Relaxation Time Scales Research Articles

Kohlrausch regime of slow relaxation and its phenomenology in isolated quantum many-body systems with strong disorder

The Kohlrausch(-Williams-Watts) law of stretched exponential relaxation has been observed for over a century and a half in diverse complex classical systems. Here we show that this law describes relaxation quite generically in closed (executing Schrödinger dynamics), interacting disordered many-body systems, using interaction range and disorder strength as primary tuning parameters. This we observe for both time-independent and periodically driven (Floquet) systems. Finite-size analysis indicates the persistence of this nonthermal relaxation regime in the thermodynamic limit thus defining a distinct dynamical regime. This regime exhibits a peak in the time scale of the long-time relaxation (following a transient), upon crossing over from weak to strong disorder. We provide a simple picture of this behavior, which naturally accounts for its generic occurrence. Formation of spin-glass — one of the possible mechanisms for stretched relaxation appears incidental to the occurrence of Kohlrausch law in our context. Finally, we provide a simple non-Hermitian Hamiltonian formulation for the dynamics of a single spin embedded in the disordered chain. This provides an analytical formula that captures not only the Kohlrausch relaxation of the disorder averaged autocorrelation but also captures the largely diverse dynamics of an arbitrary target spin in the system. Our work hence also provides a concrete quantification of the “prethermal slowness” in many-body disordered system. Published by the American Physical Society 2025

High-throughput Mucus Microrheology for Phenotyping and Disease Modeling.

Mucus plays an integral role for the barrier function of many epithelial tissues. In the human airways, mucus is constantly secreted to capture inhaled microbes and pollutants and cleared away through concerted ciliary motion. Many important respiratory diseases exhibit altered mucus flowability and impaired clearance, contributing to respiratory distress and increased risk of infections. Understanding how mucus rheology changes during disease progression and in response to treatments is thus of great interest for subtyping patients and tailoring treatments, probing disease mechanisms, and tailoring therapies; however, basic research of mucus rheology is greatly hampered by the lack of scalable and user-friendly rheometry assays for the small volumes of mucus typically produced by in vitro respiratory models and in clinical ex vivo settings. To address this challenge, we developed a streamlined, high-throughput protocol leveraging Differential Dynamic Microscopy (DDM) to reliably measure the frequency-dependent microrheology of minuscule (3-10 µ L) mucus samples using standard epifluorescence microscopy. Our method does not require time-consuming user-interventions common in particle tracking routines and measures microrheology at the time scale of mucus relaxation (1-20s), hence greatly reducing assay time. We demonstrate the successful application of our method in mucus samples harvested from state-of-the-art air-liquid-interface (ALI) human respiratory cultures to assess mucus rheology in airway disease models and different culture conditions. To show that our approach equally applies to other types and sources of human mucus, we also validated our method with clinical samples of cervical mucus. We envision that our method can be seamlessly adopted by non-expert users, without the need for specialized equipment or extensive training, to study diseases and their treatments in the respiratory, intestinal, reproductive and other mucosal organ systems. This advancement opens up new avenues for large-scale studies, providing new insights into the role of mucus rheology which was previously limited by data accessibility and resource constraints.

Elevated Rates of Tidal Disruption Events in Active Galactic Nuclei

Abstract Advances in time domain astronomy have produced a growing population of flares from galactic nuclei, including both tidal disruption events (TDEs) and flares in active galactic nuclei (AGN). Because TDEs are uncommon and AGN variability is abundant, large-amplitude AGN flares are usually not categorized as TDEs. While TDEs are normally channelled by the collisional process of two-body scatterings over a relaxation timescale, the quadrupole moment of a gas disk alters the stellar orbits, allowing them to collisionlessly approach the central massive black hole (MBH). This leads to an effectively enlarged loss cone, the loss wedge. Earlier studies found a moderate enhancement, up to a factor ~2–3, of TDE rates N ̇ 2b for a static axisymmetric perturbation. Here, we study the loss wedge problem for an evolving AGN disk, which can capture large number of stars into the growing loss wedge over much shorter times. The rates N ̇ cl of collisionless TDEs produced by these time-evolving disks are much higher than the collisional rates N ̇ 2b in a static loss wedge. We calculate the response of a stellar population to the axisymmetric potential of an adiabatically growing AGN disk and find that the highest rates of collisionless TDEs are achieved for the largest (i) MBH masses M • and (ii) disk masses M d. For M • ~ 107 M ⊙ and M d ~ 0.1M •, the rate enhancement can be up to a factor N ̇ cl / N ̇ 2b ~ 10 . The orbits of collisionless TDEs sometimes have a preferred orientation in apses, carrying implications for observational signatures of resulting flares.

Discovery of collective nonjumping motions leading to Johari–Goldstein process of stress relaxation in model ionic glass

The slow β, or Johari–Goldstein (JG) relaxation process, has been widely observed in glasses and is known to induce the stress relaxation associated with mechanical properties. So far, jumping motions of only a fraction of the particles were believed to contribute to the JG process in glass. However, there is no direct experimental evidence of the atomic-scale images due to the difficulties in microscopic observation. In this study, atomic motions in the quasi-spherical model ionic-glass-former Ca0.4K0.6(NO3)1.4 were microscopically observed with one-angstrom resolution, the highest resolution to date, using X-ray time-domain interferometry. The microscopic experiment directly indicated that most particles underwent angstrom-scale motions in the time scale of the JG relaxation. This result was further supported by molecular dynamics (MD) simulations. A combined study of experiments and MD simulations revealed that most particles contributed to the JG process through unexpected collective nonjumping motions with angstrom-scale displacement, activated by jumping motions of a fraction of particles. The discovery of nonjumping motions by our atomic-scale dynamic observations has considerably advanced our understanding of the puzzling mechanism of the JG process.

Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks

Accretion and migration usually proceeds concurrently for giant planet formation in the natal protoplanetary disks. Recent works indicate that the concurrent accretion onto a giant planet imposes significant impact on the planetary migration dynamics in the isothermal regime. In this work, we carry out a series of 2D global hydrodynamical simulations with Athena++ to explore the effect of thermodynamics on the concurrent accretion and migration process of the planets in a self-consistent manner. The thermodynamics effect is modeled with a thermal relaxation timescale using a β-cooling prescription. Our results indicate that radiative cooling has a substantial effect on the accretion and migration processes of the planet. As cooling timescales increase, we observe a slight decrease in the planetary accretion rate, and a transition from the outward migrating into inward migration. This transition occurs approximately when the cooling timescale is comparable to the local dynamical timescale (β∼1), which is closely linked to the asymmetric structures from the circumplanetary disk (CPD) region. The asymmetric structures in the CPD region which appear with an efficient cooling provide a strong positive torque driving the planet migrate outward. However, such a positive torque is strongly suppressed, when the CPD structures tend to disappear with a relatively long cooling timescale (β≳10). Our findings may also be relevant to the dynamical evolution of accreting stellar-mass objects embedded in disks around active galactic nuclei.

Quantum-State Renormalization in Semiconductor Nanoparticles.

A single photoexcited electron-hole pair within a polar semiconductor nanocrystal (SNC) alters the charge screening and shielding within it. Perturbations of the crystal lattice and of the valence and conduction bands result, and the quantum-confinement states in a SNC shift uniquely with a dependence on the states occupied by the carriers. This shifting is termed quantum-state renormalization (QSR). This Perspective highlights QSR in semiconductor quantum wires and dots identified in time-resolved transient absorption and two-dimensional electronic spectroscopy experiments. Beyond the interest in understanding the principles of QSR and energy-coupling mechanisms, we pose the contributions of QSR in time-resolved spectroscopy data must be accounted for to accurately identify the time scales for intraband relaxation of the carriers within SNCs.

Intrinsically Slow Cooling of Hot Electrons in CdSe Nanocrystals Compared to CdS.

The utilization of excited charge carriers in semiconductor nanocrystals (NCs) for optoelectronic technologies has been a long-standing goal in the field of nanoscience. Experimental efforts to extend the lifetime of excited carriers have therefore been a principal focus. To understand the limits of these lifetimes, in this work, we theoretically study the time scales of pure electron relaxation in negatively charged NCs composed of two prototypical materials: CdSe and CdS. We find that hot electrons in CdSe have lifetimes that are 5 to 6 orders of magnitude longer than in CdS when the relaxation is governed only by the intrinsic properties of the materials. Although these two materials are known to have somewhat different electronic structure, we elucidate how this enormous difference in lifetimes arises from relatively small quantitative differences in electronic energy gaps and phonon frequencies, as well as the crucial role of Fröhlich-type electron-phonon couplings.

Temperature-dependent vibrational energy relaxation of hydrogen-bonded and free OD groups at the air-water interface.

Water interfaces play a crucial role in regulating interactions and energy flow. Vibrational sum-frequency generation (vSFG) spectroscopy provides structural and dynamic information on water molecules at interfaces. It has revealed, for instance, the presence of the hydrogen-bonded and free OH groups at the air-water interface. Here, using temperature-dependent, time-resolved vSFG, we focus on the vibrational energy relaxation dynamics of interfacial heavy water (D2O). We reveal that while the relaxation timescale for hydrogen-bonded OD stretch modes is temperature-independent, the lifetime of the free OD stretch mode decreases with increasing temperature. Our data, supported by simulations, suggest that both intramolecular energy transfer and rotational reorientation mechanisms jointly contribute to the energy relaxation process of the free OD, with temperature influencing these mechanisms differently.

Defining Stable Phases of Open Quantum Systems

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. Published by the American Physical Society 2024

Exponential series approximation of the SIR epidemiological model

IntroductionThe SIR (Susceptible-Infected-Recovered) model is one of the simplest and most widely used frameworks for understanding epidemic outbreaks.MethodsA second-order dynamical system for the R variable is formulated using an infinite exponential series expansion, and a recursion relation is established between the series coefficients. A numerical approximation scheme for the R variable is also developed.ResultsThe proposed numerical method is compared to a double exponential (DE) nonlinear approximate analytic solution, which reveals two coupled timescales: a relaxation timescale, determined by the ratio of the model’s time constants, and an excitation timescale, dictated by the population size. The DE solution is applied to estimate model parameters for a well-known epidemiological dataset—the boarding school flu outbreak.DiscussionFrom a theoretical standpoint, the primary contribution of this work is the derivation of an infinite exponential, Dirichlet, series for the model variables. Truncating the series yields a finite approximation, known as a Prony series, which can be interpreted as a sequence of coupled exponential relaxation processes, each with a distinct timescale. This apparent complexity can be approximated well by the DE solution, which appears to be of main practical interest.

Universal Time-Entanglement Trade-Off in Open Quantum Systems

We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B, interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024

Fast low-temperature irradiation creep driven by athermal defect dynamics

The occurrence of high stress concentrations in reactor components is a still intractable phenomenon encountered in fusion reactor design. Here, we observe and quantitatively model a non-linear high-dose radiation mediated microstructure evolution effect that facilitates fast stress relaxation in the most challenging low-temperature limit. In situ observations of a tensioned tungsten wire exposed to a high-energy ion beam show that internal stress of up to 2 GPa relaxes within minutes, with the extent and time-scale of relaxation accurately predicted by a parameter-free multiscale model informed by atomistic simulations. As opposed to conventional notions of radiation creep, the effect arises from the self-organisation of nanoscale crystal defects, athermally coalescing into extended polarized dislocation networks that compensate and alleviate the external stress.

A dissipative extension to ideal hydrodynamics

Abstract We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established Müller-Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit.

Aligned colloidal clusters in an alternating rotating magnetic field elucidated by magnetic relaxation

Precise control at the colloidal scale is one of the most promising bottom-up approaches to fabricating new materials and devices with tunable and precisely engineered properties. Magnetically driven colloidal assembly offers great versatility because of the ability to externally tune particle-particle interactions and to construct a host of particle arrangements. However, despite previous efforts to probe the parameter space, global orientational control in conjunction with two-dimensional microstructural control has remained out of reach. Furthermore, the magnetic relaxation time of superparamagnetic beads has been largely overlooked despite being a key feature of the magnetic response. Here, we take advantage of the magnetic relaxation time of superparamagnetic beads in an alternating rotating magnetic field and show how harnessing this feature facilitates the formation of oriented clusters. The orientation of these clusters can be controlled by field parameters. Using experiments, simulations, and theory, we probe a two-particle system (dimer) under this alternating rotating magnetic field and use its dynamics to provide insights into the collective response that forms clusters. We find that the type of field has significant implications for the dipolar interactions between the colloids because of the nonnegligible magnetic relaxation. Moreover, we find that the competing time scales of the magnetic relaxation and the alternating field generate an anisotropic interaction potential that drives cluster alignment. By exploiting the magnetic relaxation time of magnetic systems, we can tailor new types of interparticle interactions, thereby expanding the capabilities of colloidal assembly in engineering unique materials and devices.

Characterizing Rotational Dynamics and Heterogeneity via Single-Molecule Intensity Measurements.

Dynamic heterogeneity in glassy systems has typically been characterized at the single-molecule level by extracting rotational relaxation time scales from linear dichroism (LD) collected via two orthogonally polarized channels. However, in such measurements, localization precision is diminished due to photons lost relative to collection in a single detection channel. This poses challenges in characterizing rotational and translational dynamics simultaneously, as translational measurements require high localization precision. In this paper, we present a method for extracting rotational dynamics of glassy systems at the single-molecule level from intensity fluctuations of fluorescent probe molecules in a wide-field configuration without the use of a polarizing optical component. Through numerical analysis, we show that LD and intensity measurements probing rotational dynamics report similar, approximately second-order rotational correlation decays even at low signal to noise. Thus, within the assumptions of small, isotropic rotations, LD and intensity autocorrelation analysis should provide identical information on the time scale and heterogeneity of rotational dynamics. We then present experimental results that validate this numerical result, with direct comparison of LD and intensity-based approaches across probe molecules in both polymeric and small-molecule glass formers as well as across optical configurations. Our results demonstrate moderate correlation on a per-probe basis between rotational time scales obtained from both approaches, with deviations consistent with those expected in a dynamically heterogeneous system. We envision that this easily accessible strategy will be of use across disciplines for characterizing single-molecule rotational dynamics in limited signal situations and/or when high-precision localization is required.

Proton Transport Scenarios in Sulfuric Acid Explored via Ab Initio Molecular Dynamics Simulations.

Sulfuric acid (H2SO4), a highly reactive reagent containing intrinsic protonic charge carriers, has been studied via ab initio molecular dynamics simulations. Specifically, we explore the solvation shell structure of the protonic defects, H1SO4- and H3SO4+, as well as the underlying proton transport mechanisms in both the neat and hydrated H2SO4 solutions. Our findings reveal a significant contraction of the dynamic hydrogen-bonded network around the protonic defects, which resembles features seen in water. The simulations provide estimates of the structural relaxation time scales for proton release from both the covalent O-H bonds (∼23 ps) and the hydrogen bonds (∼0.4 ps). In contrast to water, our analysis of the proton transfer scenarios in sulfuric acid reveals correlated events mediated by the formation of longer (up to four) hydrogen-bonded Grotthuss chains.

Rosetta stone for the population dynamics of spiking neuron networks.

Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equilibrium. Despite its general applicability, the Fokker-Planck equationgoverning such evolution is mainly studied within the borders of the linear response theory, although alternative spectral expansion approaches offer some advantages in the study of the out-of-equilibrium dynamics. This is mainly due to the difficulty in computing the state-dependent coefficients of the expanded system of differential equations. Here, we address this issue by deriving analytic expressions for such coefficients by pairing perturbative solutions of the Fokker-Planck approach with their counterparts from the spectral expansion. A tight relationship emerges between several of these coefficients and the Laplace transform of the interspike interval density (i.e., the distribution of first-passage times). "Coefficients" like the current-to-rate gain function, the eigenvalues of the Fokker-Planck operator and its eigenfunctions at the boundaries are derived without resorting to integral expressions. For the leaky integrate-and-fire neurons, the coupling terms between stationary and nonstationary modes are also worked out paving the way to accurately characterize the critical points and the relaxation timescales in networks of interacting populations.

Global subduction slow slip events and associated earthquakes.

Three decades of geodetic monitoring have established slow slip events (SSEs) as a common mode of fault slip, sometimes linked with earthquake swarms and in a few cases escalating to major seismic events. However, the connection between SSEs and earthquake hazard has been difficult to quantify and contextualize beyond regional studies. We aggregate a geodetic record of SSEs from subduction zones in the circum-Pacific region. In aggregate, earthquake rates increase up to threefold concurrent with and proximal to SSEs. The relative amplitude of this increase is correlated with the SSE size and, to a lesser extent, their depth and region. The subdued and coincident earthquake response to SSE stress transfer suggests a more limited role of static stress transfer and a very short relaxation timescale for the triggered seismicity. The observed range of behavior does not support a major connection between SSEs and earthquake hazard.

Magnetic Field Driven Dynamic Reorganization of Electrocatalytic Interface for Sustainable Enhancement in Oxygen Evolution

Hydrogen with high calorific content (150 MJ/kg) and environment-friendly combustion product (H2O) becomes the alternative fossil fuel. Catalytic electrolysis of water is one of the attractive routes for generating H2. Energy-efficient and cost-effective electrolytic production of H2 has predominantly focused on lowering the overpotential for water splitting process by developing newer non-Pt group-based catalysts.This work demonstrates a new direction towards sustainable oxygen evolution reaction (OER) by exploiting the fundamental interplay of electromagnetic forces. Introducing an external magnetic field (Hext = 100 mT) perpendicular to the heterogeneous electrocatalytic interface produces an unprecedented increase in rate of electrocatalytic OER in phosphate buffer with pH=7. Such electromagnetic catalysis is achieved with metal phosphides (NiCoP and NiCoFeP) with different morphology, leading 2.5 fold increase in the OER current density and concomitant lowering of overpotential by 10% (Hext = 100 mT). Thereby, 50% lowering of charge transfer resistance (Rct) is achieved. This is substantiated by the lowering of the Tafel slope (by 5%) in the presence of Hext. Thus, we report two important observations influenced by the magnetic field: (a) direct effect of magnetic field on the catalyst surface to reduce the charge-transfer resistance, (b) spin-dependant OER process to get influenced under magnetic field and (c) indirect effect of magnetic field to sustain the magneto-electrocatalytic enhancement even after removing the magnetic field. The time-scale of magnetic relaxation is million times higher than conventional spin-lattice relaxation events in para/ferromagnetic systems. Such long-term stability of magnetized states is predominantly proposed to be originating from the NiCoP and NiCoFeP interface. So, we attribute the long-lived states to be additionally contributed from the volumetric expansion and active site expansion of the catalyst upon magnetization. Catalyst interface is arising due to the dendritic structure of catalyst. Such synergism of magnetization, is expected to increase the applicability of magneto-electrocatalysis as a more sustainable electrocatalytic approach towards a hydrogen-driven economy. Figure 1

Investigating the Influence of Photoswitchable Lipids on the Structure and Dynamics of Lipid Membranes: Fundamentals and Potential Applications.

In this work, we delve into the impact of photoisomerization of photoswitchable lipids (PSLs) on the membrane structure and dynamics at a molecular level. Through all-atom molecular dynamics simulations, we explore how UV irradiation-induced trans-to-cis isomerization of these lipids, particularly the azobenzene-derivatized phosphatidylcholine (AzoPC) lipid, influences the structure and dynamics of a simplified lipid membrane, mimicking those of E. coli bacteria across different temperatures. Our findings align with previous experimental observations regarding membrane properties and offer insights into localized effects and microscopic heterogeneity. Additionally, we estimate the relaxation time scale of the lipid membrane following AzoPC photoisomerization. Moreover, we demonstrate the feasibility of photoactivated drug release, exemplified by the controlled liberation of doxorubicin, an anticancer agent, through the membrane, suggesting the potential of PSLs in engineering photoactivated liposomes, coined as photoazosomes, for precise targeted drug delivery applications.