Short-time Behavior Research Articles

Large deviations for some fast stochastic volatility models by viscosity methods

We consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. We study the asymptotics of a logarithmic functional of the process by methods of the theory of homogenization and singular perturbations for fully nonlinear PDEs. We point out three regimes depending on how fast the volatility oscillates relative to the horizon length. We prove a large deviation principle for each regime and apply it to the asymptotics of option prices near maturity.

Intermittency and dynamical Lee-Yang zeros of open quantum systems.

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).

Pinning time statistics for vortex lines in disordered environments.

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power-law distributions in the pinned phase as predicted by extreme-event statistics, yet they differ significantly in their effective scaling exponents and their short-time behavior.

Power-law models for infectious disease spread

Short-time human travel behaviour can be described by a power law with respect to distance. We incorporate this information in space-time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a spatio-temporal point process model for individual-level data and a multivariate time-series model for aggregated count data. In both frameworks, a power-law decay of spatial interaction is embedded into the epidemic component and estimated jointly with all other unknown parameters using (penalised) likelihood inference. Whereas the power law can be based on Euclidean distance in the point process model, a novel formulation is proposed for count data where the power law depends on the order of the neighbourhood of discrete spatial units. The performance of the new approach is investigated by a reanalysis of individual cases of invasive meningococcal disease in Germany (2002-2008) and count data on influenza in 140 administrative districts of Southern Germany (2001-2008). In both applications, the power law substantially improves model fit and predictions, and is reasonably close to alternative qualitative formulations, where distance and order of neighbourhood, respectively, are treated as a factor. Implementation in the R package surveillance allows the approach to be applied in other settings.

Short-time heat treatment of press hardened steel for laser assisted clinching

Clinching of high strength steels is currently difficult due to their relative low ductility. Hence a new method has been developed to clinch these steel grades. This could be achieved by heating the sheets locally at the joint by a laser during the clinching process. The short-time tempering behaviour of the press hardened steel 22MnB5 has been investigated by dilatometry respectively calorimetry experiments. Different stages of the tempering process have been identified depending on heating rates up to 1000 K s−1. Characteristic tempering reactions were shifted to higher temperatures with increasing heating rate. Based on these results, suitable short-time heat treatment parameters have been selected and transferred to the clinching process. Thereby the press hardened steel 22MnB5 has been successfully clinched with laser assistance for the very first time. The laser assisted clinched joint has been characterised by metallographic analysis and hardness testing. It could be shown, that in the clinching joint only a slight strength loss occurs due to the introduced laser heat.

The influence of spontaneously generated coherence on atom-photon entanglement in a Λ-type system with an incoherent pump

Abstract Owing to interference induced by spontaneous emission, the density-matrix equations in a three-level Λ-type system have an additional coherence term, which plays a critical role in modulating the inversionless gain and electromagnetically induced transparency effect. In addition, it is shown that spontaneously generated coherence (SGC) has an effect on the entanglement between an atom and a photon of the coupling laser field by calculating the degree of entanglement (DEM) of the atomic system. In this paper, we investigate the influence of the SGC effect on atom-photon entanglement in a Λ-type system, which generally remains a high entangled state. When an incoherent pump source is introduced, we find that the SGC effect could exert considerable influence on the atom reduced entropy under certain conditions for both transient and steady states. More interestingly, such an incoherent pump field could actively affect the short-time dynamic behaviors of the transient quantum entangled state at a certain range of pump rate as a typical coherent case.

Spreading dynamics on networks: the role of burstiness, topology and non-stationarity

Spreading on networks is influenced by a number of factors, including different parts of the inter-event time distribution (IETD), the topology of the network and non-stationarity. In order to understand the role of these factors we study the SI model on temporal networks with different aggregated topologies and different IETDs. Based on analytic calculations and numerical simulations, we show that if the stationary bursty process is governed by power-law IETD, the spreading can be slowed down or accelerated as compared to a Poisson process; the speed is determined by the short time behaviour, which in our model is controlled by the exponent. We demonstrate that finite, so called ‘locally tree-like’ networks, like the Barabási–Albert networks behave very differently from real tree graphs if the IETD is strongly fat-tailed, as the lack or presence of rare alternative paths modifies the spreading. A further important result is that the non-stationarity of the dynamics has a significant effect on the spreading speed for strongly fat-tailed power-law IETDs, thus bursty processes characterized by small power-law exponents can cause slow spreading in the stationary state but also very rapid spreading, with this heavily dependent on the age of the processes.

Softening of High-Strength Steel for Laser Assisted Clinching

The conventional clinching of steels is currently limited to tensile strength less than 800 N/mm2 and to elongation at fracture more than 14 %. To realise the clinching of high-strength steels, the sheet can be heated locally at the joint, to improve ductility. Thereby the material characteristics outside the joint should be maintained. This could be achieved by means of short-time laser heating. The short-time tempering behaviour of press hardened steel 22MnB5 has been analysed. The mechanical properties during a short-time heat treatment were investigated by thermo-mechanical analysis in a deformation dilatometer. Thereby laser-assisted clinching shall be established and an efficient form-closed and force-closed connection shall be produced. As a result, the press hardened steel 22MnB5 could be clinched by laser assistance for the very first time.

Hydrodynamic and nonhydrodynamic contributions to the bimolecular collision rates of solute molecules in supercooled bulk water.

Bimolecular collision rate constants of a model solute are measured in water at T = 259–303 K, a range encompassing both normal and supercooled water. A stable, spherical nitroxide spin probe, perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl, is studied using electron paramagnetic resonance spectroscopy (EPR), taking advantage of the fact that the rotational correlation time, τR, the mean time between successive spin exchanges within a cage, τRE, and the long-time-averaged spin exchange rate constants, Kex, of the same solute molecule may be measured independently. Thus, long- and short-time translational diffusion behavior may be inferred from Kex and τRE, respectively. In order to measure Kex, the effects of dipole–dipole interactions (DD) on the EPR spectra must be separated, yielding as a bonus the DD broadening rate constants that are related to the dephasing rate constant due to DD, Wdd. We find that both Kex and Wdd behave hydrodynamically; that is to say they vary monotonically with T/η or η/T, respectively, where η is the shear viscosity, as predicted by the Stokes–Einstein equation. The same is true of the self-diffusion of water. In contrast, τRE does not follow hydrodynamic behavior, varying rather as a linear function of the density reaching a maximum at 276 ± 2 K near where water displays a maximum density.

Polariton formation in a microcavity with a doped quantum well: Roles of the Fermi edge singularity and Anderson orthogonality catastrophe

A theoretical investigation of the single particle polariton properties for a microcavity embedding a charged quantum well is presented. The electron gas optical susceptibility is calculated numerically using the method devised by Combescot and Nozi\`eres. The role of many-body effects, such as the Fermi edge singularity and Anderson orthogonality catastrophe, in the polariton formation is elucidated. By tuning the light-matter coupling the short time behaviour of the electron gas response function is probed and comparison with earlier results only using the long time response are made. Various single particle polariton properties such as the Rabi splitting, line shape, Hopfield coefficients and effective mass are discussed. These are experimentally accessible quantities and thus allow for a comparison with the presented theory.

Short-time asymptotics of a rigorous path integral for N = 1 supersymmetric quantum mechanics on a Riemannian manifold

Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.

Coexistence of iso-nonergodic laponite gel and glass in 1-methyl-3-octylimidazolium chloride ionic liquid solutions.

We report unique colloidal gel-glass coexistence in aqueous laponite dispersion (2% w/v) in the presence of 1-methyl-3-octylimidazolium chloride ionic liquid (IL, [C8mim][Cl], concentration 0.01 to 0.05% w/v), where both of the phases had identical nonergodicity and were dynamically interactive. With aging, the nascent heterogeneous dispersion exhibited spontaneous two-phase separation, and the time-dependent relative viscosity followed: η(r) = |ε|(-k) where ε = (t - t(g))/t(g) and t(g) is the time required for the system to get arrested, with k decreasing from 3.13 to 2.54 as the IL concentration was increased from 0 to 0.03% (w/v), implying slowing down of the arrest kinetics. This time was measured from viscosity and rheology studies, revealing the formation of IL-mediated finite size colloidal networks on a time scale of ~4 × 10(3) s, whereas the dispersion developed a large viscosity one decade in time later (~4 × 10(4) s). Homogeneous transparent upper phase was an entropic glass and exhibited substantial storage modulus gain (300-3000 Pa) with an increase in IL concentration (0 to 0.05% (w/v)). The translucent lower gel phase had a much higher storage modulus. Dynamic light scattering measured bimodal relaxation time of concentration fluctuations. The degree of nonergodicity in the two phases was approximately the same, implying laponite-IL cluster exchange across the interface (identical slow-mode diffusivity). In summary, IL-induced first-order phase separation in laponite dispersion produced a homogeneous colloidal gel coexisting with a glass not commonly observed in soft matter systems. This implied that the two phases were dynamically coupled on long time scales, whereas their short-time behavior was distinctively different.

HIGH‐ORDER SHORT‐TIME EXPANSIONS FOR ATM OPTION PRICES OF EXPONENTIAL LÉVY MODELS

AbstractThe short‐time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In this work, a novel second‐order approximation for at‐the‐money (ATM) option prices is derived for a large class of exponential Lévy models with or without Brownian component. The results hereafter shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration. In the presence of a Brownian component, the second‐order term, in time‐t, is of the form , with d2 only depending on Y, the degree of jump activity, on σ, the volatility of the continuous component, and on an additional parameter controlling the intensity of the “small” jumps (regardless of their signs). This extends the well‐known result that the leading first‐order term is . In contrast, under a pure‐jump model, the dependence on Y and on the separate intensities of negative and positive small jumps are already reflected in the leading term, which is of the form . The second‐order term is shown to be of the form and, therefore, its order of decay turns out to be independent of Y. The asymptotic behavior of the corresponding Black–Scholes implied volatilities is also addressed. Our method of proof is based on an integral representation of the option price involving the tail probability of the log‐return process under the share measure and a suitable change of probability measure under which the pure‐jump component of the log‐return process becomes a Y‐stable process. Our approach is sufficiently general to cover a wide class of Lévy processes, which satisfy the latter property and whose Lévy density can be closely approximated by a stable density near the origin. Our numerical results show that the first‐order term typically exhibits rather poor performance and that the second‐order term can significantly improve the approximation's accuracy, particularly in the absence of a Brownian component.

Waiting time distribution of quantum electronic transport in the transient regime

Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). In this work, we present a theory to calculate WTD for coherent electronic systems in transient regime. We express the generating function of full counting statistics using Keldysh non-equilibrium Green's functions formalism. Our analysis goes beyond the wideband approximation and is suitable for first principles calculation on realistic systems. Analytic solution has been obtained for short and long time behaviors of waiting times. At short times, the WTD shows a linear dependence on the waiting time while in the long time limit, WTD follows Poisson distribution. We have applied this theory to a quantum dot connected by two leads and calculated cumulants of transferred charge as well as WTD in the transient regime. We have demonstrated how to relate WTD to experimental measured data.

Nonextensive lattice gauge theories: Algorithms and methods

High-energy phenomena presenting strong dynamical correlations, long-range interactions and microscopic memory effects are well described by nonextensive versions of the canonical Boltzmann–Gibbs statistical mechanics. After a brief theoretical review, we introduce a class of generalized heat-bath algorithms that enable Monte Carlo lattice simulations of gauge fields on the nonextensive statistical ensemble of Tsallis. The algorithmic performance is evaluated as a function of the Tsallis parameter q in equilibrium and nonequilibrium setups. Then, we revisit short-time dynamic techniques, which in contrast to usual simulations in equilibrium present negligible finite-size effects and no critical slowing down. As an application, we investigate the short-time critical behaviour of the nonextensive hot Yang–Mills theory at q-values obtained from heavy-ion collision experiments. Our results imply that, when the equivalence of statistical ensembles is obeyed, the long-standing universality arguments relating gauge theories and spin systems hold also for the nonextensive framework.

Sensitive chemical compass and quantum criticality at finite temperature

We investigate the influence of a flip operation of the central spin on the quantum criticality of a radical pair system by employing the spin echo and its product yield. It is found that with echo control on the central spin, the critical behavior can be described by the product yield at very high temperatures. Moreover, we also study the short and long time behavior of the spin echo, and show that the decay factor of the short time evolution scales linearly. The long time evolution shows different statistics for varying chain lengths, temperature and external parameters of the Hamiltonian. • The product yield can describe the critical behavior at high temperatures. • The decay factor of the short time evolution scales linearly with chain length. • The long time evolutions have interesting statistical distributions.

Short-time behavior of percolation observables at O(3) spin models: a preliminary analysis

We analyzed the short-time behavior of percolation observables at three dimensional O(3) spin models. Following the Metropolis time evolution we can compare the magnetic and percolation order parameters. The magnetic order parameter evolves with a power law M ∼ tθ, as expected. However the percolation order parameter follows a different law. We explored this particularity and raised some hypothesis. This paper is a preliminar analysis on this subject.

Topological analysis of chaotic transport through a ballistic atom pump.

We examine a system consisting of two reservoirs of particles connected by a channel. In the channel are two oscillating repulsive potential-energy barriers. It is known that such a system can transport particles from one reservoir to the other, even when the chemical potentials in the reservoirs are equal. We use computations and the theory of chaotic transport to study this system. Chaotic transport is described by passage around or through a heteroclinic tangle. Topological properties of the tangle are described using a generalization of homotopic lobe dynamics, which is a theory that gives some properties of intermediate-time behavior from properties of short-time behavior. We compare these predicted properties with direct computation of trajectories.

Unveiling the hidden structure of complex stochastic biochemical networks

Complex Markov models are widely used and powerful predictive tools to analyze stochastic biochemical processes. However, when the network of states is unknown, it is necessary to extract information from the data to partially build the network and estimate the values of the rates. The short-time behavior of the first-passage time distributions between two states in linear chains has been shown recently to behave as a power of time with an exponent equal to the number of intermediate states. For a general Markov model we derive the complete Taylor expansion of the first-passage time distribution between two arbitrary states. By combining algebraic methods and graph theory approaches it is shown that the first term of the Taylor expansion is determined by the shortest path from the initial state to the final state. When this path is unique, we prove that the coefficient of the first term can be written in terms of the product of the transition rates along the path. It is argued that the application of our results to first-return times may be used to estimate the dependence of rates on external parameters in experimentally measured time distributions.

Significance of experimental data in the design of structures made from 1.4057 steel

This paper presents experimentally-obtained data which can be of importance in the design procedure of engineering components made of 1.4057 (X17CrNi16-2; AISI 431) steel. In this manner, uniaxialy tests related to determine material mechanical properties and short-time creep behavior were performed. Based on the mentioned tests, ultimate tensile strength, 0.2 offset yield strength and modulus of elasticity at low and elevated temperatures were determined. Also, creep behavior of considered steel was tested for selected temperatures and selected stress levels. According to experimentally determined Charpy impact energy an assessment of fracture toughness was made.