No Arabic abstract
We study the evolution of an elastic string into the pinned state at driving forces slightly below the depinning threshold force $F_c$. We quantify the temporal evolution of the string by an {it activity function} $A(t)$ representing the fraction of active nodes at time $t$ and find three distinct dynamic regimes. There is an initial stage of fast decay of the activity; in the second, intermediate, regime, an exponential decay of activity is observed; and, eventually, the fast collapse of the string towards its final pinned state results in an decay in the activity with $Am sim (t_p-t)^{psi}$, where $t_p$ is the pinning time in the finite system involved.
Field-induced domain wall dynamics in ferroelectric materials underpins multiple applications ranging from actuators to information technology devices and necessitates a quantitative description of the associated mechanisms including giant electromechanical couplings, controlled non-linearities, or low coercive voltages. While the advances in dynamic Piezoresponse Force Microscopy measurements over the last two decades have rendered visualization of polarization dynamics relatively straightforward, the associated insights into the local mechanisms have been elusive. Here we explore the domain dynamics in model polycrystalline materials using a workflow combining deep learning-based segmentation of the domain structures with non-linear dimensionality reduction using multilayer rotationally-invariant autoencoders (rVAE). The former allows unambiguous identification and classification of the ferroelectric and ferroelastic domain walls. The rVAE discover the latent representations of the domain wall geometries and their dynamics, thus providing insight into the intrinsic mechanisms of polarization switching, that can further be compared to simple physical models. The rVAE disentangles the factors affecting the pinning efficiency of ferroelectric walls, offering insights into the correlation of ferroelastic wall distribution and ferroelectric wall pinning.
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the systems internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.
We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct timescales. First, on an o(1) timescale, independent of system or subsystem size and the details of the dynamics, the entanglement spectrum develops nearest-neighbor level repulsion. The second timescale sets in when the light-cone has traversed the subsystem. Between these two times, the density of states of the reduced density matrix takes a universal, scale-free 1/f form; thus, random-matrix theory captures the local statistics of the entanglement spectrum but not its global structure. The third time scale is that on which the entanglement saturates; this occurs well after the light-cone traverses the subsystem. Between the second and third times, the entanglement spectrum compresses to its thermal Marchenko-Pastur form. These features hold for chaotic Hamiltonian and Floquet dynamics as well as a range of quantum circuit models.
We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature $T_c$ and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length $xi(t)$ agrees quantitatively with the predictions of a static theory, the metastate, evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent $z(T)$ defined by $xi(t) propto t^{1/z(T)}$ and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.
Probing the out-of-equilibrium dynamics of quantum matter has gained renewed interest owing to immense experimental progress in artifcial quantum systems. Dynamical quantum measures such as the growth of entanglement entropy (EE) and out-of-time ordered correlators (OTOCs) have been shown, theoretically, to provide great insight by exposing subtle quantum features invisible to traditional measures such as mass transport. However, measuring them in experiments requires either identical copies of the system, an ancilla qubit coupled to the whole system, or many measurements on a single copy, thereby making scalability extremely complex and hence, severely limiting their potential. Here, we introduce an alternate quantity $-$ the out-of-time-ordered measurement (OTOM) $-$ which involves measuring a single observable on a single copy of the system, while retaining the distinctive features of the OTOCs. We show, theoretically, that OTOMs are closely related to OTOCs in a doubled system with the same quantum statistical properties as the original system. Using exact diagonalization, we numerically simulate classical mass transport, as well as quantum dynamics through computations of the OTOC, the OTOM, and the EE in quantum spin chain models in various interesting regimes (including chaotic and many-body localized systems). Our results demonstrate that an OTOM can successfully reveal subtle aspects of quantum dynamics hidden to classical measures, and crucially, provide experimental access to them.