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We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, s σ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for s σ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constant $\lambda$. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperature $T_c$. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space., Comment: v3: matching the published version

For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be manifested, and consider particle exchange events in the gaslike regime of fluid dynamics as a dynamical process with an intrinsic time scale. We subsequently propose a quantitative criterion of particle indistinguishability and associated quantum statistics to be inoperative at short time and emerge at long time. Verifiable experimentally, our predictions enable a systematic search for a transition between statistics-active and statistics-inactive regimes in quantum fluids.

We reply to the Comment by Bryk et al. [Phys Rev. E 106, 036601 (2022)10.1103/PhysRevE.106.036601] on our paper [Phys. Rev. E 105, 024602 (2022)2470-004510.1103/PhysRevE.105.024602].

Microfluidic and nanofluidic technologies have asserted themselves as new paradigms which have radically boomed activities dedicated to the chemical, bio-analysis and biomedical sectors. In spite of intense technological development, the fundamental physico-chemical properties of liquids confined on sub-millimeter scales have remained poorly understood. One of the most striking effects is the large elasticity (and viscosity) of confined liquids, which grows upon further decreasing the confinement length, L. Liquids under sub-millimeter confinement display a low-frequency shear modulus in the order of 1 − 10 3 Pa, contrary to our everyday experience of liquids as bodies with a zero low-frequency shear modulus. While early experimental evidence of this effect (starting with Boris Derjaguin's work) was met with skepticism due to its counterintuitive character and abandoned, further experimental results and most recently a 1 new atomistic theoretical framework have confirmed that liquids indeed possess a finite low-frequency shear modulus G and that this scales with the inverse cubic power of confinement length L. After a brief historical overview and an introduction to the theoretical description of this effect, we show that this law is universal by analyzing experimental data on a wide range of materials (water, glycerol, ionic liquids, nonentangled polymer liquids, isotropic liquids crystals). Open questions and potential applications in mechanochemistry, energy and other fields are highlighted in conclusion.

We present an analytically solvable theory of Bose–Einstein condensation (BEC) in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness L is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature T c ∼ L −1/2. For cold Bose gases, this implies an enhancement up to two orders of magnitude in T c for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. C ∼ T 2, is predicted for nano-scale films, which implies a different λ-point behavior with respect to bulk systems, while the condensate fraction is predicted to follow a [ 1 − ( T / T c ) 2 ] law.

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction $\eta$ and the P\'eclet ($\textrm{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered value of $\textrm{Pe},$ we observe a very good agreement between theoretical findings and numerical results from literature, up to rather large values of $\eta.$ The theory predicts a consistent enhancement of the structure factor $ S(k)$ at $k \to 0,$ upon increasing the $\textrm{Pe}$ number. We argue this behaviour may signal the onset of a phase transition from the isotropic phase to a non-uniform one, induced by the external shear flow.

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the superconducting critical temperature has a non-monotonic behaviour with respect to the phononic frequency in the Kramers-like point. This remarkable behaviour is produced by a resonance, that occurs when electrons and phonons on the topological surfaces have the same energy: this effectively increases the electron-phonon interaction and hence the Cooper pair binding energy, thus establishing an optimal condition for the superconducting phase. With this mechanism, the $T_{c}$ can be increased by well over a factor two, and the maximum enhancement occurs in the degenerate phononic flat-band limit.

The mechanical properties of crystals are controlled by the translational symmetry of their structures. But for glasses with a disordered structure, the link between the symmetry of local particle arrangements and stability is not well established. In this contribution, we provide experimental verification that the centrosymmetry of nearest-neighbor polyhedra in a glass strongly correlates with the local mechanical stability. We examine the distribution of local stability and local centrosymmetry in a glass during aging and deformation using microbeam x-ray scattering. These measurements reveal the underlying relationship between particle-level structure and larger-scale behavior and demonstrate that spatially connected, coordinated local transformations to lower symmetry structures are fundamental to these phenomena. While glassy structures lack obvious global symmetry breaking, local structural symmetry is a critical factor in predicting stability.

We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors k and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower k in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high k is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.

Melting is well understood in terms of the Lindemann criterion, essentially stating that crystalline materials melt when the thermal vibrations of their atoms become such vigorous that they shake themselves free of the binding forces. However, how about another common type of solids: glasses, where the nature of the solid-liquid crossover is highly controversial? The Lindemann criterion implies that the thermal expansion coefficients alpha of crystals are inversely proportional to their melting temperatures. Here we find that, unexpectedly, alpha of glasses decreases much stronger with increasing glass-transition temperature Tg marking the liquid-solid crossover in this material class. However, scaling alpha by the fragility m, a measure of particle cooperativity, restores the proportionality, i.e., alpha/m ~ 1/Tg. Obviously, for a glass to become liquid, it is not sufficient to simply overcome the interparticle binding energies. Instead, more energy has to be invested to break up the typical cooperative particle network which is considered a hallmark feature of glassy materials. Surprisingly, alpha of the liquid phase reveals similar anomalous behaviour and is universally enhanced by a constant factor of ~3. The found universalities allow estimating glass-transition temperatures from thermal expansion and vice versa., Comment: 6 pages, 2 figures + Supplementary Information (9 pages, 1 figure, 2 tables). First submitted version of manuscript

We present an analytically solvable theory of Bardeen-Cooper-Schrieffer-type superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. Closed-form expressions for the dependence of the superconducting critical temperature [Formula: see text] as a function of the confinement size [Formula: see text] are obtained, in quantitative agreement with experimental data with no adjustable parameters. Upon increasing the confinement, a crossover from a spherical Fermi surface, which contains two growing hollow spheres corresponding to states forbidden by confinement, to a strongly deformed Fermi surface, is predicted. This crossover represents a new topological transition, driven by confinement, between two Fermi surfaces belonging to two different homotopy classes. This topological transition provides a mechanistic explanation of the commonly observed non-monotonic dependence of [Formula: see text] upon film thickness with a maximum which, according to our theory, coincides with the topological transition.

The misfolding of proteins and their aggregation in the form of fibrils or amyloid-like spherulites are involved in a spectrum of degenerative diseases. Our current understanding of protein aggregation mechanisms has primarily relied on the use of conventional spectrometric methods to determine the average growth rates and microscopic morphology of the final structures, consequently masking the morphological and growth heterogeneity of the aggregates. We developed a REal-time kinetics via binding and Photobleaching LOcalisation Microscopy (REPLOM) super-resolution method to directly observe and quantify the existence and abundance of diverse aggregate morphologies and their heterogeneous growth kinetics. Specifically, our results revealed that the growth of insulin amyloid spherulites is not exclusively isotropic but, surprisingly, may also occur anisotropically. Combining our technique with machine learning, we associated growth rates to specific morphological transitions and provided energy barriers and the energy landscape for each aggregation morphology. Our unifying framework for the detection and analysis of spherulite growth can be extended to other protein systems to reveal their aggregation processes and the broad spectrum of diverse morphologies at the single-molecule level.

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density of states (VDOS) of affinely strained configurations at varying strain values. The affine strain, found analytically on the static (undeformed) snapshot of the glass, leads to configurations that are rich of soft low-energy modes as well as unstable modes (negative eigenvalues) that are otherwise completely "washed out" and lost, if one lets the system relax after strain. This procedure is fully consistent with the structure of NALD. The INM spectrum of deformed states allows for the analytical prediction of the stress-strain curve of a model glass, including the prediction of the yield point. Good parameter-free quantitative agreement is shown between the prediction and simulations of athermal quasi-static shear of a coarse-grained polymer glass.

We present an analytical derivation of the volume fractions for random close packing (RCP) in both d=3 and d=2, based on the same methodology. Using suitably modified nearest neighbor statistics for hard spheres, we obtain ϕ_{RCP}=0.658 96 in d=3 and ϕ_{RCP}=0.886 48 in d=2. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammed state and dictates ϕ_{RCP} via the coordination number z, (iii) disordered packings with ϕϕ_{RCP} are possible at the expense of creating some order, and z=12 at the fcc limit acts as a boundary condition.

The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ω

Optimizing materials' properties and functions by controlling defects in the crystalline phase has been a cornerstone of materials science and condensed matter physics. However, this paradigm has yet to be established in the broadly defined amorphous materials, which implies the identification of very subtle structural features in an otherwise uniformly disordered medium. Here we propose and define a new integrated glassy defect (IGD), based on machine learning strategy informed by atomistic physics, and also by an extremely wide configurational, thermodynamic, and dynamic variables space of the disordered state. The IGD simultaneously includes positional topology and vibrational features, as well as the local morphology of the potential energy landscape. This unprecedented combination gives rise to a much more comprehensive and more effective definition of the ``glassy defect,'' much beyond the conventional, purely structural input. IGD can be used not only as an efficient predictor of athermal plasticity but is also transferable to detect both short-time vibrational anomalies (the boson peak), and long-time relaxation and diffusion dynamics in glasses. The integrated strategy is instrumental to build the long-sought structure-property relationship in complex media.

A mathematical model to describe the emulsion polymerization kinetics of co- and ter-polymerizations is developed. The model uses the well-known pseudo-homopolymerization approach together with recently developed models for radical entry and desorption in order to monitor crucial kinetic variables such as conversion and latex composition. The model includes a series of unknown parameters related to monomer-specific gel-effect coefficients, that are needed to compute the bimolecular termination reaction rates. The unknown parameters are determined through extensive calibration of the model on literature data for homo- and co-polymerizations of n-butyl acrylate (n-BA) and methyl methacrylate (MMA). The so-obtained predictive model is then applied to the modelling of the ter-polymerization of n-BA and MMA with 2-hydroxyethyl methacrylate (2-HEMA) with sodium persulphate (SPR) as initiator: predictions for the time-evolution of particle size and conversion are in excellent agreement with experimental measurements using Dynamic Light Scattering (DLS) and Gas Chromatography (GC), upon tuning the gel-effect coefficient related to 2-HEMA. The developed model is used to quantify the surfactant surface coverage of the particles as well as the total concentration of counterions in the system throughout the entire polymerization process. This key information provides a way to rationalize and control the coagulation behavior during the whole polymerization process.

Funder: Royal Academy of Engineering; doi: https://doi.org/10.13039/501100000287, Funder: Pembroke College, University of Oxford (Pembroke College Oxford); doi: https://doi.org/10.13039/100010355, Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organisation for Scientific Research); doi: https://doi.org/10.13039/501100003246, The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents −3/2 and −5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.

Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane–Sachs–Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression ɛ 0/ɛ ∞ = |ω LO|2/|ω TO|2. The theory provides a microscopic expression for T c as a function of physical parameters, including the mode specific Grüneisen parameter. The theory also shows that ω T O ∼ ( T c − T ) 1 / 2 , and again specifies the prefactors in terms of Grüneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of ϵ 0 and to a polarization catastrophe at T c. A quantitative microscopic form of the Curie–Weiss law is derived with prefactors that depend on microscopic physical parameters.

We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus ${G}^{\ensuremath{'}}$. The nonaffine contribution is written as a sum over modes in $k$-space. With a rigorous argument based on the analysis of the $k$-space integral over modes, it is shown that the confinement size $L$ in one spatial dimension, e.g., the $z$ axis, leads to a infrared cutoff for the modes contributing to the nonaffine (softening) correction to the modulus that scales as ${L}^{\ensuremath{-}3}$. Corrections for finite sample size $D$ in the two perpendicular dimensions scale as $\ensuremath{\sim}{(L/D)}^{4}$, and are negligible for $L\ensuremath{\ll}D$. For liquids it is predicted that ${G}^{\ensuremath{'}}\ensuremath{\sim}{L}^{\ensuremath{-}3}$ is in agreement with a previous more approximate analysis, whereas for amorphous materials ${G}^{\ensuremath{'}}\ensuremath{\sim}{G}_{\text{bulk}}^{\ensuremath{'}}+\ensuremath{\beta}{L}^{\ensuremath{-}3}$. For the case of liquids, four different experimental systems are shown to be very well described by the ${L}^{\ensuremath{-}3}$ law. The theory can also explain previous simulation data of confined jammed granular packings.

Angelani et al. (1) suggest an alternative derivation of the relation between low-frequency shear modulus G ′ and confinement length L derived in ref. 2. They seem to imply that an integral over plane waves in three-dimensional (3D) isotropic media can be decoupled into a separate integral over k z (z component of wavevector k, the confined dimension), times an independent 2D integral in the unconfined ( k x , k y ) plane. This would then change the final integration in equation 9 of ref. 2 from G ′ = G ∞ − α ∫ 1 / L k D k 2 d k to G ′ = G ∞ − γ ∫ 1 / L k D d k , where α and γ are constants, and the scaling of G ′ with L … [↵][1]1To whom correspondence may be addressed. Email: az302{at}cam.ac.uk. [1]: #xref-corresp-1-1

An analytical derivation of the vibrational density of states (DOS) of liquids, and in particular of its characteristic linear in frequency low-energy regime, has always been elusive because of the presence of an infinite set of purely imaginary modes -- the instantaneous normal modes (INMs). By combining an analytic continuation of the Plemelj identity to the complex plane with the purely overdamped dynamics of the INMs, we derive a closed-form analytic expression for the low-frequency DOS of liquids. The obtained result explains from first principles the widely observed linear in frequency term of the DOS in liquids, whose slope appears to increase with the average lifetime of the INMs. The analytic results are robustly confirmed by fitting simulations data for Lennard-Jones liquids, and they also recover the Arrhenius law for the average relaxation time of the INMs, as expected., Comment: Accepted for publication in PNAS

The successful prediction of the specific heat of solids is a milestone in the kinetic theory of matter, due to Debye (1912). No such success, however, has ever been obtained for the specific heat of liquids, which has remained a mystery for over a century. A theory of specific heat of liquids is derived here using a recently proposed analytical form of the vibrational density of states (DOS) of liquids, which takes into account saddle points in the liquid energy landscape via the so-called instantaneous normal modes (INMs), corresponding to negative eigenvalues (imaginary frequencies) of the Hessian matrix. The theory is able to explain the typical monotonic decrease of specific heat with temperature observed in liquids, in terms of the average INM excitation lifetime decreasing with T (in accordance with Arrehnius law), and provides an excellent single-parameter fitting to several sets of experimental data for atomic and molecular liquids. It also correlates the height of the liquid energy barrier with the slope of the specific heat in function of temperature in accordance with the available data. These findings demonstrate that the specific heat of liquids is controlled by the instantaneous normal modes, i.e. by localized, unstable (exponentially decaying) vibrational excitations, and provide the missing connection between anharmonicity, saddle points in the energy landscape, and the thermodynamics of liquids., v2: fitting analysis extended and improved

Liquids confined to sub-millimeter scales have remained poorly understood. One of the most striking effects is the large elasticity revealed using good wetting conditions, which grows upon further decreasing the confinement length

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatio-temporal correlations in the undeformed glass that may trigger plastic instability. In contrast, here we show that the topological defects which correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) which are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular non-local peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between anti-parallel DTDs; (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45 degrees for uniaxial deformations, as widely observed in experiments and simulations., Comment: v2: matching the published version

We present a minimal theory of superconductivity enhancement in ferroelectric-type materials. Simple expressions for the optical mode responsible for the soft mode transition are assumed. A key role is played by the anharmonic phonon damping which is modulated by an external control parameter (electron doping or mechanical strain) causing the appearance of the soft mode. It is shown that the enhancement in the superconducting critical temperature $T_{c}$ upon approaching the ferroelectric transition from either side is due to the Stokes electron-phonon scattering processes promoted by strong phonon damping effects., Comment: Synopsis in APS Physics at: https://physics.aps.org/articles/v15/s11

We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira–Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. A new relativistic force term appears in this fully-relativistic limit, which has been derived here for the first time. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation–dissipation theorem, is also discussed.

The boson peak (BP) is a universal feature in the Raman and inelastic scattering spectra of both disordered and crystalline materials. The current paradigm presents the boson peak as the result of a Ioffe-Regel crossover between ballistic (phonon) and diffusive-type excitations, where the loss of coherence of phonons is described as a purely harmonic process due to structural disorder. This "harmonic disorder" paradigm for the BP has never been challenged or tested at the atomistic level. Here, through a set of atomistically-resolved characterizations of amorphous metallic alloys, we uncover a robust inverse proportionality between the intensity of boson peak and the activation energy of excitations in the potential energy landscape (PEL). Larger boson peak is linked with shallower basins and lower activation barriers and, consequently, with strongly anharmonic sectors of the PEL. Numerical evidence from atomistic simulations indicates that THz atomic vibrations contributing the most to the BP in atomic glasses are strongly anharmonic, as evidenced through very large values of the atomic- and mode-resolved Gr\"{u}neisen parameter found for the atomic vibrations that constitute the BP. These results provide a direct bridge between the vibrational spectrum and the topology of the PEL in solids, and point towards a new "giant anharmonicity" paradigm for both generic disordered materials and for the phonon-glass problem in emerging materials for energy applications. In this sense, disorder and anharmonicity emerge as the two sides of the same coin.

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses and liquids based on non-affine displacements and the consequent Goldstones phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field -- non-affinity -- which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave-vector in liquids, thus giving the first formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the $\alpha$ relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a non-equilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids and glasses has to be identified with the associated generalized higher-from global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses)., Comment: v2: presentation improved

We theoretically investigate the temperature dependence of the reversible structural relaxation time and diffusion constant of metallic glasses under pressure. The compression not only changes the glassy dynamics, but also generates a metastable state along with a higher-energy state where the system can rejuvenate. The relaxation times for forward and backward transitions in this two-state system are nearly identical and much faster than the relaxation time without accounting for barrier-recrossing. At ambient pressure, the expected irreversible relaxation process is recovered, and our numerical results agree well with prior experimental results. An increase of pressure has a minor effect on the relaxation time and diffusion constant that one computes without considering the influence of the metastable state, but it leads to a large reduction of the reversible relaxation time computed upon taking the metastable state into account. The presence of external compression is also shown to trigger a fragile-to-strong crossover in metallic glasses., Comment: This paper has been accepted for publication in Physica Status Solidi (RRL) - Rapid Research Letters

A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states $D(\omega)$ of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $\sim -\omega^{2}\ln\omega$ is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a $\sim\omega^{4}$ regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory., Comment: Topical Collection "Disordered, Non-Equilibrium Systems: From Supercooled Liquids to Amorphous Solids"

International audience; It is commonly accepted that shear waves do not propagate in a liquid medium. The shear wave energy is supposed to dissipate nearly instantaneously. This statement originates from the difficulty to access “static” shear stress in macroscopic liquids. In this paper, we take a different approach. We focus on the stability of the thermal equilibrium while the liquid (glycerol) is submitted to a sudden shear strain at sub-millimeter scale. The thermal response of the deformed liquid is unveiled. The liquid exhibits simultaneous and opposite bands up to about -0.04 to +0.04°C temperature variation, while keeping the global thermal balance unchanged. The sudden thermal changes and the long thermal relaxation highlight the ability of the liquid to convert the step strain energy in non-uniform thermodynamic states. The thermal effects depend nearly linearly on the amplitude of the deformation supporting the hypothesis of a shear wave propagation (elastic correlations) extending up to several hundreds micrometers. This new physical effect can be explained in terms of the underlying phonon physics of confined liquids, which unveils a hidden solid-like response with many similarities to glassy systems.