Complex Dynamics of Glass-Forming Liquids

Götze, W.

doi:10.1093/acprof:oso/9780199235346.001.0001

Cited by 624 publications

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“…Hence, the general scenario emerging for an arbitrary ternary mixture is that of two distinct glass transitions with ¼ 1=2 (for the discontinuous case), and ¼ 1 (for the continuous one). These critical exponents reproduce exactly the MCT results for the F 12 schematic model [2], in which the memory kernel takes the form m 12 ¼ v 1 ðtÞ þ v 2 2 ðtÞ.…”

Section: Prl 105 265704 (2010) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 75%

“…Although this line of research has been pursued very actively in recent years, little attention has been paid to the possibility of reproducing, within this framework, more complex types of glassy behavior (for some exceptions, see [8,9]). In fact, even simple schematic mode-coupling theory (MCT) models predict the occurrence of topologically stable singularities of higher complexity [2]. Liquids confined in a disordered porous matrix [10] and attractive colloids [11,12] are some examples in which these scenarios have been recently observed.…”

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Dynamic Facilitation Picture of a Higher-Order Glass Singularity

et al. 2010

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We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions. Although the glassy state of matter has been a long-time fascinating topic for physicists, it still presents several mysterious aspects [1]. Perhaps, the most controversial one is the very nature of the glass transition: that is the question of whether vitrification is a purely dynamical process or rather the (dynamical) manifestation of a genuine thermodynamic amorphous phase. In spite of much progress (for reviews, see [2][3][4][5][6]) the problem remains widely open. On one hand, there are notorious experimental and computational difficulties related to the exceedingly long equilibration times of macroscopic samples, and to the possibility of detecting unambiguously the elusive ''amorphous order.'' On the other hand, theoretical modeling of glassy systems has made clear that slow relaxation processes are ubiquitous and may result from very distinct mechanisms.

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Section: Prl 105 265704 (2010) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 75%

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confidence: 99%

Dynamic Facilitation Picture of a Higher-Order Glass Singularity

et al. 2010

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“…the normalized density timecorrelator exceeds 1.0 or becomes negative. For equilibrium systems, it is easy to prove that the absolute value of the normalized density time-correlator is less than 1.0 [35], and that the density time-correlator monotonically decays in the overdamped limit [2]. On the other hand, for general nonequilibrium systems, there seems to be no rigorous proof of the bounded property or the monotonicity of the density time-correlators.…”

Section: Fig 4 (Color Online)mentioning

confidence: 99%

“…Although not yet perfect, the mode-coupling theory (MCT) presents remarkable success in its application to glassy materials such as colloidal suspensions [1][2][3]. Probably the most striking feature of MCT is that it predicts a two-step relaxation phenomenon (the β-relaxation followed by the α-relaxation) [4,5] of the intermediate scattering function (i.e.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems

Suzuki

Hayakawa

2013

Phys. Rev. E

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Nonequilibrium mode-coupling theory (MCT) for uniformly sheared underdamped systems is developed, starting from the microscopic thermostatted SLLOD equation, and the corresponding Liouville equation. Special attention is paid to the translational invariance in the sheared frame, which requires an appropriate definition of the transient time-correlators. The derived MCT equation satisfies the alignment of the wavevectors, and is manifestly translationally invariant. Isothermal condition is implemented by the introduction of the current fluctuation in the dissipative coupling to the thermostat. This current fluctation grows in the α-relaxation regime, which generates a deviation of the yield stress in the glassy phase from the overdamped case. Response to a perturbation of the shear rate demonstrates an inertia effect which is not observed in the overdamped case. Our theory turns out to be a non-trivial extension of the theory by Fuchs and Cates (J. Rheol. 53(4), 2009) to underdamped systems. Since our starting point is identical to that by Chong and Kim (Phys. Rev. E 79, 2009), the contradictions between Fuchs-Cates and Chong-Kim are resolved.

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“…If this initial state converges to equilibrium the system is called mixing, implying ergodicity, and it is nonmixing, otherwise. An important question is: Does there exist a sharp ergodicity breaking transition under variation of a physical control parameter like temperature or strength of perturbation?Within a mode coupling theory for supercooled liquids such a dynamical glass transition has been found, but its sharpness seems to result from the mode coupling approximations (for reviews see [1,2]). It is not our purpose to contribute to the theory of glass transition, but to study the influence of anharmonicity on the relaxational behavior at zero-temperature.…”

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Delocalization-Localization Transition due to Anharmonicity

Hajnal

Schilling

2008

Phys. Rev. Lett.

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Analytical and numerical calculations for a reduced Fermi-Pasta-Ulam chain demonstrate that energy localization does not require more than one conserved quantity. Clear evidence for the existence of a sharp delocalization-localization transition at a critical amplitude Ac is given. Approaching Ac from above and below, diverging time scales occur. Above Ac, the energy packet converges towards a discrete breather. Nevertheless, ballistic energy transportation is present, demonstrating that its existence does not necessarily imply delocalization.PACS numbers: 05.60Cd, 63.20.Pw One of the classical investigations of relaxation dynamics of macroscopic systems is to determine the time evolution of a perturbed equilibrium state. If this initial state converges to equilibrium the system is called mixing, implying ergodicity, and it is nonmixing, otherwise. An important question is: Does there exist a sharp ergodicity breaking transition under variation of a physical control parameter like temperature or strength of perturbation?Within a mode coupling theory for supercooled liquids such a dynamical glass transition has been found, but its sharpness seems to result from the mode coupling approximations (for reviews see [1,2]). It is not our purpose to contribute to the theory of glass transition, but to study the influence of anharmonicity on the relaxational behavior at zero-temperature. In that case the generic lowest energy state of a particle system is a crystal. One may ask a similar question as above: Does an initially localized energy excitation spread over the complete crystal, or not? In case of small excitation amplitudes, one can use the harmonic approximation. Then the time evolution of an initial configuration can be determined, exactly [3]. For one-dimensional harmonic lattices the results are particularly simple [4,5]. Independent of the strength and size of the excitation it always spreads over the full system, and energy transportation is ballistic, provided that there is no disorder. That infinite harmonic crystals are ergodic in general, has been proven rigorously [6]. If the excitation amplitude increases, anharmonicity gets important.Let us neglect any disorder, but taking anharmonic interactions into account. Discreteness of the lattice combined with anharmonicity allows for the existence of localized periodic vibrations, called discrete breathers (DB). For reviews see Ref. [7]. Their existence suggests that under certain conditions a localized excitation may converge to a DB, whereby suppressing complete energy spreading. Indeed, numerical solutions of the discrete nonlinear Schrödinger equation (DNLS) [8] and references wherein, the Klein Gordon chain (KG) [9] and the β-Fermi-Pasta-Ulam chain (FPU) [10,11] demonstrate generation of DB and their role for slow energy relaxation. Particularly, the numerical results in Refs. [8,11] give evidence that DB generation from an initially localized excitation requires an excitation amplitude which is large enough. This has been supported by analytical stu...

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Complex Dynamics of Glass-Forming Liquids

Cited by 624 publications

References 0 publications

Dynamic Facilitation Picture of a Higher-Order Glass Singularity

Dynamic Facilitation Picture of a Higher-Order Glass Singularity

Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems

Delocalization-Localization Transition due to Anharmonicity

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