Short-time Behavior Research Articles

Active fractal networks with stochastic force monopoles and force dipoles: Application to subdiffusion of chromosomal loci.

Motivated by the well-known fractal packing of chromatin, we study the Rouse-type dynamics of elastic fractal networks with embedded, stochastically driven, active force monopoles and force dipoles that are temporally correlated. We compute, analytically-using a general theoretical framework-and via Langevin dynamics simulations, the mean square displacement (MSD) of a network bead. Following a short-time superdiffusive behavior, force monopoles yield anomalous subdiffusion with an exponent identical to that of the thermal system. In contrast, force dipoles do not induce subdiffusion, and the early superdiffusive MSD crosses over to a relatively small, system-size-independent saturation value. In addition, we find that force dipoles may lead to "crawling" rotational motion of the whole network, reminiscent of that found for triangular micro-swimmers and consistent with general theories of the rotation of deformable bodies. Moreover, force dipoles lead to network collapse beyond a critical force strength, which persists with increasing system size, signifying a true first-order dynamical phase transition. We apply our results to the motion of chromosomal loci in bacteria and yeast cells' chromatin, where anomalous sub-diffusion, MSD∼tν with ν≃0.4, was found in both normal and cells depleted of adenosine triphosphate (ATP), albeit with different apparent diffusion coefficients. We show that the combination of thermal, monopolar, and dipolar forces in chromatin is typically dominated by the active monopolar and thermal forces, explaining the observed normal cells vs the ATP-depleted cells behavior.

Curvature fluctuations of fluid vesicles reveal hydrodynamic dissipation within the bilayer

The biological function of membranes is closely related to their softness, which is often studied through the membranes' thermally driven fluctuations. Typically, the analysis assumes that the relaxation rate of a pure bending deformation is determined by the competition between membrane bending rigidity and viscous dissipation in the surrounding medium. Here, we reexamine this assumption and demonstrate that viscous flows within the membrane dominate the dynamics of bending fluctuations of nonplanar membranes with a radius of curvature smaller than the Saffman-Delbrück length. Using flickering spectroscopy of giant vesicles made of dipalmitoylphosphatidylcholine, DPPC:cholesterol mixtures and pure diblock-copolymer membranes, we experimentally detect the signature of membrane dissipation in curvature fluctuations. We show that membrane viscosity can be reliably obtained from the short time behavior of the shape time correlations. The results indicate that the DPPC:cholesterol membranes behave as a Newtonian fluid, while the polymer membranes exhibit more complex rheology. Our study provides physical insights into the time scales of curvature remodeling of biological and synthetic membranes.

Sobolev and BV functions on RCD spaces via the short-time behaviour of the heat kernel

Sobolev and BV functions on RCD spaces via the short-time behaviour of the heat kernel

Critical short-time behavior of majority-vote model on scale-free networks

Critical short-time behavior of majority-vote model on scale-free networks

Hypocoercivity in Hilbert spaces

The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a hypocoercivity index, quantitative estimates on the short-time and long-time decay behavior of a hypocoercive system are derived. As a useful tool for analyzing the structural properties, an infinite-dimensional staircase form is also derived and connections to linear systems and control theory are presented. Several examples illustrate the new concepts and the results are applied to the Lorentz kinetic equation.

Non-equilibrium rate theory for polariton relaxation dynamics.

We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

The aging-hardening behavior of short-time in high pressure die casting AlSi9MgMnZn alloy

Short-time aging is an effective industrial technique for enhancing the mechanical properties of high pressure die cast (HPDC) aluminum alloy components. However, the evolution of precipitation behavior during short-time aging of HPDC alloys remains unclear. In this study, the short-time aging behavior of HPDC AlSi9MgMnZn alloy was investigated. The results show that the AlSi9MgMnZn alloy exhibits effective aging-hardening, with an increment in hardness of approximately 30 HV through the optimal short-time aging treatment (aged at 180 °C for 120 minutes). Higher aging temperatures led to reduced peak hardness and rapid over-aging above 220 °C. The microstructure observation indicates that the peak short-time aging promotes the simultaneous precipitation of β″ precipitates, GP zones and nano Si phases. The contribution of different strengthening mechanisms to hardness was estimated, implying that the coexistence of β″ precipitates and GP zones can provide a positive contribution to aging-hardening during short-time aging. Moreover, as the aging temperature increases, the appearance of β′ precipitates reduces the strengthening effect, leading to a decrease in hardness.

Unveiling the microstructure evolution and the short-time tensile creep behavior in the CuCrZr alloy

The creep behavior of the CuCrZr alloy, used in the combustion chamber wall of reusable launch vehicles, was investigated at 600-700 K and 150–250 MPa. Results demonstrate significant differences in the creep behavior, microstructure evolution including texture component, dislocation configurations and cavities at 600 K and 700 K, particularly at 250 MPa. At 600 K, the creep life exceeds 400 h, while at 700 K it drops below 0.5 h. The texture components evolved at 600 K-250 MPa are more balanced between hard texture (Brass texture) and soft texture (Goss texture and R-Goss texture). The texture components at 700 K-250 MPa are integrally biased toward the soft texture, implying that it is favorable to accelerate creep strain. The introduced high-density dislocations before creep act as an effective barrier to impede the motion of dislocations at 600 K, inducing long-time dynamic balance of work hardening and recovery softening, while the pre-creep dense dislocations act as an energy supplement at 700 K, promoting that recovery softening dominates the creep process. The dense dislocations can provide energetic support for cavity nucleation.

Characterizing Short-Time Aging Precipitation Behavior of a Novel Nickel-Iron-Based Alloy via Electrical Performance.

In this paper, the precipitation behavior and its effect on resistivity in a new type of nickel-iron-based alloy during short-term aging were investigated. During the aging process, the γ' phase increases in average size and decreases in number, with its area fraction fluctuating over time. This fluctuation is caused by the mismatch in the redissolution and growth rates of the γ' phase. As the area fraction of the γ' phase increases, the content of solute atoms in the matrix that scatter electrons decreases, lowering the resistivity of the alloy. Additionally, the continuous precipitation of M23C6 at grain boundaries during aging causes the resistivity to gradually increase. This paper explains the fluctuation in the total amount of γ' phase during short-term aging and proposes a new method for characterizing the precipitation behavior of the γ' phase in the novel alloy using the relative trend of resistivity changes.

Observation of anisotropy-independent magnetization dynamics in spatially disordered Heisenberg spin systems

An important step towards a comprehensive understanding of far-from-equilibrium dynamics of quantum many-body systems is the identification of unifying features that are independent of microscopic details of the system. We experimentally observe such robust features in the magnetization relaxation dynamics of disordered Heisenberg XX, XXZ, and Ising Hamiltonians. We realize these Heisenberg spin models with tunable anisotropy parameter and power-law interactions in an ensemble of Rydberg atoms by encoding the spin in suitable Rydberg state combinations. We consistently observe stretched-exponential relaxation of magnetization for all considered spin models, collapsing onto a single curve after appropriate rescaling of time. This robust short-time relaxation behavior is explained by a perturbative treatment that exploits the strong disorder in pairwise couplings, which leads to a description in terms of approximately independent pairs of spins. In numerical simulations of small systems, we show that these pairs of spins constitute approximate local integrals of motion, which remain at least partially conserved on a timescale exceeding the duration of the relaxation dynamics of the magnetization. Published by the American Physical Society 2024

Hitting probabilities for fast stochastic search *

Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work we determine hitting probabilities for stochastic search processes conditioned on being faster than a random short time. Such times have been used to model stochastic resetting or stochastic inactivation. These results apply to any search process, diffusive or otherwise, whose unconditional short-time behavior can be adequately approximated, which we characterize for broad classes of stochastic search. We illustrate these results in several examples and show that the conditional hitting probabilities depend predominantly on the relative geodesic lengths between the initial position of the searcher and the targets. Finally, we apply these results to a canonical evidence accumulation model for decision making.

Path-dependent correlations in dynamically tuned Ising models and its short-time behavior: Application of Magnus expansion

We study both analytically and numerically the buildup of antiferromagnetic (AF) correlation in the dynamically tuned Ising models. In short-time scale, we apply Magnus expansion (ME) to derive the high-order analytic expression of the connected correlation functions and compare it with exactly numerical results for the different lattice geometries, e.g., 1D chain, 2×n lattice, and n×n lattice. It is shown that the high-order expansion is required to describe accurately the buildup of AF correlation in the quench dynamics. Moreover, through a 2D square lattice, we find that the magnitude of AF correlation for the same Manhattan distance is proportional to the number of the shortest paths in a sufficiently long time until long and distinct paths are involved significantly. Finally, we propose an applicable experimental setup to realize our findings.

Interference-induced suppression of particle emission from a Bose–Einstein condensate in lattice with time-periodic modulations

Abstract Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications. In this work, we investigate the collective particle emission from a Bose–Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions. We give the regimes for discrete modes, and find that the emission can be distinctly suppressed. The configuration induces a broad band, but few particles are ejected due to the interference of the matter waves. We further qualitatively model the emission process and demonstrate the short-time behaviors. This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices, and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

Dissipative systems fractionally coupled to a bath.

Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system through a Liouville fractional derivative. The Liouville fractional Langevin equation is then derived in the classical regime, without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement, we show that this model is able to describe a large variety of anomalous diffusion. Indeed, we find ballistic, sub-ballistic, and super-ballistic behavior for short times, whereas for long times, we find saturation and sub- and super-diffusion.

Time distribution of stimulated transition probabilities

In recent years, an increasing number of experimental results have been published for a wide variety of systems in which high-precision, ultra-fast, and ultra-short laser pulses techniques have been used to study time-resolved dynamical processes. In the absence of a theoretical prediction of the time distribution of the transition probabilities, the lifetimes τ are generally extracted by fitting the decay time with an exponential, bi-exponential or three-exponential function. In fitting the data, the short-time behavior is generally neglected. The purpose of this study is to show that an explicit formula for the time distribution of the transition probability can be determined rigorously using time-dependent perturbation theory. A formula that perfectly fits an important subset of the experimental results from t = 0 to t=∞ . We show that by following a route different from the usual procedure for deriving transition amplitudes and Einstein coefficients in time-dependent perturbation theory, one ends up with a time-dependent factor, that is, a temporal distribution function of the transition probabilities, and for the Einstein coefficients. The time distribution reported here looks in the time domain similar to the Planck distribution in the frequency domain. In fact, the behavior of the time distribution, with a maximum at 2τln⁡2 , and with τ playing the role of temperature, resembles the behavior of the Planck frequency distribution. We present several examples to demonstrate that the theoretical formula allows for easier fitting of the experimental results reported in the literature. We also show that the time distribution explains the difference in resonance heights between the experimental and theoretical blue laser spectra.

Short-time high-temperature oxidation behavior of nanocrystalline Ta coating at 850 °C

Short-time high-temperature oxidation behavior of nanocrystalline Ta coating at 850 °C

Long and Short Time Behavior of Non-local in Time Subdiffusion Equations

Long and Short Time Behavior of Non-local in Time Subdiffusion Equations

Short-time creep behavior of (TiB + TiC + Y2O3) reinforced titanium matrix composite in the range of 600 °C to 700 °C

A titanium matrix composite reinforced by TiB, TiC and Y2O3 was prepared by induction skull melting. The creep behavior of the composite was tested at the temperature range from 600 °C to 700 °C in short time to investigate the deformation mechanism and microstructure involution. The as-cast composite shows a typical basket-weave microstructure. At the stress of 150 MPa, the stress exponents of the composite are 3.48 at 600 °C and 5.33 at 700 °C, corresponding to the deformation mechanism mainly controlled by solute-dragging and dislocation climbing respectively. Reinforcements added hinder dislocations movement effectively, which improves the creep resistance of the composite. As the creep temperature rises, the solubility of β-Ti increases, accompanied by the precipitation of silicides with different morphologies. Silicides play a role in pinning dislocations and hindering interface from migration. The dislocation movement and rearrangement during creep lead to the formation of sub-grains.

Universal Short-Time Conductance Behavior Emerges between Two Adjacent Reservoirs

When a shutter, which differentiates between two adjacent particles’ reservoirs with a voltage gap, is lifted, a current emerges. In this paper, the temporal dynamics of this emerging current is analyzed. The main results are as follows: (A) the current’s prefactor in the short-time behavior is related to the long-time frequencies, by which the current converges to its equilibrium value (the conductance quantum unit 2e2/h). (B) In the short-time regime, the current is proportional to the square root of the time. (C) The maximum overshoot conductance is bounded by Gmax = ζe2/h, where ζ is a universal value which is very close to Euler’s number. (D) Most of these results are valid for a thin wire in 3D, even in the presence of electron–electron interactions.

Interfacial Rheological Study of β-Casein/Pectin Mixtures at the Air/Water Interface.

Colloidal food products, such as emulsions, foams, gels, and dispersions, are complex systems that need the presence of stabilizing agents to enable their formation and provide stability. Proteins are often used for food foams and emulsions because of their ability to lower interfacial tension and make viscoelastic interfaces. Generally, to improve the resistance against rupture, polysaccharides are used in association with the proteins. Pectin is a complex polysaccharide that can help to stabilize foams or emulsions. This work aims at studying the mechanical resistance of the interface formed by mixtures of β-casein and pectin at high and low methoxylation degrees at the air/water interface using dilatational and shear kinematics. Frequency sweep tests, in the linear region, were performed in shear at different aging times and in dilatational mode, and the rheological data were analyzed. The transient data of the surface tension were analyzed by kinetic models to obtain the characteristic rates of the interfacial phenomena. The kinetic mechanisms of the protein/pectin mixed systems are controlled by protein and show a weak gel behavior for short aging times. The interfaces obtained with both pectins in a mixture with β-casein evolved with time, gelling and showing a solid-like behavior at concentrations of 1 and 10 g/L and after 3.5 h of aging time. The interfacial shear trend obtained suggests a good stabilizing effect of the pectins from citrus with long aging times.