Exponential Regime Research Articles

High performance single-molecule magnets, Orbach or Raman relaxation suppression?

Relaxation mechanisms limiting the blocking temperature for high-performance single molecule magnets (SMMs) are investigated. Best SMMs are limited by the exponential regime. Current ab initio methods can yield accurate estimations for this limit.

Analysis of the Breakdown of Exponential Decays of Resonances

In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of Green's function representation and numerical solution of the time-dependent Schr\odinger equation. In particular, finite depth potential wells and behavior between the exponential and power law regimes, which are situations that could not be described in detail analytically, are studied. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, the constructive and destructive interference is observed in the intermediate stage of the process. The simple alpha decay model is compared to the results of Rothe- Hintschich-Monkman experiment which was the first experimental proof of violation of the exponential law.

Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems.

We study heating rates in strongly interacting quantum lattice systems in the thermodynamic limit. Using a numerical linked cluster expansion, we calculate the energy as a function of the driving time and find a robust exponential regime. The heating rates are shown to be in excellent agreement with Fermi's golden rule. We discuss the relationship between heating rates and, within the eigenstate thermalization hypothesis, the smooth function that characterizes the off-diagonal matrix elements of the drive operator in the eigenbasis of the static Hamiltonian. We show that such a function, in nonintegrable and (remarkably) integrable Hamiltonians, can be probed experimentally by studying heating rates as functions of the drive frequency.

Evolution of two-time correlations in dissipative quantum spin systems: Aging and hierarchical dynamics

We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For initial times, their evolution is dominated by the system unitary dynamics and depends on the initial state and the Hamiltonian parameters. For weak spin-spin interaction anisotropy, after this initial dynamical regime, two-time correlations enter an algebraic scaling regime signaling the breakdown of time-translation invariance and the emergence of aging. For stronger interaction anisotropy, these correlations first go through a stretched exponential regime before entering the algebraic one. Such complex relaxation arises due to the competition between the proliferation dynamics of energetically costly excitations and their motion. As a result, dissipative heating dynamics of spin systems can be used to probe the entire spectrum of the underlying Hamiltonian.

On the expected maximum of a birth-and-death process

We describe a simple continuous time process obtained by pointwise addition of finitely many i.i.d. 0–1 processes with alternating exponential regimes. We investigate the asymptotic mean value of the maxima (the peaks) reached within the non-zero zones. In this short communication we show that the computation of this quantity leads to a transcendental equation that, to the best of our knowledge, has not appeared before in the literature.

Biomass and Nutrients Variation of Chinese Fir Rooted Cuttings under Conventional and Exponential Fertilization Regimes of Nitrogen

Exponential fertilization has been regarded as an important technique for improving seedling quality at the initial plant-growth stage. In our study, containerized one-year-old Chinese fir (Cunninghamia lanceolata (Lamb.) Hook) rooted cuttings were reared at four nitrogen (N) fertilizer levels (0, 0.5, 1.0, 2.0 g cutting−1 season−1) under two topdressing methods (conventional and exponential) for a 210-day greenhouse rotation to evaluate growth and nutrient loading capacity of seedlings. N fertilizer was applied 20 times at an interval of 10 days during the study period. The results indicated that the schedule and rate of fertilization significantly affected the height, ground diameter, and biomass of Chinese fir rooted cuttings. The nitrogen concentration of different plant organs followed the order of leaves > root > stem. Compared to the CK, the N concentrations in root, stem, and leaves increased by 39.6%, 16.6%, and 41.1% in the conventional fertilizer treatment, and by 22.6% to 81.4%, 27.3% to 152.6%, and 73.6% to 135.5% in exponential fertilization treatments, respectively. The N concentrations of root, stem, and leaves of Chinese fir rooted cuttings under EF2 (1.0 N g cutting−1) were significantly higher than that of conventional fertilization (p < 0.05). However, there was no significant difference of phosphorus and potassium concentrations among different plant organs. Steady-state nutrition and superior growth performance were achieved by rooted cuttings fertilized exponentially at the rate of 1.0 g cutting−1 yielding (EF2).

Experimental Investigation of Quantum Decay at Short, Intermediate, and Long Times via Integrated Photonics.

The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.

Büyük Etki Parametreleri Bölgesi İçin Elastik Saçılma Genliği

The work is dedicated to consequences of analyticity and unitarity of the scattering amplitude. Using the Gaussian quasipotential an equation for the scattering amplitude matrix is obtained and formula is derived for the cross sections. The dependence of the cross section and ratio of the real part of the amplitude in the forward scattering to its imaginary part of on the momentum are discussed. The steep Gaussian peak for cross section at small angles is followed by the exponential (Orear) regime. Results from theoretical approach are compared with experimental data.

Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator Sn−Bi1.1Sb0.9Te2S devices

The scaling physics of quantum Hall transport in optimized topological insulators with a plateau precision of ~1/1000 e2/h is considered. Two exponential scaling regimes are observed in temperature-dependent transport dissipation, one of which accords with thermal activation behavior with a gap of 2.8 meV (> 20 K), the other being attributed to variable range hopping (1-20 K). Magnetic field-driven plateau-to-plateau transition gives scaling relations of (dR$_{xy}$/dB)$^{max}$ \propto T$^{-\kappa}$ and \DeltaB$^{-1}$ \propto T$^{-\kappa}$ with a consistent exponent of \kappa ~ 0.2, which is half the universal value for a conventional two-dimensional electron gas. This is evidence of percolation assisted by quantum tunneling, and reveals the dominance of electron-electron interaction of the topological surface states.

Inferring critical transitions in paleoecological time series with irregular sampling and variable time-averaging

Many ecosystems have abruptly changed in the past and may again in the future, yet prediction and inference of mechanisms causing abrupt changes remains challenging. Critical transitions are one such mechanism, occurring when systems with alternative states cross a threshold. Such transitions are associated with a loss of resilience, often signaled by increasing variability or autocorrelation over time. However, critical transitions are difficult to distinguish from other causal mechanisms, and detection of resilience loss in sedimentary archives can be confounded by time-averaging and discontinuous sampling. Here, we simulate woodland-grassland regime shifts resulting from critical transitions and other mechanisms. We then test the diagnostic ability of two widely-used resilience indicators, standard deviation and autocorrelation time, after alterations common in sedimentary records: time averaging, discontinuous sampling, and varying sedimentation rates. Standard deviation—but not autocorrelation time—still distinguishes gradually forced critical transitions from other regime shifts when sedimentation rates are constant, and can be robust to abrupt changes in sedimentation rate. Unfortunately, shifts in standard deviation alone are rarely definitive evidence of critical transitions. Under exponential sedimentation regimes, which are common in younger upper-column sediments, neither resilience indicator is effective. Discontinuous sampling weakened the strength of resilience indicators. A demonstrative analysis of abrupt early Holocene deforestation recorded at Steel Lake, Minnesota showed signals consistent with resilience loss during early Holocene aridification. Hence, signals of resilience loss can be recovered from sedimentary archives, but efficacy varies among indicators and sedimentation regime. High-resolution and multi-proxy records remain essential to inferring causes, while process-based time series modeling such as this can be calibrated to systems of interest to explicitly test hypotheses about abrupt change causes.

Force spectroscopy analysis in polymer translocation

This paper reports the force spectroscopy analysis of a polymer that translocates from one side of a membrane to the other side through an extended pore, pulled by a cantilever that moves with constant velocity against the damping and the potential barrier generated by the reaction of the membrane walls. The polymer is modeled as a beads-springs chain with both excluded volume and bending contributions, and moves in a stochastic three dimensional environment described by a Langevin dynamics at fixed temperature. The force trajectories recorded at different velocities reveal two unexplored exponential regimes: the force increases when the first part of the chain enters the pore, and then decreases when the first monomer reaches the trans region. The spectroscopy analysis of the force values permit the estimation of the free energy barrier as well as the limit force to permit the translocation. The stall force to maintain the polymer fixed has been also calculated independently, and its value confirms the force spectroscopy outcomes.

Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models

AbstractExponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill‐suited as a regime weighting function because of two undesirable properties. Firstly, it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is ‘small’. This leads to an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of γ. This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter μ. We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise.

CaBER vs ROJER—Different time scales for the thinning of a weakly elastic jet

In this paper, we demonstrate that the capillary thinning dynamics of a weakly viscoelastic jet follow a different timescale than a liquid bridge of the same fluid between two stationary surfaces for similar geometrical scales. The thinning in the latter case observed with capillary breakup extensional rheometry (or CaBER) follows a well established scaling of the radius with time for an elasto-capillary (EC) balance of R∼exp⁡(−t/3λ). However, for the thinning of the filaments between droplets in a jet, it was so far just assumed that the same scaling law holds. In this paper, we experimentally demonstrate that the jet thinning in a Rayleigh–Ohnesorge jetting extensional rheometer (or ROJER) follows a different scaling of R∼exp⁡(−t/2λ). This is demonstrated by a direct comparison of the thinning dynamics of weakly viscoelastic (Oh<0.01) aqueous solutions of polyethylene oxide in the two experimental setups, covering a wide range of jetting velocities or Weber numbers of 1–70. We demonstrate outgoing from a momentum balance that includes inertia and elasticity that this difference in scaling is due to a constant axial tension in the jet arising from the constant creation rate of new surface at the nozzle. Numerical simulations using the FENE-P model support this theory and demonstrate that in the exponential thinning regime of the jet the elastic stresses are indeed balanced by the axial tension (rather than by capillary pressure as in the EC balance regime of the CaBER experiment). It is readily shown from the reduced stress balance that this axial-elastic balance regime in the ROJER experiment leads to a faster exponential thinning, following the new scaling of R∼exp⁡(−t/2λ) that was experimentally observed. Furthermore, we observe both in experiment and simulation that a jet thinning does not exhibit a self-similar structure of the corner region where the thinning filament connects to the drop as it is generally observed for a filament with an axial tension decaying with the filament radius as in the CaBER. The resulting difference of 50% in extensional relaxation time λ extracted from ROJER experiments might require one to revisit previously reported ROJER experiments and is required for the correct evaluation of future jetting rheometry experiments.

Spatiotemporal Analysis of Coronal Loops Using Seismology of Damped Kink Oscillations and Forward Modeling of EUV Intensity Profiles

Abstract The shape of the damping profile of kink oscillations in coronal loops has recently allowed the transverse density profile of the loop to be estimated. This requires accurate measurement of the damping profile that can distinguish the Gaussian and exponential damping regimes, otherwise there are more unknowns than observables. Forward modeling of the transverse intensity profile may also be used to estimate the width of the inhomogeneous layer of a loop, providing an independent estimate of one of these unknowns. We analyze an oscillating loop for which the seismological determination of the transverse structure is inconclusive except when supplemented by additional spatial information from the transverse intensity profile. Our temporal analysis describes the motion of a coronal loop as a kink oscillation damped by resonant absorption, and our spatial analysis is based on forward modeling the transverse EUV intensity profile of the loop under the isothermal and optically thin approximations. We use Bayesian analysis and Markov chain Monte Carlo sampling to apply our spatial and temporal models both individually and simultaneously to our data and compare the results with numerical simulations. Combining the two methods allows both the inhomogeneous layer width and density contrast to be calculated, which is not possible for the same data when each method is applied individually. We demonstrate that the assumption of an exponential damping profile leads to a significantly larger error in the inferred density contrast ratio compared with a Gaussian damping profile.

Inflation from a nonlinear magnetic monopole field nonminimally coupled to curvature

In the context of nonminimally coupled f(R) gravity theories, we study early inflation driven by a nonlinear monopole magnetic field which is nonminimally coupled to curvature. In order to isolate the effects of the nonminimal coupling between matter and curvature we assume the pure gravitational sector to have the Einstein-Hilbert form. Thus, we study the most simple model with a nonminimal coupling function which is linear in the Ricci scalar. From an effective fluid description, we show the existence of an early exponential expansion regime of the Universe, followed by a transition to a radiation-dominated era. In particular, by applying the most recent results of the Planck collaboration we set the limits on the parameter of the nonminimal coupling, and the quotient of the nonminimal coupling and the nonlinear monopole magnetic scales. We found that these parameters must take large values in order to satisfy the observational constraints. Furthermore, by obtaining the relation for the graviton mass, we show the consistency of our results with the recent gravitational wave data GW170817 of LIGO and Virgo.

Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws

Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography. We tackle this problem in 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a `hydrodynamical' equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy). In this hydrodynamic picture quantum information travels in a front with a `butterfly velocity' $v_{\text{B}}$ that is smaller than the light cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do \emph{not} observe a prolonged exponential regime of the form $\sim e^{\lambda_\text{L}(t-x/v)}$ for a fixed Lyapunov exponent $\lambda_\text{L}$. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic ergodic systems and support this by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional non-random Floquet spin-chain. We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization.

Stimulated X-Ray Emission Spectroscopy in Transition Metal Complexes.

We report the observation and analysis of the gain curve of amplified Kα x-ray emission from solutions of Mn(II) and Mn(VII) complexes using an x-ray free electron laser to create the 1s core-hole population inversion. We find spectra at amplification levels extending over 4 orders of magnitude until saturation. We observe bandwidths below the Mn 1s core-hole lifetime broadening in the onset of the stimulated emission. In the exponential amplification regime the resolution corrected spectral width of ∼1.7 eV FWHM is constant over 3 orders of magnitude, pointing to the buildup of transform limited pulses of ∼1 fs duration. Driving the amplification into saturation leads to broadening and a shift of the line. Importantly, the chemical sensitivity of the stimulated x-ray emission to the Mn oxidation state is preserved at power densities of ∼10^{20} W/cm^{2} for the incoming x-ray pulses. Differences in signal sensitivity and spectral information compared to conventional (spontaneous) x-ray emission spectroscopy are discussed. Our findings build a baseline for nonlinear x-ray spectroscopy for a wide range of transition metal complexes in inorganic chemistry, catalysis, and materials science.

Forecasting the 2001 Foot-and-Mouth Disease Epidemic in the UK

Near real-time epidemic forecasting approaches are needed to respond to the increasing number of infectious disease outbreaks. In this paper, we retrospectively assess the performance of simple phenomenological models that incorporate early sub-exponential growth dynamics to generate short-term forecasts of the 2001 foot-and-mouth disease epidemic in the UK. For this purpose, we employed the generalized-growth model (GGM) for pre-peak predictions and the generalized-Richards model (GRM) for post-peak predictions. The epidemic exhibits a growth-decelerating pattern as the relative growth rate declines inversely with time. The uncertainty of the parameter estimates (r{text{ and }}p) narrows down and becomes more precise using an increasing amount of data of the epidemic growth phase. Indeed, using only the first 10–15 days of the epidemic, the scaling of growth parameter (p) displays wide uncertainty with the confidence interval for p ranging from values ~ 0.5 to 1.0, indicating that less than 15 epidemic days of data are not sufficient to discriminate between sub-exponential (i.e., p < 1) and exponential growth dynamics (i.e., p = 1). By contrast, using 20, 25, or 30 days of epidemic data, it is possible to recover estimates of p around 0.6 and the confidence interval is substantially below the exponential growth regime. Local and national bans on the movement of livestock and a nationwide cull of infected and contiguous premises likely contributed to the decelerating trajectory of the epidemic. The GGM and GRM provided useful 10-day forecasts of the epidemic before and after the peak of the epidemic, respectively. Short-term forecasts improved as the model was calibrated with an increasing length of the epidemic growth phase. Phenomenological models incorporating generalized-growth dynamics are useful tools to generate short-term forecasts of epidemic growth in near real time, particularly in the context of limited epidemiological data as well as information about transmission mechanisms and the effects of control interventions.

A microstructural based creep model applied to alloy 718

In this work a creep model based on the microstructural evolution of precipitation strengthening metals is presented. The model describes the influence of precipitates on the threshold stress as well as the power-law and the exponential creep rates depending on the aging condition. To show the predictive capabilities of this model, it was applied to the nickel based superalloy Alloy 718. This alloy is precipitation strengthened by the γ′ and γ’’ phases. Thermo-kinetic simulations based on a calibrated MatCalc routine were performed to determine the evolution of the volume fraction and mean radius of the precipitates. In addition, sequential creep and tensile tests were performed to characterize the mechanical material behavior. The simulated microstructural evolution and the corresponding measured mechanical properties were used to parametrize the creep model. Finally, the fully parametrized model was applied to simulate deformation mechanism diagrams for different aging conditions. From these diagrams the purely elastic, the power-law and the exponential deformation regimes can be estimated depending on the precipitate volume fraction and mean precipitate radius.

Criteria for accurate determination of the magnon relaxation length from the nonlocal spin Seebeck effect

The nonlocal transport of thermally generated magnons not only unveils the underlying mechanism of the spin Seebeck effect, but also allows for the extraction of the magnon relaxation length ($\lambda_m$) in a magnetic material, the average distance over which thermal magnons can propagate. In this study, we experimentally explore in yttrium iron garnet (YIG)/platinum systems much further ranges compared with previous investigations. We observe that the nonlocal SSE signals at long distances ($d$) clearly deviate from a typical exponential decay. Instead, they can be dominated by the nonlocal generation of magnon accumulation as a result of the temperature gradient present away from the heater, and decay geometrically as $1/d^2$. We emphasize the importance of looking only into the exponential regime (i.e., the intermediate distance regime) to extract $\lambda_m$. With this principle, we study $\lambda_m$ as a function of temperature in two YIG films which are 2.7 and 50 $\mu$m in thickness, respectively. We find $\lambda_m$ to be around 15 $\mu$m at room temperature and it increases to 40 $\mu$m at $T=$ 3.5 K. Finite element modeling results agree with experimental studies qualitatively, showing also a geometrical decay beyond the exponential regime. Based on both experimental and modeling results we put forward a general guideline for extracting $\lambda_m$ from the nonlocal spin Seebeck effect.