Quantifying electron-phonon interactions for the surface states of topological materials can provide key insights into surface-state transport, topological superconductivity, and potentially how to manipulate the surface state using a structural degree of freedom. We perform time-resolved x-ray diffraction (XRD) and angle-resolved photoemission (ARPES) measurements on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, following the excitation of coherent $A_{1g}$ optical phonons. We extract and compare the deformation potentials coupling the surface electronic states to local $A_{1g}$-like displacements in these two materials using the experimentally determined atomic displacements from XRD and electron band shifts from ARPES. We find the coupling in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to be similar and in general in agreement with expectations from density functional theory. We establish a methodology that quantifies the mode-specific electron-phonon coupling experimentally, allowing detailed comparison to theory. Our results shed light on fundamental processes in topological insulators involving electron-phonon coupling.

The Mott insulator provides an excellent foundation for exploring a wide range of strongly correlated physical phenomena, such as high-temperature superconductivity, quantum spin liquid, and colossal magnetoresistance. A Mott insulator with the simplest degree of freedom is an ideal and highly desirable system for studying the fundamental physics of Mottness. In this study, we have unambiguously identified such an anticipated Mott insulator in a van der Waals layered compound ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$. In the high-temperature phase, where interlayer coupling is negligible, density functional theory calculations for the monolayer of ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ suggest a half-filled flat band at the Fermi level, whereas angle-resolved photoemission spectroscopy experiments observe a large gap. This observation is perfectly reproduced by dynamical mean-field theory calculations considering strong electron correlations, indicating a correlation-driven Mott insulator state. Since this half-filled band derived from a single $2a_1$ orbital is isolated from all other bands, the monolayer of ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ is an ideal realization of the celebrated single-band Hubbard model. Upon decreasing the temperature, the bulk system undergoes a phase transition, where structural changes significantly enhance the interlayer coupling. This results in a bonding-antibonding splitting in the Hubbard bands, while the Mott gap remains dominant. Our discovery provides a simple and seminal model system for investigating Mott physics and other emerging correlated states.

Detection and parameter inference of gravitational-wave signals from compact mergers rely on the comparison of the incoming detector strain data $d(t)$ to waveform templates for the gravitational-wave strain $h(t)$ that ultimately rely on the resolution of Einstein’s equations via numerical relativity simulations. These, however, commonly output a quantity known as the Newman-Penrose scalar ${\psi }_4(t)$ which, under the Bondi gauge, is related to the gravitational-wave strain by ${\psi }_4(t)={\mathit{d}}^{2}h(t)/\mathit{d}{t}^2$. Therefore, obtaining strain templates involves an integration process that introduces artifacts that need to be treated in a rather manual way. By taking second-order finite differences on the detector data and inferring the corresponding background noise distribution, we develop a framework to perform gravitational-wave data analysis directly using ${\psi }_4(t)$ templates. We first demonstrate this formalism, and the impact of integration artifacts in strain templates, through the recovery of numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. Next, we reanalyze the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those previously published [Phys. Rev. Lett. 126, 081101 (2021)], where we used the classical strain framework. We find, however, that integration errors would strongly impact our analysis if GW190521 was 4 times louder. Finally, we show that our framework fixes significant biases in the interpretation of the high-mass gravitational-wave trigger S200114f arising from the usage of strain templates. We remove the need to obtain strain waveforms from numerical relativity simulations, avoiding the associated systematic errors.

The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual neurons, while biological neurons are highly complex cells. Integrate-and-fire models retain a key nonlinear feature of neuronal activity: Action potentials return the membrane potential to a nearly fixed reset value. This nonlinear reset of the membrane voltage after a spike is absent from classic neural field theories. Here, we develop a statistical field theory for networks of integrate-and-fire neurons with stochastic spike emission. This reveals a new mean-field theory for the activity in these networks, fluctuation corrections to the mean-field dynamics, and a mapping to a self-consistent renewal process. We use these to study the impact of the spike-driven reset of the membrane voltage on population activity. The spike reset gives rise to a multiplicative, rate-dependent leak term in the mean-field membrane voltage dynamics. This leads to bistability between quiescent and active states in the mean-field theory of homogeneous and excitatory-inhibitory pulse-coupled networks. We uncover two types of fluctuation correction to the mean-field theory, due to the nonlinear mapping from membrane voltage to spike emission and the nonlinear reset. These can have competing effects, promoting and suppressing activity, respectively. We then examine the roles of spike resets and recurrent inhibition in stabilizing network activity. We calculate the phase diagram for inhibitory stabilization and find that an inhibition-stabilized regime occurs in wide regions of parameter space, consistent with experimental reports of inhibitory stabilization in diverse brain regions. Fluctuations narrow the region of inhibitory stabilization, consistent with their role in suppressing activity through spike resets.

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, $\gamma /J\ll 1$ (where $\gamma$ is measurement rate per site and $J$ is hopping constant in the tight-binding model), we derive a nonlinear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a $\mathrm{U}(2)/\mathrm{U}(1)\times \mathrm{U}(1)\simeq S^2$ sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on $\mathrm{SU}(R)$ manifold with the replica limit $R\to 1$. On the Gaussian level, valid in the limit $\gamma /J\to 0$, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value $\sim (J/\gamma {)}^2$ even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, $\ln l_{\mathrm{corr}}\sim J/\gamma$. This makes this crossover very sharp as a function of the measurement frequency $\gamma /J$, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal $N\times N$ matrix, in the replica limit $N\to 1$. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases—nontrivially entangled and disentangled, respectively—in the physically relevant replica limit $N\to 1$. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size $L$ scales as $(\ln L{)}^2$, in contrast to findings in previously studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model’s phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems.

First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze, because they cannot be inferred from a simple free energy minimization principle. Rather, the mechanism of these transitions depends crucially on the system’s dynamics, which requires us to analyze them in trajectory space rather than in phase space. Here, we consider situations where the path of these transitions can be characterized as the minimizer of an action, whose minimum value can be used in a nonequilibrium generalization of the Arrhenius law to calculate the system’s phase diagram. We also develop efficient numerical tools for the minimization of this action. These tools are general enough to be transportable to many situations of interest, in particular, when the fluctuations present in the microscopic system are non-Gaussian and its dynamics is not governed by the standard Langevin equation. As an illustration, first-order phase transitions in two spatially extended nonequilibrium systems are analyzed: a modified Ginzburg-Landau equation with a chemical potential which is nongradient and a reaction-diffusion network based on the Schlögl model. The phase diagrams of both systems are calculated as a function of their control parameters, and the paths of the transitions, including their critical nuclei, are identified. These results clearly demonstrate the nonequilibrium nature of the transitions, with differing forward and backward paths.

Motivated by advances in the field of active matter where nonequilibrium forcing has been shown to activate new assembly pathways, here we study how nonequilibrium driving in prototypical memory formation models can affect their information processing capabilities. Our results reveal that activity can provide a new and surprisingly general way to dramatically improve the memory and information processing performance of the memory-forming systems without the need for additional interactions or changes in connectivity. Nonequilibrium dynamics can allow these systems to have memory capacity, assembly or pattern recognition properties, and learning ability, in excess of their corresponding equilibrium counterparts. Our results demonstrate the generality of the enhancement of memory capacity arising from nonequilibrium, active dynamics when compared to noise sources characteristic of equilibrium dynamics. These results are of significance to a variety of processes that take place under nonequilibrium dynamics, and involve information storage and retrieval, as well as in silico learning and memory-forming systems for which nonequilibrium dynamics may provide an approach for modulating memory formation.

Quantum critical systems constitute appealing platforms for exploring novel measurement-induced phenomena due to their innate sensitivity to perturbations. We study the impact of measurements on paradigmatic Ising quantum-critical chains using an explicit protocol, whereby correlated ancillae are entangled with the critical chain and then projectively measured. Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter critical correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations. We further show that measurement-altered Ising criticality can be pursued surprisingly efficiently in experiments featuring of order 100 qubits by postselecting for high-probability measurement outcomes or, in certain cases, by averaging observables separately over measurement outcomes residing in distinct symmetry sectors. Our framework naturally adapts to more exotic quantum-critical points and highlights opportunities for realization in noisy intermediate-scale quantum hardware and in Rydberg arrays.

We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schrödinger equation and Newton’s equation for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in $n$, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time. We show that any classical algorithm solving this same problem is inefficient and must make $2^{\mathrm{\Omega }(n)}$ queries to the oracle, and when the oracles are instantiated by efficient quantum circuits, the problem is bounded-error quantum polynomial time complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with $2^n$ modes.

The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive, and trace preserving, and reduces to Einstein’s theory of general relativity in the classical limit. Consequently, the dynamics does not suffer from the pathologies of the semiclassical theory based on expectation values. The assumption that general relativity is classical necessarily modifies the dynamical laws of quantum mechanics; the theory must be fundamentally stochastic in both the metric degrees of freedom and in the quantum matter fields. This breakdown in predictability allows it to evade several no-go theorems purporting to forbid classical quantum interactions. The measurement postulate of quantum mechanics is not needed; the interaction of the quantum degrees of freedom with classical space-time necessarily causes decoherence in the quantum system. We first derive the general form of classical quantum dynamics and consider realizations which have as its limit deterministic classical Hamiltonian evolution. The formalism is then applied to quantum field theory interacting with the classical space-time metric. One can view the classical quantum theory as fundamental or as an effective theory useful for computing the backreaction of quantum fields on geometry. We discuss a number of open questions from the perspective of both viewpoints.

The third Gravitational-Wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, $15:00$ Coordinated Universal Time (UTC) and 27 March 2020, $17:00$ UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin $p_{\text{astro}}>0.5$. Of these, 18 were previously reported as low-latency public alerts, and 17 are reported here for the first time. Based upon estimates for the component masses, our O3b candidates with $p_{\text{astro}}>0.5$ are consistent with gravitational-wave signals from binary black holes or neutron-star–black-hole binaries, and we identify none from binary neutron stars. However, from the gravitational-wave data alone, we are not able to measure matter effects that distinguish whether the binary components are neutron stars or black holes. The range of inferred component masses is similar to that found with previous catalogs, but the O3b candidates include the first confident observations of neutron-star–black-hole binaries. Including the 35 candidates from O3b in addition to those from GWTC-2.1, GWTC-3 contains 90 candidates found by our analysis with $p_{\text{astro}}>0.5$ across the first three observing runs. These observations of compact binary coalescences present an unprecedented view of the properties of black holes and neutron stars.

We develop a multiscale approach to estimate high-dimensional probability distributions. Our approach applies to cases in which the energy function (or Hamiltonian) is not known from the start. Using data acquired from experiments or simulations we can estimate the energy function. We obtain a representation of the approximate probability distribution based on a multiscale cascade of conditional probabilities. This representation allows for fast sampling of many-body systems in various domains, from statistical physics to cosmology. Our method—the wavelet-conditional renormalization group (WCRG)—proceeds scale by scale, estimating models for the conditional probabilities of “fast degrees of freedom” conditioned by coarse-grained fields. These probability distributions are modeled by energy functions associated with scale interactions, and are represented in an orthogonal wavelet basis. The WCRG decomposes the microscopic energy function as a sum of interaction energies at all scales and can efficiently generate new samples by going from coarse to fine scales. Near phase transitions, this representation of the approximate probability distribution completely avoids the “critical slowing-down” of direct estimation and sampling algorithms. This is explained theoretically by combining results from RG and wavelet theories, and verified numerically for the Gaussian and ${\phi }^4$-field theories. We show that multiscale WCRG energy-based models are more general than local potential models and can capture the physics of complex many-body interacting systems at all length scales. This is demonstrated for weak-gravitational-lensing fields reflecting dark-matter distributions in cosmology, which include long-range interactions with long-tail probability distributions. The WCRG has a large number of potential applications in nonequilibrium systems, where the underlying distribution is not known a priori. Finally, we discuss the connection between the WCRG and deep network architectures.

Robust spin-photon interfaces in solids are essential components in quantum networking and sensing technologies. Ideally, these interfaces combine a long-lived spin memory, coherent optical transitions, fast and high-fidelity spin manipulation, and straightforward device integration and scaling. The tin-vacancy center (SnV) in diamond is a promising spin-photon interface with desirable optical and spin properties at 1.7 K. However, the SnV spin lacks efficient microwave control, and its spin coherence degrades with higher temperature. In this work, we introduce a new platform that overcomes these challenges—SnV centers in uniformly strained thin diamond membranes. The controlled generation of crystal strain introduces orbital mixing that allows microwave control of the spin state with 99.36(9)% gate fidelity and spin coherence protection beyond a millisecond. Moreover, the presence of crystal strain suppresses temperature-dependent dephasing processes, leading to a considerable improvement of the coherence time up to $223(10)\mathrm{\mu }\mathrm{s}$ at 4 K, a widely accessible temperature in common cryogenic systems. Critically, the coherence of optical transitions is unaffected by the elevated temperature, exhibiting nearly lifetime-limited optical linewidths. Combined with the compatibility of diamond membranes with device integration, the demonstrated platform is an ideal spin-photon interface for future quantum technologies.

Understanding the materials dependence together with the universal controlling parameter of superconductivity (SC) in copper oxide superconductors is one of the major challenges in condensed matter physics. Here, we numerically analyze SC by using ab initio low-energy effective Hamiltonians consisting of the antibonding combination of Cu $3d_{x^2-y^2}$ and O $2p_{\sigma }$ orbitals without adjustable parameters. We have performed the state-of-the-art variational Monte Carlo calculations for the four carrier doped cuprates with diverse experimental optimal SC critical temperature $T_c^{\mathrm{opt}}$: ${\mathrm{CaCuO}}_2$ ($T_c^{\mathrm{opt}}\sim 110\mathrm{K}$), ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_6$ ($T_c^{\mathrm{opt}}\sim 10–40\mathrm{K}$), ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ ($T_c^{\mathrm{opt}}\sim 85–100\mathrm{K}$), and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ ($T_c^{\mathrm{opt}}\sim 90\mathrm{K}$). Materials and hole doping concentration ($\delta$) dependencies of the SC order parameter $F_{\mathrm{SC}}$ and the competition with spin or charge order show essential and quantitative agreement with the available experiments on the four materials in the following points. (1) In a wide range $0.05\le \delta \le 0.25$, the ground state is commonly the uniform SC state, which is severely competing with the charge or spin stripe and antiferromagnetic states. (2) $F_{\mathrm{SC}}$ at the optimum doping shows amplitude consistent with the superfluid density measured in the muon spin resonance and its dome structure found in $\delta$ dependence shows consistency with that of the SC gap in the tunneling and photoemission measurements. Based on the confirmed materials dependence, we further find insights into the universal SC mechanism. (I) $F_{\mathrm{SC}}$ increases with the ratio $U/|t_1|$ within the available realistic materials, indicating that $U/|t_1|$ is the principal component controlling the strength of the SC in the real materials dependence. Here, $U$ and $t_1$ are the on-site Coulomb repulsion and the nearest neighbor hopping, respectively, in the ab initio Hamiltonians. (II) A universal scaling $T_c^{\mathrm{opt}}\sim 0.16|t_1|F_{\mathrm{SC}}$ holds. (III) SC is enhanced and optimized if $U$ is increased beyond the real available materials, and it is further enhanced when the off-site interaction is reduced, while the presence of the off-site interaction is important to make the SC ground state against other competing states. The present findings provide useful clues for the design of new SC materials with even higher $T_c^{\mathrm{opt}}$.

Midcircuit operations, such as qubit state measurement or reset, are central to many tasks in quantum information science, including quantum computing, entanglement generation, and metrology. For instance, in quantum error correction, the information gained from a measurement on a subset of qubits is used to influence the state of the remaining unmeasured qubits, rectifying inevitable errors that arise in a quantum circuit. Such partial projective operations pose a challenge for dense neutral atom arrays and trapped ions, where accidental exposure to resonant laser light during quantum state initialization and detection can spoil the state of untargeted qubits. In this work, we implement midcircuit operations in a 48-site array of neutral atoms, enabled by new methods for high-fidelity control of the omg (optical-metastable-ground-state qubit) architecture present in ${}^{171}\mathrm{Yb}$. Here, the quantum information is encoded in either of the three qubit manifolds and can be shuttled between them. With state-sensitive shelving between the ground and metastable states, we realize a nondestructive state detection for ${}^{171}\mathrm{Yb}$, incorporating global control and local feed-forward operations. Using new schemes for local addressing of the optical clock transition, we shelve a subset of qubits to the metastable state, hiding them from projective operations performed on the qubits remaining in the ground state, demonstrating midcircuit measurement, spin reset, and motional reset in the form of ground-state cooling.

Measurement-based quantum error correction relies on the ability to determine the state of a subset of qubits (ancillas) within a processor without revealing or disturbing the state of the remaining qubits. Among neutral-atom-based platforms, a scalable, high-fidelity approach to midcircuit measurement that retains the ancilla qubits in a state suitable for future operations has not yet been demonstrated. In this work, we perform maging using a narrow-linewidth transition in an array of tweezer-confined ${}^{171}\mathrm{Yb}$ atoms to demonstrate nondestructive state-selective and site-selective detection. By applying site-specific light shifts, selected atoms within the array can be hidden from imaging light, which allows a subset of qubits to be measured while causing only percent-level errors on the remaining qubits. As a proof-of-principle demonstration of conditional operations based on the results of the midcircuit measurements, and of our ability to reuse ancilla qubits, we perform conditional refilling of ancilla sites to correct for occasional atom loss, while maintaining the coherence of data qubits. Looking toward true continuous operation, we demonstrate loading of a magneto-optical trap with a minimal degree of qubit decoherence.

One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The traditional approach is to derive these terms from elementary processes and then use the resulting model to make predictions for the entire system. But what if the underlying processes are unknown? Can we reverse the approach and learn the microscopic action by observing the entire system? We use invertible neural networks to first learn the observed data distribution. By the choice of a suitable nonlinearity for the neuronal activation function, we are then able to compute the action from the weights of the trained model; a diagrammatic language expresses the change of the action from layer to layer. This process uncovers how the network hierarchically constructs interactions via nonlinear transformations of pairwise relations. We test this approach on simulated datasets of interacting theories and on an established image dataset (MNIST). The network consistently reproduces a broad class of unimodal distributions; outside this class, it finds effective theories that approximate the data statistics up to the third cumulant. We explicitly show how network depth and data quantity jointly improve the agreement between the learned and the true model. This work shows how to leverage the power of machine learning to transparently extract microscopic models from data.

Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, in both nanotechnology and biology. Progress in computing optimal protocols to extremize thermodynamic variables has, thus far, been limited to either simple systems or near-equilibrium evolution. Here, we present an approach for computing optimal protocols based on automatic differentiation. Our methodology is applicable to complex systems and multidimensional protocols and is valid arbitrarily far from equilibrium. We validate our method by reproducing theoretical optimal protocols for a Brownian particle in a time-varying harmonic trap. We also compute departures from near-equilibrium behavior for magnetization reversal on an Ising lattice and for barrier crossing driven by a harmonic trap, which is used to represent a range of biological processes including biomolecular unfolding reactions. Algorithms based on automatic differentiation outperform the near-equilibrium theory for far-from-equilibrium magnetization reversal and for driven barrier crossing beyond the linear regime. The optimal protocol for far-from-equilibrium driven barrier crossing is found to hasten the approach to, and slow the departure from, the barrier region compared to the near-equilibrium theoretical protocol. We demonstrate the utility of our method in a real-world use case by reducing the work required to unfold a DNA hairpin in the coarse-grained oxDNA model and improving its nonequilibrium free-energy landscape reconstruction compared to a naive linear protocol.

A solid loaded beyond the yield stress loses its elastic properties and becomes plastic. From a microscopic point of view, this limit corresponds to the condition where plastic regions become so densely packed that they give rise to system-spanning structures. This limit for glasses is abrupt, which makes experimental investigations challenging. Here, the yield point is reached by the alternative approach of increasing the density of plastic regions by generation of point defects during x-ray irradiation. For the case of a ${\mathrm{LiBO}}_2$ glass, we show that at low doses, i.e., for a low density of defects, the defects behave as isolated stress sources that induce atomic displacements typical of an elastic solid. As the density of defects increases, the mechanical response of the glass at the local scale changes from elastic to more and more plastic, until reaching the limit where it becomes characteristic of a flowing system, which signals that the yield point is reached.