose average value correlates with the viscosity) [20] and, notably, (v) fluid dynamics-the focus of our work. Before proceeding further, we must briefly comment on a well known exception to activated liquid dynamicsthat of supercooled fluids, e.g., [21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Deviations from Arrhenius dynamics in high temperature liquids, a possible collapse, and a viscosity bound

Xue¹,

Nogueira²,

Kelton³

et al. 2021

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Liquids realize a highly complex state of matter in which strong competing kinetic and interaction effects come to life. As such, liquids are, generally, more challenging to understand than either gases or solids. In weakly interacting gases, the kinetic effects dominate. By contrast, low temperature solids typically feature far smaller fluctuations about their ground state. Notwithstanding their complexity, with the exception of quantum fluids (e.g., superfluid Helium) and supercooled liquids (including glasses), various aspects of common liquid dynamics such as their dynamic viscosity are often assumed to be given by rather simple, Arrhenius-type, activated forms with nearly constant (i.e., temperature independent) energy barriers. In this work, we analyze experimentally measured viscosities of numerous liquids far above their equilibrium melting temperature to see how well this assumption fares. We find marked deviations from simple activated dynamics. Even far above their equilibrium melting temperatures, as the temperature drops, the viscosity of these liquids increases more strongly than predicted by activated dynamics dominated by a single uniform energy barrier. For metallic fluids, the scale of the prefactor in the Arrhenius form for the viscosity is consistent with that given by the product ( ℎ) with the number density and ℎ Planck's constant. More generally, in all fluids (whether metallic or non-metallic), ( ℎ) constitutes a lower bound on the viscosity. We find that a scaling of the temperature axis (complementing that of the viscosity) leads to a partial collapse of the temperature dependent viscosities of different fluids; such a scaling allows for a functional dependence of the viscosity on temperature that includes yet is far more general than activated Arrhenius form alone. We speculate on relations between non-Arrhenius dynamics and thermodynamic observables.

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“…In the present work we hence focus on the eigenvector field for the different modes, and in particular study its topological properties. The idea that topological properties might be useful to understand certain thermodynamic and kinetic features of glasses has been suggested only in recent years 44,45 . Subsequently Baggioli et al have put forward the relevance of topological properties by showing that plasticity is mediated by topological features in the non-affine displacement field of glasses under deformation 39 .…”

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confidence: 99%

Topology of vibrational modes predicts plastic events in glasses

et al. 2023

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The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events to structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation.

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The “glass transition” as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse

Cited by 3 publications

References 71 publications

Macroscopic length correlations in non-equilibrium systems and their possible realizations

Macroscopic length correlations in non-equilibrium systems and their possible realizations

Deviations from Arrhenius dynamics in high temperature liquids, a possible collapse, and a viscosity bound

Topology of vibrational modes predicts plastic events in glasses

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