Stretched-exponential Decay Research Articles

Confinement Effects on Reorientation Dynamics of Water Confined within Graphite Nanoslits.

Molecular dynamics simulations were used to investigate the reorientation dynamics of water confined within graphite nanoslits of size less than 2 nm, where molecules formed inner and interfacial layers parallel to the confining walls. Significantly related to molecular reorientations, the hydrogen-bond (HB) network of nanoconfined water therein was scrutinized by HB configuration fractions compared to those of bulk water and the influences on interfacial-molecule orientations relative to a nearby C atom plate. The second-rank orientation time correlation functions (OTCFs) of nanoconfined water were calculated and found to follow stretched-exponential, power-law, and power-law decays in a time series. To understand this naïve behavior of reorientation relaxation, the approach of statistical mechanics was adopted in our studies. In terms of the orientation Van Hove function (OVHF), an alternative meaning was given to the second-rank OTCF, which is a measure of the deviation of the OVHF between a molecular system and free molecules in random orientations. Indicated by the OVHFs at related time scales, the stretched-exponential decay of the second-rank OTCF resulted from molecules evacuating out of HB cages formed by their neighbors. After the evacuations, the inner molecules relaxed at relatively fast rates toward random orientations, but the interfacial molecules reoriented at slow rates due to restrictions by hydrophobic interactions with graphite walls. The first power-law decay of the second-rank OTCF was attributed to the distinct relaxation rates of inner and interfacial molecules within a graphite nanoslit. When the inner molecules were completely random in orientation, the second-rank OTCFs changed to another power law decay with a power smaller than the first one.

Stretched-exponential melting of a dynamically frozen state under imprinted phase noise in the ising chain in a transverse field

The concept of dynamical freezing is a phenomenon where a suitable set of local observables freezes under a strong periodic drive in a quantum many-body system. This happens because of the emergence of approximate but perpetual conservation laws when the drive is strong enough. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is “slow”: a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization. Here we observe this in a simple translationally invariant system dynamically frozen under a periodic drive. Moreover, the melting here does not obliterate the entire memory of the initial state but leaves behind a steady remnant that depends on the initial conditions. This underscores the stability of dynamically frozen states.Graphical abstract

Structural dynamics of a model of amorphous silicon

We perform extensive simulations and systematic statistical analyses on the structural dynamics of a model of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating potential, and the dynamics consists of bond transpositions proposed at random locations and accepted with the Metropolis acceptance ratio. The structural quantities we track are the variations in time of the lateral lengths (Lx, Ly, Lz) of the cuboid simulation cell. We transform these quantities into the volume V and two aspect ratios B1 and B2. Our analysis reveals that at short times, the mean squared displacement (MSD) for all of them exhibits normal diffusion. At longer times, they cross over to anomalous diffusion (AD), with a temperature-dependent anomalous exponent α<1. We analyze our findings in the light of two standard models in statistical physics that feature anomalous dynamics, viz., continuous time random walker (CTRW) and fractional Brownian motion (fBm). We obtain the distribution of waiting times, and find that the data are consistent with a stretched-exponential decay. We also show that the three quantities, V, B1 and B2 exhibit negative velocity autocorrelation functions. These observations together suggest that the dynamics of the material belong to the fBm class.

Dynamical critical behavior of the two-dimensional three-state Potts model.

We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization M (MSD_{M}) as a function of time, as well as on the autocorrelation function of M. Our simulations reveal the existence of two crossover behaviors at times τ_{1}∼L^{z_{1}} and τ_{2}∼L^{z_{2}}, separating three dynamical regimes. MSD_{M} appears to shift from ordinary diffusion in the first regime, to anomalous diffusion in the second, and finally to be constant in the third regime. The magnetization autocorrelation function, on the other hand, is found to fluctuate between exponential decay, stretched-exponential decay, and then again exponential decay along these three regimes. This behavior is in agreement with the one reported recently for the two-dimensional Ising ferromagnet [Phys. Rev. E 108, 034118 (2023)2470-004510.1103/PhysRevE.108.034118], indicating that the existence of two dynamic critical exponents is not a peculiarity of the Ising model itself. A comparison of both MSD_{M} and the magnetization's autocorrelation function suggests that within our numerical accuracy the exponents z_{1} and z_{2} are shared between the Ising and three-state Potts models at least for the particular case of single spin-flip dynamics studied here, even though their equilibrium universality classes are clearly distinct. Continuity of MSD_{M} requires that α(z_{2}-z_{1})=γ/ν-z_{1}, in which α is the anomalous exponent in the intermediate regime. Since the ratio γ/ν is not shared between the two models, it follows that α is not shared either, an aspect well verified in our simulations. Finally, we also discuss the relevance of our main findings using another useful observable, namely the line magnetization M_{l}.

Long-lived, pulse-induced transient absorption inLiNb1-x Ta x O3 (0≤x≤1) solid solutions: the case of three intrinsic defect sites for electron localization with strong coupling

Abstract Femto-/nanosecond pulse-induced, red and near-infrared absorption is studied in LiNb1-x Ta x O3 (0≤x≤1, LNT) solid solutions with the aim of studying transient optical nonlinearities associated with the formation, transport and recombination of optically generated small bound electron polarons with strong coupling to the lattice. As a result, a pronounced, long-lived transient absorption is uncovered for LNT which exceed lifetimes and starting amplitudes of LiNbO3 (LN) and LiTaO3 (LT) by a factor of up to 100 and 10, respectively. The transients reveal a stretched-exponential decay behavior and a thermally activated process which provide strong evidence for an underlying hopping transport mechanism of small bound polarons. All findings are discussed in comparison to the model systems LN and LT within the framework of appropriate band models and optical generation of polarons via two-photon excitation. To explain the significant differences, the simultaneous presence of Nb5+ Li , Ta5+ Li antisites, and Ta5+ V interstitial defects, i.e. a mixture of the intrinsic defects widely established for LN and LT, is assumed for LNT.

Duty ratio drive prediction model of lifetime degradation for organic light emitting diode-on-silicon microdisplay.

A duty ratio drive prediction (DRDP) model of luminance degradation for organic light emitting diodes (OLED) microdisplay is proposed in this paper. The traditional stretched exponential decay (SED) model is not applicable for OLED driven by duty ratio. The DRDP model introduces the duty ratio as the variables affecting the lifetime of OLED. By fitting the undetermined coefficients with the measured luminance data, the quantitative relationships among the initial luminance, duty ratio, and OLED lifetime are obtained. Meanwhile, the model quantifies the phenomenon of spontaneous luminance recovery, which occurs when OLED switches from bright to dark. Finally, the DRDP model is used to compensate the luminance degradation of OLED driven by duty ratio. The experimental results show that the average prediction accuracy of DRDP model for white, red, green, and blue (W/R/G/B) OLED degradation trend is 0.9623. The average prediction accuracy of W/R/G/B OLED lifetime is 0.6119, which is greater than that of SED model. The lifetime is extended by 89.83% after compensation.

Critical dynamical behavior of the Ising model.

We investigate the dynamical critical behavior of the two- and three-dimensional Ising models with Glauber dynamics in equilibrium. In contrast to the usual standing, we focus on the mean-squared deviation of the magnetization M,MSD_{M}, as a function of time, as well as on the autocorrelation function of M. These two functions are distinct but closely related. We find that MSD_{M} features a first crossover at time τ_{1}∼L^{z_{1}}, from ordinary diffusion with MSD_{M}∼t, to anomalous diffusion with MSD_{M}∼t^{α}. Purely on numerical grounds, we obtain the values z_{1}=0.45(5) and α=0.752(5) for the two-dimensional Ising ferromagnet. Related to this, the magnetization autocorrelation function crosses over from an exponential decay to a stretched-exponential decay. At later times, we find a second crossover at time τ_{2}∼L^{z_{2}}. Here, MSD_{M} saturates to its late-time value ∼L^{2+γ/ν}, while the autocorrelation function crosses over from stretched-exponential decay to simple exponential one. We also confirm numerically the value z_{2}=2.1665(12), earlier reported as the single dynamic exponent. Continuity of MSD_{M} requires that α(z_{2}-z_{1})=γ/ν-z_{1}. We speculate that z_{1}=1/2 and α=3/4, values that indeed lead to the expected z_{2}=13/6 result. A complementary analysis for the three-dimensional Ising model provides the estimates z_{1}=1.35(2),α=0.90(2), and z_{2}=2.032(3). While z_{2} has attracted significant attention in the literature, we argue that for all practical purposes z_{1} is more important, as it determines the number of statistically independent measurements during a long simulation.

Multiscale heterogeneous dynamics in two-dimensional glassy colloids.

On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and, thus, seldom performed. By using two-dimensional hard-sphere colloids at various area fractions ϕ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As ϕ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2) with diffusion coefficient DL∼(ϕc-ϕ)2.8, and ϕc ≃ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose ϕ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q, t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length scales.

Molecular Origin of Driving-Dependent Friction in Fluids.

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski's identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

Renewal Model for Dependent Binary Sequences

We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed renewal processes, we investigate correlations and the ability of the model to implement a prescribed autocovariance structure, showing that a large variety of subexponential decay of correlations can be accounted for. In particular, robustness and efficiency of the method are tested by generating binary sequences with polynomial and stretched-exponential decay of correlations. Moreover, to justify the maximum entropy principle for model selection, an asymptotic equipartition property for typical sequences that naturally leads to the Shannon entropy of the waiting time distribution is demonstrated. To support the comparison of the theory with data, a law of large numbers and a central limit theorem are established for the time average of general observables.

Glassy quantum dynamics of disordered Ising spins

We study the out-of-equilibrium dynamics of the quantum Ising model with power-law interactions and positional disorder. For arbitrary dimension $d$ and interaction range $\ensuremath{\alpha}\ensuremath{\ge}d$ we analytically find a stretched-exponential decay of the global magnetization and ensemble-averaged single-spin purity with a stretch power $\ensuremath{\beta}=d/\ensuremath{\alpha}$ in the thermodynamic limit. Numerically, we confirm that glassy behavior persists for finite system sizes and sufficiently strong disorder. We identify dephasing between disordered coherent pairs as the main mechanism leading to a relaxation of global magnetization, whereas genuine many-body interactions lead to a loss of single-spin purity which signifies the buildup of entanglement. The emergence of glassy dynamics in the quantum Ising model extends prior findings in classical and open quantum systems, where the stretched-exponential law is explained by a scale-invariant distribution of timescales, to both integrable and nonintegrable quantum systems.

Defect Tolerance Mechanism Revealed! Influence of Polaron Occupied Surface Trap States on CsPbBr3 Nanocrystal Photoluminescence: Ab Initio Excited-State Dynamics.

Lead halide perovskite (LHP) nanocrystals (NCs) show exceptional defect tolerance which has been attributed to their unique electronic structure, where defect energy levels are not introduced inside the fundamental bandgap, and the role of polarons in screening charge carriers from defects. Here, we use ab initio atomistic simulations to explore the interplay between various surface chemistries (A = Cs+, R'NH3+; X = Br-, RCOO-) used to passivate a CsPbBr3 NC surface and their impact on the ground-state (GS) and excited-state (ES) photophysical properties. We investigate pristine fully passivated surfaces and A-X vacancy defects that reflect chemical reactions A+ + X- → AX on the surface, which result in ligand desorption. For each surface configuration, calculations are performed in the GS and lowest ES (L-ES) electronic configurations, approximating polaron formation after photoexcitation. For models with A-X surface vacancies, we find that localized electron surface trap (ST) states emerge ∼100-400 meV below the pristine Se band in the L-ES configuration due to polaronic nuclear reorganization. Surprisingly, these trap states contribute relatively bright Sh → ST spectral features. To test if these surface trap states remain bright in a dynamic (thermal) situation we implement excited-state molecular dynamics simulations. It is found that the surface defected model shows an enhanced nonradiative recombination rate which reduces the photoluminescence quantum yield (PLQY) from 95% for the pristine surface to 75%. This is accompanied by an order of magnitude reduction in PL intensity and a red shift of the transition energy. This study provides more evidence of the defect tolerance of LHP NCs along with evidence of surface trap states contributing to efficient photoluminescence. The observation of relatively bright surface trap states could provide insight into photophysical phenomena, such as size-dependent stretched-exponential photoluminescence decay and Stokes shifts.

On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics.

A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times. With an increase in observation time, the contribution from end effects to the FID increases. In the regime of incoherent reptation, contributions to the FID from central segments yield an exponent of 1/4 for the stretched decay and contributions from end segments yield an exponent of 3/16. In the regime of coherent reptation, the central segments generate a stretching exponent of 1/2, whereas the end segments contribute with an exponent of 1/4. These predictions are shown to be in qualitative agreement with the experimental FIDs of perdeuterated poly(ethylene oxide) with molecular masses of 132 kg/mol and 862 kg/mol.

Localization regime in diffusion NMR: Theory and experiments.

In this work we investigate the emergence of the localization regime for diffusion NMR in various geometries: inside slabs, inside cylinders and outside rods arranged on a square array. At high gradients, the transverse magnetization is strongly attenuated in the bulk, whereas the macroscopic signal is formed by the remaining magnetization localized near boundaries of the sample. As a consequence, the signal is particularly sensitive to the microstructure. The theoretical analysis relies on recent mathematical advances on the study of the Bloch-Torrey equation. Experiments were conducted with hyperpolarized xenon-129 gas in 3D-printed phantoms and show an excellent agreement with numerical simulations and theoretical predictions. Our mathematical arguments and experimental evidence indicate that the localization regime with a stretched-exponential decay of the macroscopic signal is a generic feature of diffusion NMR that can be observed at moderately high gradients in most NMR scanners.

Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities

We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities (e.g., energy and/or particle number) we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. More specifically, our data is consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and can not rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of non-monotonic dependence of the exponents with time, with dynamics initially slowing down but accelerating again at even larger times, consistent with the slow dynamics being a crossover phenomena with a localized critical point.

Polaron-Mediated Luminescence in Lithium Niobate and Lithium Tantalate and Its Domain Contrast

In this review article, we discuss photoluminescence phenomena mediated by polarons in lithium niobate (LNO). At first we present the fundamentals on polaron states in LNO and their energy levels, i.e., on free and bound electron polarons, on hole polarons as well as on bipolarons. We discuss the absorption measurements on reduced as well as on doped LNO that made the characterization of the formed polaron states possible by their absorption bands. Next, we proceed by reporting on the two polaron-mediated photoluminescence bands that have been observed in LNO: (1) A near-infrared luminescence band in the range of 1.5 eV shows a mono-exponential decay and a strong dependence on iron doping. This luminescence is emitted by bound polarons returning from an excited state to the ground state. (2) A luminescence band at visible wavelengths with a maximum at 2.6 eV shows a stretched-exponential decay and is strongly enhanced by optical damage resistant doping around the doping threshold. This luminescence stems from the recombination of free electron and hole polarons. The next major topic of this review are domain contrasts of the visible photoluminescence that have been observed after electrical poling of the substrate, as singly inverted domains show a slightly reduced and faster decaying luminescence. Subsequent annealing results in an exponential decrease of that domain contrast. We show that this contrast decay is strongly related to the mobility of lithium ions, thus confirming the role of polar defect complexes, including lithium vacancies, for these domain contrasts. Finally we discuss the extension of our investigations to lithium tantalate (LTO) samples. While the results on the domain contrast and its decay are similar to LNO, there are remarkable differences in their luminescence spectra.

Static and dynamic properties of two-dimensional Coulomb clusters.

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.

Diffusion MRI/NMR at high gradients: Challenges and perspectives

We discuss some challenges and recent advances in understanding the macroscopic signal formation at high non-narrow magnetic field gradients at which both the narrow pulse and the Gaussian phase approximations fail. The transverse magnetization and the resulting signal are fully determined by the spectral properties of the non-selfadjoint Bloch-Torrey operator which incorporates the microstructure of a sample through boundary conditions. Since the spectrum of this operator is known to be discrete for isolated pores, the signal can be decomposed onto the eigenmodes of the operator that yields the stretched-exponential decay at high gradients and long times. Moreover, the eigenmodes are localized near specific boundary points that makes the signal more sensitive to the boundaries and thus opens new ways of probing the microstructure. We argue that this behavior is much more general than earlier believed, and should also be valid for unbounded and multi-compartmental domains. In particular, the signal from the extracellular space is not Gaussian at high gradients, in contrast to the common assumption of standard fitting models.

Kinetics of the hydration reaction at the electrolyte–insulator interface

The instability of the dc operating point in the pH-sensitive ion-selective field effect transistors (ISFETs) has been ascribed to a chemical ageing at the electrolyte–insulator. This instability, commonly referred to as a drift, is believed to involve formation of a chemically-modified insulator surface layer as a result of hydration of the insulator material. A kinetic model for hydration of the amorphous insulator material is presented. The kinetics of hydration is limited by the hopping and/or trap-limited transport mechanism known as dispersive transport, the key characteristic of which is a power-law time dependence of the diffusion coefficient. The power-law time dependence of the diffusion coefficient will be shown to lead to a stretchedexponential decay in the form exp[–(t/τ)β] for the excess density of sites or traps occupied by the hydrating chemical species undergoing dispersive diffusion, where τ is the time constant associated with a structural relaxation and β is the dispersion parameter satisfying 0 < β < 1. The kinetics associated with a hydration reaction limited by the dispersive diffusion has been shown to lead to a hydrated layer thickness exhibiting a time dependence in the form {1–exp[–(t/τ)β]}. The first order rate equation describing the kinetics of the hydration reaction is characterized by the time-dependent rate coefficient.

The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.