Relaxation Time Scales Research Articles

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

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.

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.

Nitric Oxide and Temperature Measurement Using Laser Absorption Spectroscopy in Arc-Heater Plenum

A mid-infrared tunable diode laser absorption spectroscopy (TDLAS) sensor to measure rovibrational temperature and nitric oxide (NO) mole fraction in the arc-heater plenum was developed and employed in the Arc Heated Combustion Tunnel-II (ACT-II) facility at the University of Illinois at Urbana-Champaign. From this study, TDLAS-inferred temperatures were found to differ from the conventional method to estimate temperature by over 13%. Chemical equilibrium simulations were performed at the TDLAS-inferred temperatures to understand how chemical relaxation timescales compare with plenum residence times. Results from this study show NO levels higher than equilibrium concentrations, with relaxation timescales that exceed plenum residence times. With insufficient time to reach equilibrium, elevated NO levels are expected to remain in the test gas and persist into the scramjet model.

Brownian particle diffusion in generalized polynomial shear flows.

This study presents a mathematical framework for calculating the diffusion of Brownian particles in generalized shear flows. By solving the Langevin equationsusing stochastic instead of classical calculus, we propose a mathematical formulation that resolves the particle mean-square displacement (MSD) at all timescales for any two-dimensional parallel shear flow described by a polynomial velocity profile. We show that at long timescales, the polynomial order of time of the particle MSD is n+2, where n is the polynomial order of the transverse coordinate of the velocity profile. We generalize the method to resolve particle diffusion in any polynomial shear flow at all timescales, including the order of particle relaxation timescale, which is unresolved in current theories. Particle diffusion at all timescales is then studied for the cases of Couette and plane Poiseuille flows and a polynomial approximation of a hyperbolic tangent flow while neglecting the boundary effects. We observe three main stages of particle diffusion along the timeline for Couette and plane Poiseuille flows and four main stages for hyperbolic tangent flow. The particle MSD is distinctly different across these stages due to different dominant physical mechanisms. Thus, higher temporal and spatial resolution for diffusion processes in shear flows may be realized, suggesting a more accurate analytical approach for the diffusion of Brownian particles.

Dynamic Ultrastrong Coupling in a 2 nm Gap Plasmonic Cavity at the Sub-Picosecond Scale.

Localized surface plasmon resonances (LSPRs) can enhance the electromagnetic fields on metallic nanostructures upon light illumination, providing an approach for manipulating light-matter interactions at the sub-wavelength scale. However, currently, there is no thorough investigation of the physical mechanism in the dynamic formation of the strongly coupled LSPRs on sub-5 nm plasmonic cavities at the sub-picosecond scale. In this work, through femtosecond broadband transient absorption spectroscopy, we reveal the dynamic ultrastrong coupling processes in a nanoparticle-in-trench (NPiT) structure containing 2 nm gap cavities, and demonstrate a coherent motional coupling between vibrating AuNPs and the nanogaps. We achieve a maximum Rabi splitting energy of ∼660 meV in the sub-picosecond hot-electron relaxation time scale under the resonant excitation of the nanogap cavity's LSPR, reaching the ultrastrong coupling regime. This leads to a change of global vibration modes for the 2 nm gap cavity, potentially related to the dynamical Casimir effect with nanogap resonators.

Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes.

ML-GLE: A machine learning enhanced Generalized Langevin equation framework for transient anomalous diffusion in polymer dynamics

In this work we introduce ML-GLE, a machine learning framework to generate long-term single-polymer dynamics by exploiting short-term trajectories from molecular dynamics (MD) simulations of polymer melts. Even with current advances in machine learning for MD, these polymeric materials remain difficult to simulate and characterize due to prohibitive computational costs when long relaxation timescales are involved. Our method relies on a 3D neural auto-regressive model for single polymer lower dimensional collective variables, called normal modes. This enhances the Generalized Langevin Equation (GLE) capabilities in modelling diffusion phenomena. We exploit a particular GLE solution which is known to reproduce the mean square displacement curve relative to transient anomalous diffusion and connect it with the normal modes collective variables. ML-GLE is capable of emulating the single polymer statistical properties in the long-term, predicting the diffusion coefficient. As a consequence, this results in an enormous acceleration in terms of simulation time with respect to the full-size simulation. Moreover, this approach is also scalable with system size.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7–2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8–14 ps, with a significantly inhibited ground state recovery.

Full time-dependent SOLPS-ITER simulation of the SPARC tokamak: actuator design for particle and divertor condition control *

This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 ⋅10−3 second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.