Mean first-passage times in confined media: from Markovian to non-Markovian processes
International Nuclear Information System (INIS)
Bénichou, O; Voituriez, R; Guérin, T
2015-01-01
We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and non-Markovian walkers. For the Markovian problem, we present a general theory which allows one to accurately evaluate the MFPT and its extensions to related first-passage observables such as splitting probabilities and occupation times. We show that this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source–target distance in the case of general scale-invariant processes. This analysis is applicable to a broad range of stochastic processes characterized by length scale-invariant properties, and reveals the key role that can be played by the starting position of the random walker. We then present an extension to non-Markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement. We show that the MFPT can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction. Such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for Markovian walks. Finally, we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain, and review the various theoretical approaches of this non- Markovian problem. (topical review)
First passage time probability in risk analysis
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Karmeshu; Ariaratnam, S.T.
1982-01-01
Many natural phenomena are subject to uncertain fluctuations due to a variety of internal or external factors. These phenomena can be described using stochastic models. An important quantity of interest involves the time lapse before some variables reach unacceptable values: the first passage time. A related question pertains to the statistical distributions of the extreme values of these variables in a given period of time. The authors discuss some problems drawn from population ecology and environmental engineering to illustrate the usefulness of the first passage time concept
First Passage Time Intervals of Gaussian Processes
Perez, Hector; Kawabata, Tsutomu; Mimaki, Tadashi
1987-08-01
The first passage time problem of a stationary Guassian process is theretically and experimentally studied. Renewal functions are derived for a time-dependent boundary and numerically calculated for a Gaussian process having a seventh-order Butterworth spectrum. The results show a multipeak property not only for the constant boundary but also for a linearly increasing boundary. The first passage time distribution densities were experimentally determined for a constant boundary. The renewal functions were shown to be a fairly good approximation to the distribution density over a limited range.
Zero-crossing statistics for non-Markovian time series.
Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias
2018-03-01
In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.
Zero-crossing statistics for non-Markovian time series
Nyberg, Markus; Lizana, Ludvig; Ambjörnsson, Tobias
2018-03-01
In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.
A simple method to calculate first-passage time densities with arbitrary initial conditions
Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig
2016-06-01
Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.
Algorithms for Brownian first-passage-time estimation
Adib, Artur B.
2009-09-01
A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.
Critical behavior of the two-dimensional first passage time
International Nuclear Information System (INIS)
Chayes, J.T.; Chayes, L.; Durrett, R.
1986-01-01
We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probability p and 1-p, respectively. We provide that as the zero-time bonds approach the percolation threshold p/sub c/, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys ξ(p)--chemical bondp-p/sub c/chemical bond/sup -//sup v/, then the first passage time constant satisfies μ(p)--chemical bondp-p/sub c/chemical bond/sup v/. At p/sub c/, where it has been asserted that the first passage time from 0 to x scales as chemical bondxchemical bond to a power psi with 0< psi<1, we show that the passage times grow like log chemical bondxchemical bond, i.e., the fluid spreads exponentially rapidly
First passage time to allopatric speciation.
Yamaguchi, Ryo; Iwasa, Yoh
2013-12-06
Allopatric speciation is a mechanism to evolve reproductive isolation; it is caused by the accumulation of genetic differences between populations while they are geographically isolated. Here, we studied a simple stochastic model for the time until speciation caused by geographical isolation in fragmented populations that experience recurrent but infrequent migration between subpopulations. We assumed that mating incompatibility is controlled by a number of loci that behave as neutral characters in the accumulation of novel mutations within each population. Genetic distance between populations was defined as the number of incompatibility-controlling loci that differ between them. Genetic distance increases through the separate accumulation of mutations in different populations, but decreases after a successful migration event followed by genetic mixing between migrants and residents. We calculated the time to allopatric speciation, which occurs when the genetic distance exceeds a specified threshold. If the number of invasive individuals relative to the resident population is not very large, diffusion approximation provides an accurate prediction. There is an intermediate optimal rate of migration that maximizes the rate of species creation by recurrent invasion and diversification. We also examined cases that involved more than two populations.
Stochastic first passage time accelerated with CUDA
Pierro, Vincenzo; Troiano, Luigi; Mejuto, Elena; Filatrella, Giovanni
2018-05-01
The numerical integration of stochastic trajectories to estimate the time to pass a threshold is an interesting physical quantity, for instance in Josephson junctions and atomic force microscopy, where the full trajectory is not accessible. We propose an algorithm suitable for efficient implementation on graphical processing unit in CUDA environment. The proposed approach for well balanced loads achieves almost perfect scaling with the number of available threads and processors, and allows an acceleration of about 400× with a GPU GTX980 respect to standard multicore CPU. This method allows with off the shell GPU to challenge problems that are otherwise prohibitive, as thermal activation in slowly tilted potentials. In particular, we demonstrate that it is possible to simulate the switching currents distributions of Josephson junctions in the timescale of actual experiments.
First passage time problems in time-dependent fields
International Nuclear Information System (INIS)
Fletcher, J.E.; Havlin, S.; Weiss, G.H.
1988-01-01
This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency omega* for which the mean residence time on the line segment in a minimum. It is shown that for a random walk on a line segment of length L the mean residence time goes like L 2 for large L when omega omega*, but when omega = omega* the dependence is proportional to L. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation
First-Passage-Time Distribution for Variable-Diffusion Processes
Barney, Liberty; Gunaratne, Gemunu H.
2017-05-01
First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically—often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time—and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221-233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra- and inter-day behavior similar to those of empirical first-passage-time distributions.
Mapping absorption processes onto a Markov chain, conserving the mean first passage time
International Nuclear Information System (INIS)
Biswas, Katja
2013-01-01
The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k′; t, t + dt) between a set of states {k} represented by the regions {ζ k } in phase or discrete state space. Depending on the dynamics Γ i (t) of the original process and the choice of ζ k , the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates W-bar (k→k ' ) can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities p-bar (k ' |k) is derived based on either time-discrete measurements {t i } with variable time stepping Δ (i+1)i = t i+1 − t i or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory. (paper)
First-passage time: a conception leading to superstatistics
Directory of Open Access Journals (Sweden)
V.V.Ryazanov
2006-01-01
Full Text Available To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter -- the lifetime (the first passage time of a system. The statistical distributions that can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written. Superstatistics, introduced in [Beck C., Cohen E.G.D., Physica A, 2003, 322A, 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from statistical distribution with lifetime (random time to system degeneracy as thermodynamical parameter (and also generalization of superstatistics.
Reaction paths based on mean first-passage times
International Nuclear Information System (INIS)
Park, Sanghyun; Sener, Melih K.; Lu Deyu; Schulten, Klaus
2003-01-01
Finding representative reaction pathways is important for understanding the mechanism of molecular processes. We propose a new approach for constructing reaction paths based on mean first-passage times. This approach incorporates information about all possible reaction events as well as the effect of temperature. As an application of this method, we study representative pathways of excitation migration in a photosynthetic light-harvesting complex, photosystem I. The paths thus computed provide a complete, yet distilled, representation of the kinetic flow of excitation toward the reaction center, thereby succinctly characterizing the function of the system
First passage time in a two-layer system
International Nuclear Information System (INIS)
Lee, J.; Koplik, J.
1995-01-01
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function formalism and a variety of analytic and numerical techniques, we calculate the asymptotic behavior of the first passage time probability distribution. We show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities. The decay constant is given in terms of the largest eigenvalue of an operator related to a half-space Green's function. For the anti-symmetric case of opposite velocities in the layers, we show that the decay constant for system length L crosses over from L -2 behavior in the diffusive limit to L -1 behavior in the convective regime, where the crossover length L* is given in terms of the velocities. We also have formulated a general self-consistency relation, from which we have developed a recursive approach which is useful for studying the short-time behavior
International Nuclear Information System (INIS)
Goan, Hsi-Sheng; Jian, Chung-Chin; Chen, Po-Wen
2010-01-01
We evaluate the non-Markovian finite-temperature two-time correlation functions (CF's) of system operators of a pure-dephasing spin-boson model in two different ways, one by the direct exact operator technique and the other by the recently derived evolution equations, valid to second order in the system-environment interaction Hamiltonian. This pure-dephasing spin-boson model that is exactly solvable has been extensively studied as a simple decoherence model. However, its exact non-Markovian finite-temperature two-time system operator CF's, to our knowledge, have not been presented in the literature. This may be mainly due to the fact, illustrated in this article, that in contrast to the Markovian case, the time evolution of the reduced density matrix of the system (or the reduced quantum master equation) alone is not sufficient to calculate the two-time system operator CF's of non-Markovian open systems. The two-time CF's obtained using the recently derived evolution equations in the weak system-environment coupling case for this non-Markovian pure-dephasing model happen to be the same as those obtained from the exact evaluation. However, these results significantly differ from the non-Markovian two-time CF's obtained by wrongly directly applying the quantum regression theorem (QRT), a useful procedure to calculate the two-time CF's for weak-coupling Markovian open systems. This demonstrates clearly that the recently derived evolution equations generalize correctly the QRT to non-Markovian finite-temperature cases. It is believed that these evolution equations will have applications in many different branches of physics.
International Nuclear Information System (INIS)
Fulinski, A.
1994-01-01
The properties of non-Markovian noises with exponentially correlated memory are discussed. Considered are dichotomic noise, white shot noise, Gaussian white noise, and Gaussian colored noise. The stationary correlation functions of the non-Markovian versions of these noises are given by linear combinations of two or three exponential functions (colored noises) or of the δ function and exponential function (white noises). The non-Markovian white noises are well defined only when the kernel of the non-Markovian master equation contains a nonzero admixture of a Markovian term. Approximate equations governing the probability densities for processes driven by such non-Markovian noises are derived, including non-Markovian versions of the Fokker-Planck equation and the telegrapher's equation. As an example, it is shown how the non-Markovian nature changes the behavior of the driven linear process
First passage times for combinations of random loads
Jacobs, Patricia A.
1985-01-01
Structures are subject to changing loads from various sources. In many instances these loads fluctuate in time apparently random fashion. Models are considered for which the stress put on the structure by various loads simultaneously can be described by a regenerative process. The distribution of the first time until the stress on the structure exceeds a given level x is studied. Asymptotic properties of the distribution are given for a large stress level x and for the tail of the distributio...
Predictions of first passage times in sparse discrete fracture networks using graph-based reductions
Hyman, J.; Hagberg, A.; Srinivasan, G.; Mohd-Yusof, J.; Viswanathan, H. S.
2017-12-01
We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.
Stationary Probability and First-Passage Time of Biased Random Walk
International Nuclear Information System (INIS)
Li Jing-Wen; Tang Shen-Li; Xu Xin-Ping
2016-01-01
In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0 ⩽ p, q ⩽ 1, p + q = 1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F ∼ (N − 1) γ , where the exponent γ = 2 for N < |p − q| −1 and γ = 1 for N > |p − q| −1 . Our study sheds useful insights into the biased random-walk process. (paper)
Recursive approach for non-Markovian time-convolutionless master equations
Gasbarri, G.; Ferialdi, L.
2018-02-01
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.
First-passage time in a bistable potential with colored noise
International Nuclear Information System (INIS)
Ramirez-Piscina, L.; Maria Sancho, J.; Javier de la Rubia, F.; Lindenberg, K.; Tsironis, G.P.
1989-01-01
A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework
Statistics of the first passage time of Brownian motion conditioned by maximum value or area
International Nuclear Information System (INIS)
Kearney, Michael J; Majumdar, Satya N
2014-01-01
We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated. (paper)
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with
First passage times for multiple particles with reversible target-binding kinetics
Grebenkov, Denis S.
2017-10-01
We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles. We compute analytically the mean first passage time (MFPT) for two independent particles by mapping the original problem to higher-dimensional surface-mediated diffusion and solving the coupled partial differential equations. The respective effects of the adsorption and desorption rates on the MFPT are revealed and discussed.
First passage time for a diffusive process under a geometric constraint
International Nuclear Information System (INIS)
Tateishi, A A; Michels, F S; Dos Santos, M A F; Lenzi, E K; Ribeiro, H V
2013-01-01
We investigate the solutions, survival probability, and first passage time for a two-dimensional diffusive process subjected to the geometric constraints of a backbone structure. We consider this process governed by a fractional Fokker–Planck equation by taking into account the boundary conditions ρ(0,y;t) = ρ(∞,y;t) = 0, ρ(x, ± ∞;t) = 0, and an arbitrary initial condition. Our results show an anomalous spreading and, consequently, a nonusual behavior for the survival probability and for the first passage time distribution that may be characterized by different regimes. In addition, depending on the choice of the parameters present in the fractional Fokker–Planck equation, the survival probability indicates that part of the system may be trapped in the branches of the backbone structure. (paper)
Scaling of the first-passage time of biased diffusion on hierarchical comb structures
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Lin Zhifang; Tao Ruibao.
1989-12-01
Biased diffusion on hierarchical comb structures is studied within an exact renormalization group scheme. The scaling exponents of the moments of the first-passage time for random walks are obtained. It is found that the scaling properties of the diffusion depend only on the direction of bias. In this particular case, the presence of bias may give rise to a new multifractality. (author). 7 refs, 2 figs
Mean first passage time for random walk on dual structure of dendrimer
Li, Ling; Guan, Jihong; Zhou, Shuigeng
2014-12-01
The random walk approach has recently been widely employed to study the relations between the underlying structure and dynamic of complex systems. The mean first-passage time (MFPT) for random walks is a key index to evaluate the transport efficiency in a given system. In this paper we study analytically the MFPT in a dual structure of dendrimer network, Husimi cactus, which has different application background and different structure (contains loops) from dendrimer. By making use of the iterative construction, we explicitly determine both the partial mean first-passage time (PMFT, the average of MFPTs to a given target) and the global mean first-passage time (GMFT, the average of MFPTs over all couples of nodes) on Husimi cactus. The obtained closed-form results show that PMFPT and EMFPT follow different scaling with the network order, suggesting that the target location has essential influence on the transport efficiency. Finally, the impact that loop structure could bring is analyzed and discussed.
First-passage time asymptotics over moving boundaries for random walk bridges
Sloothaak, F.; Zwart, B.; Wachtel, V.
2017-01-01
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the re...
The first-passage time distribution for the diffusion model with variable drift
DEFF Research Database (Denmark)
Blurton, Steven Paul; Kesselmeier, Miriam; Gondan, Matthias
2017-01-01
across trials. This extra flexibility allows accounting for slow errors that often occur in response time experiments. So far, the predicted response time distributions were obtained by numerical evaluation as analytical solutions were not available. Here, we present an analytical expression...... for the cumulative first-passage time distribution in the diffusion model with normally distributed trial-to-trial variability in the drift. The solution is obtained with predefined precision, and its evaluation turns out to be extremely fast.......The Ratcliff diffusion model is now arguably the most widely applied model for response time data. Its major advantage is its description of both response times and the probabilities for correct as well as incorrect responses. The model assumes a Wiener process with drift between two constant...
Kim, Young Shin
2018-01-01
In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied to the perpetual American option pricing and the barrier option pricing. Numerical illustrations are provided for the calibrated parameters using the market call and put prices.
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
Flegg, Mark B.
2013-01-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration
Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise
Institute of Scientific and Technical Information of China (English)
Zhang Xiao-Yan; Xu Wei
2007-01-01
In this paper, the effect of every parameter (including p, q,r, λ,τ) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small λ (e.g. λ＜ 0.5) but there is a peak on the curve of the MFPT when λ is big (e.g.λ＞ 0.5), and (3) with different values of r (e.g. r = 0.1, 0.5, 1.5), the effort of τ on the MFPT is diverse.
Nonlocal non-Markovian effects in dephasing environments
International Nuclear Information System (INIS)
Xie Dong; Wang An-Min
2014-01-01
We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian–non-Markovian (both of the two local dynamics are non-Markovian) or Markovian–non-Markovian, but not under the condition of Markovian–Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian–Markovian. It shows that the function of correlations between two environments has an upper bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration, we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects. (general)
The distribution of first-passage times and durations in FOREX and future markets
Sazuka, Naoya; Inoue, Jun-ichi; Scalas, Enrico
2009-07-01
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting
Persistence of non-Markovian Gaussian stationary processes in discrete time
Nyberg, Markus; Lizana, Ludvig
2018-04-01
The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n . Few results are known for the persistence P0(n ) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n ) ˜θn . Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n ) analytically in z -transform space in terms of the autocorrelation function A (n ) . If A (n )→0 as n →∞ , we extract θ numerically, while if A (n )=0 , for finite n >N , we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A (n )=0 for n >1 , the double exponential-correlated "second order autoregressive process", where A (n ) =c1λ1n+c2λ2n , and power-law-correlated variables, where A (n ) ˜n-μ . Apart from the power-law case when μ <5 , we find excellent agreement with simulations.
Non-Markovian nuclear dynamics
International Nuclear Information System (INIS)
Kolomietz, V.M.
2011-01-01
A prove of equations of motion for the nuclear shape variables which establish a direct connection of the memory effects with the dynamic distortion of the Fermi surface is suggested. The equations of motion for the nuclear Fermi liquid drop are derived from the collisional kinetic equation. In general, the corresponding equations are non-Markovian. The memory effects appear due to the Fermi surface distortions and depend on the relaxation time. The main purpose of the present work is to apply the non-Markovian dynamics to the description of the nuclear giant multipole resonances (GMR) and the large amplitude motion. We take also into consideration the random forces and concentrate on the formation of both the conservative and the friction forces to make more clear the memory effect on the nuclear dynamics. In this respect, the given approach represents an extension of the traditional liquid drop model (LDM) to the case of the nuclear Fermi liquid drop. In practical application, we pay close attention to the description of the descent of the nucleus from the fission barrier to the scission point.
First passage times in homogeneous nucleation: Dependence on the total number of particles
International Nuclear Information System (INIS)
Yvinec, Romain; Bernard, Samuel; Pujo-Menjouet, Laurent; Hingant, Erwan
2016-01-01
Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory
Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications
Directory of Open Access Journals (Sweden)
Zhongtuan Zheng
2017-01-01
Full Text Available This paper investigates, both theoretically and numerically, preferential random walks (PRW on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW. Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.
Effect of crowding and confinement on first-passage times: A model study
Antoine, C.; Talbot, J.
2016-06-01
We study the "color dynamics" of a hard-disk fluid confined in an annulus, as well as the corresponding hard-sphere system in three dimensions, using event-driven simulation in order to explore the effect of confinement and self-crowding on the search for targets. We compute the mean first-passage times (MFPTs) of red particles transiting from the outer to the inner boundary as well as those of blue particles passing from the inner to the outer boundary for different packing fractions and geometries. In the steady state the reaction rate, defined as the rate of collision of red particles with the inner boundary, is inversely proportional to the sum of the MFPTs. The reaction rate is wall mediated (ballistic) at low densities and diffusion controlled at higher densities and displays a maximum at intermediate densities. At moderate to high densities, the presence of layering has a strong influence on the search process. The numerical results for the reaction rate and MFPTs are compared with a ballistic model at low densities and a Smoluchowski approach with uniform diffusivities at higher densities. We discuss the reasons for the limited validity of the theoretical approaches. The maximum in the reaction rate is qualitatively well rendered by a Bosanquet-like approach that interpolates between the two regimes. Finally, we compute the position-dependent diffusivity from the MFPTs and observe that it is out of phase with the radial density.
International Nuclear Information System (INIS)
Torquato, S.; Kim, I.C.; Cule, D.
1999-01-01
We generalize the Brownian motion simulation method of Kim and Torquato [J. Appl. Phys. 68, 3892 (1990)] to compute the effective conductivity, dielectric constant and diffusion coefficient of digitized composite media. This is accomplished by first generalizing the first-passage-time equations to treat first-passage regions of arbitrary shape. We then develop the appropriate first-passage-time equations for digitized media: first-passage squares in two dimensions and first-passage cubes in three dimensions. A severe test case to prove the accuracy of the method is the two-phase periodic checkerboard in which conduction, for sufficiently large phase contrasts, is dominated by corners that join two conducting-phase pixels. Conventional numerical techniques (such as finite differences or elements) do not accurately capture the local fields here for reasonable grid resolution and hence lead to inaccurate estimates of the effective conductivity. By contrast, we show that our algorithm yields accurate estimates of the effective conductivity of the periodic checkerboard for widely different phase conductivities. Finally, we illustrate our method by computing the effective conductivity of the random checkerboard for a wide range of volume fractions and several phase contrast ratios. These results always lie within rigorous four-point bounds on the effective conductivity. copyright 1999 American Institute of Physics
International Nuclear Information System (INIS)
Wang, J.; Cao, L.; Wu, D.J.
2003-01-01
We present an analytic investigation of the mean first passage time in two opposite directions (from the left well to the right well and from right to left) by studying symmetrical bistable systems driven by correlated Gaussian white noises, and prove that the mean first passage time in two opposite directions is not symmetrical any more when noises are correlated. As examples, the mean first passage time in the quartic bistable model and the sawtooth bistable model are calculated, respectively. From the analytic results of the mean first passage time, we testify further the relation T(from x - to x + ,λ)≠T(from x + to x - ,λ) in the same area of the parameter plan. Moreover, it is found that the dependences of T + (i.e., T(from x - to x + ,λ)) and T - (i.e., T(from x + to x - ,λ)) upon the multiplicative noise intensity Q and the additive noise intensity D exhibit entirely different properties. For same areas of the parameter plan: in the quartic bistable system, when the T + vs. Q curve exhibits a maximum, while the T - vs. Q curve is monotonous; when the T + vs. D curve is monotonous, while the T - vs. D curve experiences a phase transition from decreasing monotonously to possessing one minimum. Increasing Q, when the T + vs. D curve experiences a phase transition from decreasing monotonously to possessing one maximum, while the T - vs. D curve only increases monotonously. Similar behaviours also exist in the sawtooth bistable model
Non-Markovian decoherent quantum walks
International Nuclear Information System (INIS)
Xue Peng; Zhang Yong-Sheng
2013-01-01
Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker's behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
Quantum non-Markovianity: characterization, quantification and detection
International Nuclear Information System (INIS)
Rivas, Ángel; Huelga, Susana F; Plenio, Martin B
2014-01-01
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions. (review article)
Quantum non-Markovianity: characterization, quantification and detection
Rivas, Ángel; Huelga, Susana F.; Plenio, Martin B.
2014-09-01
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.
Jump probabilities in the non-Markovian quantum jump method
International Nuclear Information System (INIS)
Haerkoenen, Kari
2010-01-01
The dynamics of a non-Markovian open quantum system described by a general time-local master equation is studied. The propagation of the density operator is constructed in terms of two processes: (i) deterministic evolution and (ii) evolution of a probability density functional in the projective Hilbert space. The analysis provides a derivation for the jump probabilities used in the recently developed non-Markovian quantum jump (NMQJ) method (Piilo et al 2008 Phys. Rev. Lett. 100 180402).
Directory of Open Access Journals (Sweden)
David M Williams
Full Text Available Advances in animal tracking technologies have reduced but not eliminated positional error. While aware of such inherent error, scientists often proceed with analyses that assume exact locations. The results of such analyses then represent one realization in a distribution of possible outcomes. Evaluating results within the context of that distribution can strengthen or weaken our confidence in conclusions drawn from the analysis in question. We evaluated the habitat-specific positional error of stationary GPS collars placed under a range of vegetation conditions that produced a gradient of canopy cover. We explored how variation of positional error in different vegetation cover types affects a researcher's ability to discern scales of movement in analyses of first-passage time for white-tailed deer (Odocoileus virginianus. We placed 11 GPS collars in 4 different vegetative canopy cover types classified as the proportion of cover above the collar (0-25%, 26-50%, 51-75%, and 76-100%. We simulated the effect of positional error on individual movement paths using cover-specific error distributions at each location. The different cover classes did not introduce any directional bias in positional observations (1 m≤mean≤6.51 m, 0.24≤p≤0.47, but the standard deviation of positional error of fixes increased significantly with increasing canopy cover class for the 0-25%, 26-50%, 51-75% classes (SD = 2.18 m, 3.07 m, and 4.61 m, respectively and then leveled off in the 76-100% cover class (SD = 4.43 m. We then added cover-specific positional errors to individual deer movement paths and conducted first-passage time analyses on the noisy and original paths. First-passage time analyses were robust to habitat-specific error in a forest-agriculture landscape. For deer in a fragmented forest-agriculture environment, and species that move across similar geographic extents, we suggest that first-passage time analysis is robust with regard to
DEFF Research Database (Denmark)
Ditlevsen, Susanne Dalager; Ditlevsen, Ove Dalager
2008-01-01
a subjective graphical test of the applicability of the OU process or the Feller process when applied to a reasonably large sample of observed first-passage data. These non-stationary processes have several applications in biomedical research, for example as idealized models of the neuron membrane potential...... random time break through to the material surface and become observable. However, the OU process has as a model of physical phenomena the defect of not being bounded to the negative side. This defect is not present for the Feller process, which therefore may provide a useful modeling alternative...
International Nuclear Information System (INIS)
Kumar, N.
1984-07-01
Quantum first passage problem (QUIPP) is formulated and solved in terms of a constrained Feynman path integral. The related paradox of blocking of unitary evolution by continuous observation on the system implicit in QUIPP is briefly discussed. (author)
The mean first passage time in an energy-diffusion controlled regime with power-law distributions
International Nuclear Information System (INIS)
Zhou, Yanjun; Du, Jiulin
2013-01-01
Based on the mean first passage time (MFPT) theory, we derive an expression of the MFPT in an energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. the thermal energy k B T is not small with respect to the potential barrier E b ) and compare it with Kramers’ infinite barrier result both in a power-law distribution and in a Maxwell–Boltzmann distribution. It is shown that the MFPT with a power-law distribution extends Kramers’ low-damping result to a relatively low barrier. We pay attention to the energy-diffusion controlled regime, which is of great interest in the context of Josephson junctions, and study how the power-law parameter κ affects the current distribution function in experiments with Josephson junctions. (paper)
Richter, Martin; Fingerhut, Benjamin P.
2017-06-01
The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.
Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul
2017-11-01
A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.
Maruddani, Di Asih I.; Rosadi, Dedi; Gunardic, Abdurakhman
2015-02-01
The value of a corporate bond is conventionally expressed in terms of zero coupon bond. In practice, the most common form of debt instrument is coupon bond and allows early default before maturity as safety covenant for the bondholder. This paper study valuation for one period coupon bond, a coupon bond that only give one time coupon at the bond period. It assumes that the model give bondholder the right to reorganize a firm if its value falls below a given barrier. Revised first passage time approach is applied for default time rule. As a result, formulas of equity, liability, and probability of default is derived for this specified model. Straightforward integration under risk neutral pricing is used for deriving those formulas. For the application, bond of Bank Rakyat Indonesia (BRI) as one of the largest bank in Indonesia is analyzed. R computing show that value of the equity is IDR 453.724.549.000.000, the liability is IDR 2.657.394.000.000, and the probability if default is 5.645305E-47 %.
An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
International Nuclear Information System (INIS)
Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.
2014-01-01
We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands
An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
Energy Technology Data Exchange (ETDEWEB)
Bezzola, Andri, E-mail: andri.bezzola@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Bales, Benjamin B., E-mail: bbbales2@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Alkire, Richard C., E-mail: r-alkire@uiuc.edu [Department of Chemical Engineering, University of Illinois, Urbana, IL 61801 (United States); Petzold, Linda R., E-mail: petzold@engineering.ucsb.edu [Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA 93106 (United States)
2014-01-01
We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.
Bulk-mediated surface diffusion: non-Markovian desorption dynamics
International Nuclear Information System (INIS)
Revelli, Jorge A; Budde, Carlos E; Prato, Domingo; Wio, Horacio S
2005-01-01
Here we analyse the dynamics of adsorbed molecules within the bulk-mediated surface diffusion framework, when the particle's desorption mechanism is characterized by a non-Markovian process, while the particle's adsorption as well as its motion in the bulk is governed by Markovian dynamics. We study the diffusion of particles in both semi-infinite and finite cubic lattices, analysing the conditional probability to find the system on the reference absorptive plane as well as the surface dispersion as functions of time. The results are compared with known Markovian cases showing the differences that can be exploited to distinguish between Markovian and non-Markovian desorption mechanisms in experimental situations
Counting statistics of non-markovian quantum stochastic processes
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, T.; Braggio, A.
2008-01-01
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants...
Solutions for a non-Markovian diffusion equation
International Nuclear Information System (INIS)
Lenzi, E.K.; Evangelista, L.R.; Lenzi, M.K.; Ribeiro, H.V.; Oliveira, E.C. de
2010-01-01
Solutions for a non-Markovian diffusion equation are investigated. For this equation, we consider a spatial and time dependent diffusion coefficient and the presence of an absorbent term. The solutions exhibit an anomalous behavior which may be related to the solutions of fractional diffusion equations and anomalous diffusion.
International Nuclear Information System (INIS)
Maggiore, Michele; Riotto, Antonio
2010-01-01
A classic method for computing the mass function of dark matter halos is provided by excursion set theory, where density perturbations evolve stochastically with the smoothing scale, and the problem of computing the probability of halo formation is mapped into the so-called first-passage time problem in the presence of a barrier. While the full dynamical complexity of halo formation can only be revealed through N-body simulations, excursion set theory provides a simple analytic framework for understanding various aspects of this complex process. In this series of papers we propose improvements of both technical and conceptual aspects of excursion set theory, and we explore up to which point the method can reproduce quantitatively the data from N-body simulations. In Paper I of the series, we show how to derive excursion set theory from a path integral formulation. This allows us both to derive rigorously the absorbing barrier boundary condition, that in the usual formulation is just postulated, and to deal analytically with the non-Markovian nature of the random walk. Such a non-Markovian dynamics inevitably enters when either the density is smoothed with filters such as the top-hat filter in coordinate space (which is the only filter associated with a well-defined halo mass) or when one considers non-Gaussian fluctuations. In these cases, beside 'Markovian' terms, we find 'memory' terms that reflect the non-Markovianity of the evolution with the smoothing scale. We develop a general formalism for evaluating perturbatively these non-Markovian corrections, and in this paper we perform explicitly the computation of the halo mass function for Gaussian fluctuations, to first order in the non-Markovian corrections due to the use of a top-hat filter in coordinate space. In Paper II of this series we propose to extend excursion set theory by treating the critical threshold for collapse as a stochastic variable, which better captures some of the dynamical complexity of the
International Nuclear Information System (INIS)
Li Dongxi; Xu Wei; Guo Yongfeng; Li Gaojie
2008-01-01
The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter (measures deviation from Gaussian character) r, the delay time τ, the noise correlation time τ 0 , the intensities D and α of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ 0 , or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system
Non-Markovian features of deeply inelastic collisions
International Nuclear Information System (INIS)
Pal, D.; Chattopadhyay, S.; Kar, K.
1988-01-01
To study the effect of memory in the diffusion processes (of charge, mass etc) observed in deeply inelastic heavy-ion reactions, we derive non-Markovian transport equations for the exponential and Gaussian memory kernels. The centroid and the variance of the distribution are expressed in terms of the memory time, drift and diffusion coefficients. The predictions based on this theory show better agreement with the experimental data than the Markovian results. (author)
Connecting two jumplike unravelings for non-Markovian open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Luoma, Kimmo; Suominen, Kalle-Antti; Piilo, Jyrki [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto (Finland)
2011-09-15
The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.
Connecting two jumplike unravelings for non-Markovian open quantum systems
International Nuclear Information System (INIS)
Luoma, Kimmo; Suominen, Kalle-Antti; Piilo, Jyrki
2011-01-01
The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.
A framework for the direct evaluation of large deviations in non-Markovian processes
International Nuclear Information System (INIS)
Cavallaro, Massimo; Harris, Rosemary J
2016-01-01
We propose a general framework to simulate stochastic trajectories with arbitrarily long memory dependence and efficiently evaluate large deviation functions associated to time-extensive observables. This extends the ‘cloning’ procedure of Giardiná et al (2006 Phys. Rev. Lett. 96 120603) to non-Markovian systems. We demonstrate the validity of this method by testing non-Markovian variants of an ion-channel model and the totally asymmetric exclusion process, recovering results obtainable by other means. (letter)
Non-Markovian dynamics of charge carriers in quantum dots
International Nuclear Information System (INIS)
Vaz, E; Kyriakidis, J
2008-01-01
We have investigated the dynamics of bound particles in multilevel current-carrying quantum dots. We look specifically in the regime of resonant tunnelling transport, where several channels are available for transport. Through a non-Markovian formalism under the Born approximation, we investigate the real-time evolution of the confined particles including transport-induced decoherence and relaxation. In the case of a coherent superposition between states with different particle number, we find that a Fock-space coherence may be preserved even in the presence of tunneling into and out of the dot. Real-time results are presented for various asymmetries of tunneling rates into different orbitals
Non-markovian boltzmann equation
International Nuclear Information System (INIS)
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-01-01
A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc
Wu, Jianlan; Silbey, Robert J; Cao, Jianshu
2013-05-17
An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer in light-harvesting systems. A quantum state orthogonal to the trap will exhibit noise-assisted transfer, clarifying the significance of initial preparation. For such an initial state, the efficiency is enhanced in the weak damping limit (⟨t⟩ ∼ 1/Γ), and suppressed in the strong damping limit (⟨t⟩ ∼ Γ), analogous to Kramers turnover in classical rate theory. An interpolating expression ⟨t⟩ = A/Γ + B + CΓ quantitatively describes the trapping time over the entire range of the dissipation strength, and predicts the optimal efficiency at Γ(opt) ∼ J for homogenous systems. In the presence of static disorder, the scaling law of transfer time with respect to dephasing rate changes from linear to square root, suggesting a weaker dependence on the environment. The prediction of the scaling theory is verified in a symmetric dendrimer system by numerically exact quantum calculations. Though formulated in the context of excitation energy transfer, the analysis and conclusions apply in general to open quantum processes, including electron transfer, fluorescence emission, and heat conduction.
Optimal management of non-Markovian biological populations
Williams, B.K.
2007-01-01
Wildlife populations typically are described by Markovian models, with population dynamics influenced at each point in time by current but not previous population levels. Considerable work has been done on identifying optimal management strategies under the Markovian assumption. In this paper we generalize this work to non-Markovian systems, for which population responses to management are influenced by lagged as well as current status and/or controls. We use the maximum principle of optimal control theory to derive conditions for the optimal management such a system, and illustrate the effects of lags on the structure of optimal habitat strategies for a predator-prey system.
Quantum Non-Markovian Langevin Equations and Transport Coefficients
International Nuclear Information System (INIS)
Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.
2005-01-01
Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed
Colloquium: Non-Markovian dynamics in open quantum systems
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2003-01-01
Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit
Non-Markovianity hinders Quantum Darwinism
Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina
2016-01-01
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.
Rate processes with non-Markovian dynamical disorder
International Nuclear Information System (INIS)
Goychuk, Igor
2005-01-01
Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasistatic disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
Chen, Yusui; You, J. Q.; Yu, Ting
2014-11-01
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
Markovianity and non-Markovianity in quantum and classical systems
International Nuclear Information System (INIS)
Vacchini, Bassano; Smirne, Andrea; Laine, Elsi-Mari; Piilo, Jyrki; Breuer, Heinz-Peter
2011-01-01
We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition of non-Markovianity of a classical stochastic process represents a condition on the Kolmogorov hierarchy of the n-point joint probability distributions. Since this definition cannot be transferred to the quantum regime, quantum non-Markovianity has recently been defined and quantified in terms of the underlying quantum dynamical map, using either its divisibility properties or the behavior of the trace distance between pairs of initial states. Here, we investigate and compare these definitions and their relations to the classical notion of non-Markovianity by employing a large class of non-Markovian processes, known as semi-Markov processes, which admit a natural extension to the quantum case. A number of specific physical examples are constructed that allow us to study the basic features of the classical and the quantum definitions and to evaluate explicitly the measures of quantum non-Markovianity. Our results clearly demonstrate several fundamental differences between the classical and the quantum notion of non-Markovianity, as well as between the various quantum measures of non-Markovianity. In particular, we show that the divisibility property in the classical case does not coincide with Markovianity and that the non-Markovianity measure based on divisibility assigns equal infinite values to different dynamics, which can be distinguished by exploiting the trace distance measure. A simple exact expression for the latter is also obtained in a special case.
Basic mechanisms in the laser control of non-Markovian dynamics
Puthumpally-Joseph, R.; Mangaud, E.; Chevet, V.; Desouter-Lecomte, M.; Sugny, D.; Atabek, O.
2018-03-01
Referring to a Fano-type model qualitative analogy we develop a comprehensive basic mechanism for the laser control of the non-Markovian bath response and fully implement it in a realistic control scheme, in strongly coupled open quantum systems. Converged hierarchical equations of motion are worked out to numerically solve the master equation of a spin-boson Hamiltonian to reach the reduced electronic density matrix of a heterojunction in the presence of strong terahertz laser pulses. Robust and efficient control is achieved increasing by a factor of 2 the non-Markovianity measured by the time evolution of the volume of accessible states. The consequences of such fields on the central system populations and coherence are examined, putting the emphasis on the relation between the increase of non-Markovianity and the slowing down of decoherence processes.
Quantum operation for a one-qubit system under a non-Markovian environment
International Nuclear Information System (INIS)
Xue Shibei; Zhang Jing; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong
2011-01-01
This paper introduces a simple alternating-current (AC) control strategy to perform quantum state manipulations under non-Markovian noise. A genetic algorithm is adopted to optimize the parameters of the AC control, which can be further used to fulfil one-qubit quantum operations at a given final time. Theoretical analysis and simulations show that our method works almost equally well for 1/f noise, ohmic, sub-ohmic and super-ohmic noise, which demonstrates the robustness of our strategy for noise with various spectra. In comparison with the Markovian cases, our method is more suitable to be used to suppress non-Markovian noise.
Delineating incoherent non-Markovian dynamics using quantum coherence
Energy Technology Data Exchange (ETDEWEB)
Chanda, Titas, E-mail: titaschanda@hri.res.in; Bhattacharya, Samyadeb, E-mail: samyadebbhattacharya@hri.res.in
2016-03-15
We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system–environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our proposed measure captures the back-flow of information from the environment to the system and compatible with well known distinguishability criteria of non-Markovianity.
Exploiting Non-Markovianity for Quantum Control.
Reich, Daniel M; Katz, Nadav; Koch, Christiane P
2015-07-22
Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the back-flow of amplitude and phase can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. Our paradigmatic example considers a weakly anharmonic ladder with resonant amplitude control only, restricting realizable operations to SO(N). The coupling to the environment, when harnessed with optimization techniques, allows for full SU(N) controllability.
System–environment correlations and non-Markovian dynamics
International Nuclear Information System (INIS)
Pernice, A; Helm, J; Strunz, W T
2012-01-01
We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system–environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of ‘non-Markovianity’ will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system–environment correlations. Depending on the initial purity of the qubit state, these system–environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system–environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and ‘non-Markovianity’. (paper)
Fault-tolerant quantum computation for local non-Markovian noise
International Nuclear Information System (INIS)
Terhal, Barbara M.; Burkard, Guido
2005-01-01
We derive a threshold result for fault-tolerant quantum computation for local non-Markovian noise models. The role of error amplitude in our analysis is played by the product of the elementary gate time t 0 and the spectral width of the interaction Hamiltonian between system and bath. We discuss extensions of our model and the applicability of our analysis
Enhancement of Quantum Correlations in Qubit-Qutrit Systems under the non-Markovian Environment
Institute of Scientific and Technical Information of China (English)
Abdul Basit; Hamad Ali; Fazal Badshah; Guo-Qin Ge
2017-01-01
We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise.Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs.A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters,the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations.In addition,it is observed that the non-Markovian strength (γ/F) has a positive impact on the correlations time.For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property.Moreover,its decay can be significantly delayed.
Optical signatures of non-Markovian behavior in open quantum systems
DEFF Research Database (Denmark)
McCutcheon, Dara
2016-01-01
for the correlation functions, making only a second-order expansion in the system-environment coupling strength and invoking the Born approximation at a fixed initial time. The results are used to investigate a driven semiconductor quantum dot coupled to an acoustic phonon bath, where we find the non-Markovian nature...
Non-Markovian dynamics of quantum systems: formalism, transport coefficients
International Nuclear Information System (INIS)
Kanokov, Z.; Palchikov, Yu.V.; Antonenko, N.V.; Adamian, G.G.; Kanokov, Z.; Adamian, G.G.; Scheid, W.
2004-01-01
Full text: The generalized Linbland equations with non-stationary transport coefficients are derived from the Langevin equations for the case of nonlinear non-Markovian noise [1]. The equations of motion for the collective coordinates are consistent with the generalized quantum fluctuation dissipation relations. The microscopic justification of the Linbland axiomatic approach is performed. Explicit expressions for the time-dependent transport coefficients are presented for the case of FC- and RWA-oscillators and a general linear coupling in coordinate and in momentum between the collective subsystem and heat bath. The explicit equations for the correlation functions show that the Onsanger's regression hypothesis does not hold exactly for the non-Markovian equations of motion. However, under some conditions the regression of fluctuations goes to zero in the same manner as the average values. In the low and high temperature regimes we found that the dissipation leads to long-time tails in correlation functions in the RWA-oscillator. In the case of the FC-oscillator a non-exponential power-like decay of the correlation function in coordinate is only obtained only at the low temperature limit. The calculated results depend rather weakly on the memory time in many applications. The found transient times for diffusion coefficients D pp (t), D qp (t) and D qq (t) are quite short. The value of classical diffusion coefficients in momentum underestimates the asymptotic value of quantum one D pp (t), but the asymptotic values of classical σ qq c and quantum σ qq second moments are close due to the negativity of quantum mixed diffusion coefficient D qp (t)
Investigating non-Markovian dynamics of quantum open systems
Chen, Yusui
Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple
Mixing-induced quantum non-Markovianity and information flow
Breuer, Heinz-Peter; Amato, Giulio; Vacchini, Bassano
2018-04-01
Mixing dynamical maps describing open quantum systems can lead from Markovian to non-Markovian processes. Being surprising and counter-intuitive, this result has been used as argument against characterization of non-Markovianity in terms of information exchange. Here, we demonstrate that, quite the contrary, mixing can be understood in a natural way which is fully consistent with existing theories of memory effects. In particular, we show how mixing-induced non-Markovianity can be interpreted in terms of the distinguishability of quantum states, system-environment correlations and the information flow between system and environment.
Czech Academy of Sciences Publication Activity Database
Šolc, Milan
2002-01-01
Roč. 216, 07 (2002), s. 869-893 ISSN 0942-9352 R&D Projects: GA AV ČR IAA4032101 Institutional research plan: CEZ:AV0Z4032918 Keywords : stochastic kinetics * fluctuation * first-passage time Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.854, year: 2002
Non-Markovian spontaneous emission from a single quantum dot
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Ates, Serkan; Lund-Hansen, Toke
2011-01-01
We observe non-Markovian dynamics of a single quantum dot when tuned into resonance with a cavity mode. Excellent agreement between experiment and theory is observed providing the first quantitative description of such a system.......We observe non-Markovian dynamics of a single quantum dot when tuned into resonance with a cavity mode. Excellent agreement between experiment and theory is observed providing the first quantitative description of such a system....
Non-Markovianity in the collision model with environmental block
Jin, Jiasen; Yu, Chang-shui
2018-05-01
We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system–environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.
Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
International Nuclear Information System (INIS)
Shushin, A I
2005-01-01
Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc
Non-Markovian dynamics of a qubit due to single-photon scattering in a waveguide
Fang, Yao-Lung L.; Ciccarello, Francesco; Baranger, Harold U.
2018-04-01
We investigate the open dynamics of a qubit due to scattering of a single photon in an infinite or semi-infinite waveguide. Through an exact solution of the time-dependent multi-photon scattering problem, we find the qubit's dynamical map. Tools of open quantum systems theory allow us then to show the general features of this map, find the corresponding non-Linbladian master equation, and assess in a rigorous way its non-Markovian nature. The qubit dynamics has distinctive features that, in particular, do not occur in emission processes. Two fundamental sources of non-Markovianity are present: the finite width of the photon wavepacket and the time delay for propagation between the qubit and the end of the semi-infinite waveguide.
International Nuclear Information System (INIS)
Zhao Xinyu; Jing Jun; Corn, Brittany; Yu Ting
2011-01-01
Non-Markovian dynamics is studied for two interacting qubits strongly coupled to a dissipative bosonic environment. We derive a non-Markovian quantum-state-diffusion (QSD) equation for the coupled two-qubit system without any approximations, and in particular, without the Markov approximation. As an application and illustration of our derived time-local QSD equation, we investigate the temporal behavior of quantum coherence dynamics. In particular, we find a strongly non-Markovian regime where entanglement generation is significantly modulated by the environmental memory. Additionally, we study residual entanglement in the steady state by analyzing the steady-state solution of the QSD equation. Finally, we discuss an approximate QSD equation.
Exact solution for a non-Markovian dissipative quantum dynamics.
Ferialdi, Luca; Bassi, Angelo
2012-04-27
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
Sufficient conditions for positivity of non-Markovian master equations with Hermitian generators
International Nuclear Information System (INIS)
Wilkie, Joshua; Wong Yinmei
2009-01-01
We use basic physical motivations to develop sufficient conditions for positive semidefiniteness of the reduced density matrix for generalized non-Markovian integrodifferential Lindblad-Kossakowski master equations with Hermitian generators. We show that it is sufficient for the memory function to be the Fourier transform of a real positive symmetric frequency density function with certain properties. These requirements are physically motivated, and are more general and more easily checked than previously stated sufficient conditions. We also explore the decoherence dynamics numerically for some simple models using the Hadamard representation of the propagator. We show that the sufficient conditions are not necessary conditions. We also show that models exist in which the long time limit is in part determined by non-Markovian effects
Population dynamics of excited atoms in non-Markovian environments at zero and finite temperature
International Nuclear Information System (INIS)
Zou Hong-Mei; Fang Mao-Fa
2015-01-01
The population dynamics of a two-atom system, which is in two independent Lorentzian reservoirs or in two independent Ohmic reservoirs respectively, where the reservoirs are at zero temperature or finite temperature, is studied by using the time-convolutionless master-equation method. The influences of the characteristics and temperature of a non-Markovian environment on the population of the excited atoms are analyzed. We find that the population trapping of the excited atoms is related to the characteristics and the temperature of the non-Markovian environment. The results show that, at zero temperature, the two atoms can be effectively trapped in the excited state both in the Lorentzian reservoirs and in the Ohmic reservoirs. At finite temperature, the population of the excited atoms will quickly decay to a nonzero value. (paper)
First passage Brownian functional properties of snowmelt dynamics
Dubey, Ashutosh; Bandyopadhyay, Malay
2018-04-01
In this paper, we model snow-melt dynamics in terms of a Brownian motion (BM) with purely time dependent drift and difusion and examine its first passage properties by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We introduce several probability distribution functions (PDFs) associated with such time dependent BMs. For instance, for a BM with initial starting point x0, we derive analytical expressions for : (i) the PDF P(tf|x0) of the first passage time tf which specify the lifetime of such stochastic process, (ii) the PDF P(A|x0) of the area A till the first passage time and it provides us numerous valuable information about the total fresh water availability during melting, (iii) the PDF P(M) associated with the maximum size M of the BM process before the first passage time, and (iv) the joint PDF P(M; tm) of the maximum size M and its occurrence time tm before the first passage time. These P(M) and P(M; tm) are useful in determining the time of maximum fresh water availability and in calculating the total maximum amount of available fresh water. These PDFs are examined for the power law time dependent drift and diffusion which matches quite well with the available data of snowmelt dynamics.
Continuous quantum error correction for non-Markovian decoherence
International Nuclear Information System (INIS)
Oreshkov, Ognyan; Brun, Todd A.
2007-01-01
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics
International Nuclear Information System (INIS)
Zou, Hong-Mei; Fang, Mao-Fa; Yang, Bai-Yuan; Guo, You-Neng; He, Wei; Zhang, Shi-Yang
2014-01-01
The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments are studied using the time-convolutionless master-equation approach. The influence of the non-Markovian effect and detuning on the lower bound of the quantum entropic uncertainty relation and entanglement witness is discussed in detail. The results show that, only if the two non-Markovian reservoirs are identical, increasing detuning and non-Markovian effect can reduce the lower bound of the entropic uncertainty relation, lengthen the time region during which the entanglement can be witnessed, and effectively protect the entanglement region witnessed by the lower bound of the entropic uncertainty relation. The results can be applied in quantum measurement, quantum cryptography tasks and quantum information processing. (paper)
Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels
International Nuclear Information System (INIS)
An, J.-H.; Zhang, W.-M.
2007-01-01
We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influence on the entanglement dynamics due to the sensitive time dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case
Non-Markovian linear response theory for quantum open systems and its applications.
Shen, H Z; Li, D X; Yi, X X
2017-01-01
The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.
Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion
International Nuclear Information System (INIS)
Shu, Wenchong; Zhao, Xinyu; Jing, Jun; Yu, Ting; Wu, Lian-Ao
2013-01-01
In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the non-Markovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both coloured phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian QSD equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment is comprised of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses. (paper)
Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments
Zhang, Yanliang; Fang, Maofa; Kang, Guodong; Zhou, Qingping
2018-03-01
Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink's entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.
Foundations and measures of quantum non-Markovianity
International Nuclear Information System (INIS)
Breuer, Heinz-Peter
2012-01-01
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behaviour. Here, we review recent ideas developing a general mathematical definition for non-Markovianity in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems, which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system–environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system. (topical review)
Femtosecond Non-Markovian Optical Dynamics in Solution
Nibbering, Erik T.J.; Wiersma, Douwe A.; Duppen, Koos
1991-01-01
Femtosecond photon-echo experiments on sodium resorufin in dimethylsulfoxide at room temperature show that optical dephasing in solution is of non-Markovian character. A single Gauss-Markov stochastic modulation process is used to interpret both the femtosecond light-scattering results and the
Non-Markovian dissipative quantum mechanics with stochastic trajectories
International Nuclear Information System (INIS)
Koch, Werner
2010-01-01
All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called ''the environment'' may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until
Non-Markovian dissipative quantum mechanics with stochastic trajectories
Energy Technology Data Exchange (ETDEWEB)
Koch, Werner
2010-09-09
All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called ''the environment'' may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time
Entanglement, non-Markovianity, and causal non-separability
Milz, Simon; Pollock, Felix A.; Le, Thao P.; Chiribella, Giulio; Modi, Kavan
2018-03-01
Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. In detail, we provide an explicit construction to implement arbitrary a causal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: entanglement, non-Markovianity, and causal non-separability.
Non-Markovianity and memory of the initial state
Hinarejos, Margarida; Bañuls, Mari-Carmen; Pérez, Armando; de Vega, Inés
2017-08-01
We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the Breuer-Laine-Piilo measure proposed in Breuer et al (2009 Phys. Rev. Lett. 103 210401). We illustrate our findings with explicit calculations for the case of a structured environment.
From BBGKY hierarchy to non-Markovian evolution equations
International Nuclear Information System (INIS)
Gerasimenko, V.I.; Shtyk, V.O.; Zagorodny, A.G.
2009-01-01
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for the average value of the microscopic phase density is given, and the non-Markovian generalization of the Fokker-Planck collision integral is proposed
First-passage percolation on the random graph
Hofstad, van der R.W.; Hooghiemstra, G.; Van Mieghem, P.
2001-01-01
We study first-passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph, this problem can be described in terms of a continuous-time Markov chain and recursive trees. The Markov chain X(t) describes the number of
Joint probability distributions for a class of non-Markovian processes.
Baule, A; Friedrich, R
2005-02-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.
On correlations between certain random variables associated with first passage Brownian motion
International Nuclear Information System (INIS)
Kearney, Michael J; Pye, Andrew J; Martin, Richard J
2014-01-01
We analyse how the area swept out by a Brownian motion up to its first passage time correlates with the first passage time itself, obtaining several exact results in the process. Additionally, we analyse the relationship between the time average of a Brownian motion during a first passage and the maximum value attained. The results, which find various applications, are in excellent agreement with simulations. (paper)
Spherical particle Brownian motion in viscous medium as non-Markovian random process
International Nuclear Information System (INIS)
Morozov, Andrey N.; Skripkin, Alexey V.
2011-01-01
The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.
Li, Zhen; Lee, Hee Sun; Darve, Eric; Karniadakis, George Em
2017-01-01
Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.
Data-based Non-Markovian Model Inference
Ghil, Michael
2015-04-01
This talk concentrates on obtaining stable and efficient data-based models for simulation and prediction in the geosciences and life sciences. The proposed model derivation relies on using a multivariate time series of partial observations from a large-dimensional system, and the resulting low-order models are compared with the optimal closures predicted by the non-Markovian Mori-Zwanzig formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a very broad generalization and a time-continuous limit of existing multilevel, regression-based approaches to data-based closure, in particular of empirical model reduction (EMR). We show that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the Mori-Zwanzig formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are given for the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a very broad class of MSM applications. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. The resulting reduced model with energy-conserving nonlinearities captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lokta-Volterra model of population dynamics in its chaotic regime. The positivity constraint on the solutions' components replaces here the quadratic-energy-preserving constraint of fluid-flow problems and it successfully prevents blow-up. This work is based on a close
Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
2012-09-01
Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.
Non-Markovian effects on quantum-communication protocols
International Nuclear Information System (INIS)
Yeo, Ye; Oh, C. H.; An, Jun-Hong
2010-01-01
We show how, under the influence of non-Markovian environments, two different maximally entangled Bell states give rise to states that have equal classical correlations and the same capacities to violate the Bell-Clauser-Horne-Shimony-Holt inequality, but intriguingly differing usefulness for teleportation and dense coding. We elucidate how different entanglement measures like negativity and concurrence, and two different measures of quantum discord, could account for these behaviors. In particular, we explicitly show how the Ollivier-Zurek measure of discord directly accounts for one state being a better resource for dense coding compared to another. Our study leads to several important issues about these measures of discord.
Perturbative approach to non-Markovian stochastic Schroedinger equations
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)
A classical appraisal of quantum definitions of non-Markovian dynamics
International Nuclear Information System (INIS)
Vacchini, Bassano
2012-01-01
We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian processes. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behaviour is analysed in detail for quantum dynamics which can be built taking as input a class of classical processes. (paper)
International Nuclear Information System (INIS)
Yao, Yao
2015-01-01
The deep sub-Ohmic spin–boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model
Non-Markovian electron dynamics in nanostructures coupled to dissipative contacts
Novakovic, B.; Knezevic, I.
2013-02-01
In quasiballistic semiconductor nanostructures, carrier exchange between the active region and dissipative contacts is the mechanism that governs relaxation. In this paper, we present a theoretical treatment of transient quantum transport in quasiballistic semiconductor nanostructures, which is based on the open system theory and valid on timescales much longer than the characteristic relaxation time in the contacts. The approach relies on a model interaction between the current-limiting active region and the contacts, given in the scattering-state basis. We derive a non-Markovian master equation for the irreversible evolution of the active region's many-body statistical operator by coarse-graining the exact dynamical map over the contact relaxation time. In order to obtain the response quantities of a nanostructure under bias, such as the potential and the charge and current densities, the non-Markovian master equation must be solved numerically together with the Schr\\"{o}dinger, Poisson, and continuity equations. We discuss how to numerically solve this coupled system of equations and illustrate the approach on the example of a silicon nin diode.
Non-Markovian quantum processes: Complete framework and efficient characterization
Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan
2018-01-01
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.
Anchoring effect on first passage process in Taiwan financial market
Liu, Hsing; Liao, Chi-Yo; Ko, Jing-Yuan; Lih, Jiann-Shing
2017-07-01
Empirical analysis of the price fluctuations of financial markets has received extensive attention because a substantial amount of financial market data has been collected and because of advances in data-mining techniques. Price fluctuation trends can help investors to make informed trading decisions, but such decisions may also be affected by a psychological factors-the anchoring effect. This study explores the intraday price time series of Taiwan futures, and applies diffusion model and quantitative methods to analyze the relationship between the anchoring effect and price fluctuations during first passage process. Our results indicate that power-law scaling and anomalous diffusion for stock price fluctuations are related to the anchoring effect. Moreover, microscopic price fluctuations before switching point in first passage process correspond with long-term price fluctuations of Taiwan's stock market. We find that microscopic trends could provide useful information for understanding macroscopic trends in stock markets.
Non-Markovian near-infrared Q branch of HCl diluted in liquid Ar.
Padilla, Antonio; Pérez, Justo
2013-08-28
By using a non-Markovian spectral theory based in the Kubo cumulant expansion technique, we have qualitatively studied the infrared Q branch observed in the fundamental absorption band of HCl diluted in liquid Ar. The statistical parameters of the anisotropic interaction present in this spectral theory were calculated by means of molecular dynamics techniques, and found that the values of the anisotropic correlation times are significantly greater (by a factor of two) than those previously obtained by fitting procedures or microscopic cell models. This fact is decisive for the observation in the theoretical spectral band of a central Q resonance which is absent in the abundant previous researches carried out with the usual theories based in Kubo cumulant expansion techniques. Although the theory used in this work only allows a qualitative study of the Q branch, we can employ it to study the unknown characteristics of the Q resonance which are difficult to obtain with the quantum simulation techniques recently developed. For example, in this study we have found that the Q branch is basically a non-Markovian (or memory) effect produced by the spectral line interferences, where the PR interferential profile basically determines the Q branch spectral shape. Furthermore, we have found that the Q resonance is principally generated by the first rotational states of the first two vibrational levels, those more affected by the action of the dissolvent.
Liu, Qiang; Van Mieghem, Piet
2018-02-01
Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1 /ln(λ1+1 ) , where λ1 is the largest eigenvalue of the network's adjacency matrix, then the infection will persist on the network under the mean-field approximation. Thus, 1 /ln(λ1+1 ) is possibly the largest epidemic threshold for a general non-Markovian SIS process with a Poisson curing process under the mean-field approximation. Furthermore, non-Markovian SIS processes may result in a multimodal prevalence. As a byproduct, we show that a limiting Weibullian SIS process has the potential to model bursts of a synchronized infection.
First-passage exponents of multiple random walks
International Nuclear Information System (INIS)
Ben-Naim, E; Krapivsky, P L
2010-01-01
We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive half-line, we study S n (t), the probability that the nth rightmost particle remains in the positive half-line up to time t. This quantity decays algebraically, S n (t)∼t -β n , in the long-time limit. Interestingly, there is a family of nontrivial first-passage exponents, β 1 2 N-1 ; the only exception is the two-particle case where β 1 = 1/3. In the N → ∞ limit, however, the exponents attain a scaling form, β n (N) → β(z) with z=(n-N/2)/√N. We also demonstrate that the smallest exponent decays exponentially with N. We deduce these results from first-passage kinetics of a random walk in an N-dimensional cone and confirm them using numerical simulations. Additionally, we investigate the family of exponents that characterizes leadership statistics of multiple random walks and find that in this case, the cone provides an excellent approximation.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, E; Scala, M; Napoli, A [CNISM and Dipartimento di Scienze Fisiche ed Astronomiche, Universita di Palermo, via Archirafi 36, 90123 Palermo (Italy); Migliore, R, E-mail: ferraro@fisica.unipa.i, E-mail: matteo.scala@fisica.unipa.i [CNR-INFM, Research Unit CNISM of Palermo, via Archirafi 36, 90123 Palermo (Italy)
2010-09-01
In the framework of the dissipative dynamics of coupled qubits interacting with independent reservoirs, a comparison between non-Markovian master equation techniques and an exact solution is presented here. We study various regimes in order to find the limits of validity of the Nakajima-Zwanzig and the time-convolutionless master equations in the description of the entanglement dynamics. A comparison between the performances of the concurrence and the negativity as entanglement measures for the system under study is also presented.
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
International Nuclear Information System (INIS)
Bolivar, A.O.
2011-01-01
Highlights: → Classical Brownian motion described by a non-Markovian Fokker-Planck equation. → Quantization process. → Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. → A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.
Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
Chen, Hong-Bin; Chen, Guang-Yin; Chen, Yueh-Nan
2017-12-01
One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity. Here, by using the concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We present a simple protocol to show how a system attempts to share information with its environment and how it builds up system-environment correlations. We also show that the information returned from the correlations characterizes the non-Markovianity and a hierarchy of indivisibility of the system dynamics.
Non-Markovian Investigation of an Autonomous Quantum Heat Engine
Goyal, Ketan
A systematic study of a quantum heat engine is presented in this thesis. In particular, we study heat conduction through a two-two level composite system, which is then connected to a photon cavity to extract work, forming an autonomous quantum heat engine. The question as to what extent quantum effects such as quantum coherence and correlations impact thermodynamic properties of such a system is addressed. The investigated heat engine has been previously studied using the popular Born-Markovian quantum master equation under weak internal coupling approximation. However, we show that the used approach is quite limited in addressing such problems as it is incapable of correctly accounting for the quantum effects. By using a non-Markovian approach involving hierarchical equations of motion, we show that quantum coherence and correlations between system and environments play a significant role in energy transfer processes of heat conduction and work.
Mangaud, E.; Puthumpally-Joseph, R.; Sugny, D.; Meier, C.; Atabek, O.; Desouter-Lecomte, M.
2018-04-01
Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.
Selected Aspects of Markovian and Non-Markovian Quantum Master Equations
Lendi, K.
A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.
50 years of first-passage percolation
Auffinger, Antonio; Hanson, Jack
2017-01-01
First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved. In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a...
He, Zhi; Zhu, Lie-Qiang; Li, Li
2017-03-01
A non-Markovianity measure based on Brukner-Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner-Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner-Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information. Supported by the National Natural Science Foundation of China under Grant No. 61505053, the Natural Science Foundation of Hunan Province under Grant No. 2015JJ3092, the Research Foundation of Education Bureau of Hunan Province, China under Grant No. 16B177, the School Foundation from the Hunan University of Arts and Science under Grant No. 14ZD01
International Nuclear Information System (INIS)
He Zhi; Zhu Lie-Qiang; Li Li
2017-01-01
A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information. (paper)
Dynamics of density fluctuations in a non-Markovian Boltzmann- Langevin model
International Nuclear Information System (INIS)
Ayik, S.
1996-01-01
In the course of the past few years, the nuclear Boltzmann-Langevin (BL)model has emerged as a promising microscopic model for nuclear dynamics at intermediate energies. The BL model goes beyond the much employed Boltzmann-Uehling-Uhlenbeck (BUU) model, and hence it provides a basis for describing dynamics of density fluctuations and addressing processes exhibiting spontaneous symmetry breaking and catastrophic transformations in nuclear collisions, such as induced fission and multifragmentation. In these standard models, the collision term is treated in a Markovian approximation by assuming that two-body collisions are local in both space and time, in accordance with Boltzmann's original treatment. This simplification is usually justified by the fact that the duration of a two-body collision is short on the time scale characteristic of the macroscopic evolution of the system. As a result, transport properties of the collective motion has then a classical character. However, when the system possesses fast collective modes with characteristic energies that are not small in comparision with the temperature, then the quantum-statistical effects are important and the standard Markovian treatment is inadequate. In this case, it is necessary to improve the one-body transport model by including the memory effect due to the finite duration of two-body collisions. First we briefly describe the non-Markovian extension of the BL model by including the finite memory time associated with two-body collisions. Then, using this non-Markovian model in a linear response framework, we investigate the effect of the memory time on the agitation of unstable modes in nuclear matter in the spinodal zone, and calculate the collisional relaxation rates of nuclear collective vibrations
Mortezapour, Ali; Ahmadi Borji, Mahdi; Lo Franco, Rosario
2017-05-01
Efficient entanglement preservation in open quantum systems is a crucial scope towards a reliable exploitation of quantum resources. We address this issue by studying how two-qubit entanglement dynamically behaves when two atom qubits move inside two separated identical cavities. The moving qubits independently interact with their respective cavity. As a main general result, we find that under resonant qubit-cavity interaction the initial entanglement between two moving qubits remains closer to its initial value as time passes compared to the case of stationary qubits. In particular, we show that the initial entanglement can be strongly protected from decay by suitably adjusting the velocities of the qubits according to the non-Markovian features of the cavities. Our results supply a further way of preserving quantum correlations against noise with a natural implementation in cavity-QED scenarios and are straightforwardly extendable to many qubits for scalability.
Directory of Open Access Journals (Sweden)
Pengqin Shi
2016-09-01
Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.
Stochastic representation of a class of non-Markovian completely positive evolutions
International Nuclear Information System (INIS)
Budini, Adrian A.
2004-01-01
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose solution is a completely positive map. The structure of these master equations is associated with a random renewal process where each event consist in the application of a superoperator over a density matrix. Strong nonexponential decay arise by choosing different statistics of the renewal process. As examples we analyze the stochastic and averaged dynamics of simple systems that admit an analytical solution. The problem of positivity in quantum master equations induced by memory effects [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)] is clarified in this context
Exact master equations for the non-Markovian decay of a qubit
International Nuclear Information System (INIS)
Vacchini, Bassano; Breuer, Heinz-Peter
2010-01-01
Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.
Bulk-mediated surface diffusion: non-Markovian desorption and biased behaviour in an infinite system
International Nuclear Information System (INIS)
Revelli, Jorge A; Budde, Carlos E; Wio, Horacio S
2005-01-01
We analyse the dynamics of adsorbed molecules within the bulk-mediated surface diffusion framework. We consider that the particle's desorption mechanism is characterized by a non-Markovian process, while the particle's adsorption and its motion in the bulk are governed by Markovian dynamics, and include the effect of an external field in the form of a bias in the normal motion to the surface. We study this system for the diffusion of particles in a semi-infinite lattice, analysing the conditional probability to find the system on the reference absorptive plane as well as the surface dispersion as functions of time. The agreement between numerical and analytical asymptotic results is discussed
Intermediate-level crossings of a first-passage path
International Nuclear Information System (INIS)
Bhat, Uttam; Redner, S
2015-01-01
We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient D that starts at the origin and: (i) is at X at time T, or (ii) first reaches X at time T. We determine the most likely location of the first-passage trajectory from (0, 0) to (X, T) and its distribution at any intermediate time t < T. A first-passage path typically starts out by being repelled from its final location when X 2 /DT ≪ 1. We also determine the distribution of times when the trajectory first crosses and last crosses an arbitrary intermediate position x < X. The distribution of first-crossing times may be unimodal or bimodal, depending on whether X 2 /DT ≪ 1 or X 2 /DT ≫ 1. The form of the first-crossing probability in the bimodal regime is qualitatively similar to, but more singular than, the well-known arcsine law. (paper)
Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits
Hamedani Raja, Sina; Borrelli, Massimo; Schmidt, Rebecca; Pekola, Jukka P.; Maniscalco, Sabrina
2018-03-01
The exploitation and characterization of memory effects arising from the interaction between system and environment is a key prerequisite for quantum reservoir engineering beyond the standard Markovian limit. In this paper we investigate a prototype of non-Markovian dynamics experimentally implementable with superconducting qubits. We rigorously quantify non-Markovianity, highlighting the effects of the environmental temperature on the Markovian to non-Markovian crossover. We investigate how memory effects influence, and specifically suppress, the ability to perform work on the driven qubit. We show that the average work performed on the qubit can be used as a diagnostic tool to detect the presence or absence of memory effects.
International Nuclear Information System (INIS)
Hoerhammer, C.
2007-01-01
In this thesis, non-Markovian dynamics, decoherence and entanglement in dissipative quantum systems are studied. In particular, applications to quantum information theory of continuous variable systems are considered. The non-Markovian dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. In this context the focus is on non-Markovian effects on decoherence and separability time scales of various single- mode and two-mode continuous variable states. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial recurrence of coherence can occur in case of non-Lindblad-type dynamics. The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir and two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian and non-Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Therefore, new quantum correlations may emerge between the two modes. Below a critical bath temperature entanglement is preserved even in the steady state. A separability criterion is derived, which depends
Non-Markovian modification of the golden rule rate expression
International Nuclear Information System (INIS)
Basilevsky, M. V.; Davidovich, G. V.; Titov, S. V.; Voronin, A. I.
2006-01-01
The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
ference between Markovian and non-Markovian systems lies in the memory ... In recent years, research on quantum entanglement has attracted a lot of attention, which .... Hamiltonians for three types of atoms in the interaction picture are.
Non-Markovian Effects on the Brownian Motion of a Free Particle
Bolivar, A. O.
2010-01-01
Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.
Non-Markovianity-assisted high-fidelity Deutsch-Jozsa algorithm in diamond
Dong, Yang; Zheng, Yu; Li, Shen; Li, Cong-Cong; Chen, Xiang-Dong; Guo, Guang-Can; Sun, Fang-Wen
2018-01-01
The memory effects in non-Markovian quantum dynamics can induce the revival of quantum coherence, which is believed to provide important physical resources for quantum information processing (QIP). However, no real quantum algorithms have been demonstrated with the help of such memory effects. Here, we experimentally implemented a non-Markovianity-assisted high-fidelity refined Deutsch-Jozsa algorithm (RDJA) with a solid spin in diamond. The memory effects can induce pronounced non-monotonic variations in the RDJA results, which were confirmed to follow a non-Markovian quantum process by measuring the non-Markovianity of the spin system. By applying the memory effects as physical resources with the assistance of dynamical decoupling, the probability of success of RDJA was elevated above 97% in the open quantum system. This study not only demonstrates that the non-Markovianity is an important physical resource but also presents a feasible way to employ this physical resource. It will stimulate the application of the memory effects in non-Markovian quantum dynamics to improve the performance of practical QIP.
International Nuclear Information System (INIS)
Misguich, J.H.
1978-09-01
The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, Tomás; Braggio, Alessandro
2010-01-01
Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics...... interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nanoelectromechanical system with dynamical Franck...
Study on the security of discrete-variable quantum key distribution over non-Markovian channels
International Nuclear Information System (INIS)
Huang Peng; Zhu Jun; He Guangqiang; Zeng Guihua
2012-01-01
The dynamic of the secret key rate of the discrete-variable quantum key distribution (QKD) protocol over the non-Markovian quantum channel is investigated. In particular, we calculate the secret key rate for the six-state protocol over non-Markovian depolarizing channels with coloured noise and Markovian depolarizing channels with Gaussian white noise, respectively. We find that the secure secret key rate for the non-Markovian depolarizing channel will be larger than the Markovian one under the same conditions even when their upper bounds of tolerable quantum bit error rate are equal. This indicates that this coloured noise in the non-Markovian depolarizing channel can enhance the security of communication. Moreover, we show that the secret key rate fluctuates near the secure point when the coupling strength of the system with the environment is high. The results demonstrate that the non-Markovian effects of the transmission channel can have a positive impact on the security of discrete-variable QKD. (paper)
Polyakov, Evgeny A.; Rubtsov, Alexey N.
2018-02-01
When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called "sign problem". In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.
Non-Markovian dynamics of dust charge fluctuations in dusty plasmas
Asgari, H.; Muniandy, S. V.; Ghalee, Amir; Ghalee
2014-06-01
Dust charge fluctuates even in steady-state uniform plasma due to the discrete nature of the charge carriers and can be described using standard Langevin equation. In this work, two possible approaches in order to introduce the memory effect in dust charging dynamics are proposed. The first part of the paper provides the generalization form of the fluctuation-dissipation relation for non-Markovian systems based on generalized Langevin equations to determine the amplitudes of the dust charge fluctuations for two different kinds of colored noises under the assumption that the fluctuation-dissipation relation is valid. In the second part of the paper, aiming for dusty plasma system out of equilibrium, the fractionalized Langevin equation is used to derive the temporal two-point correlation function of grain charge fluctuations which is shown to be non-stationary due to the dependence on both times and not the time difference. The correlation function is used to derive the amplitude of fluctuations for early transient time.
Giorgi, Gian Luca; Galve, Fernando; Zambrini, Roberta
2015-08-01
Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX model, which exhibits different phases; we find that the different phases have different abilities to redundantly acquire classical information about the system, the "ferromagnetic phase" being the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated with backflow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.
Non-markovian effects in semiconductor cavity QED: Role of phonon-mediated processes
DEFF Research Database (Denmark)
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter
We show theoretically that the non-Markovian nature of the carrier-phonon interaction influences the dynamical properties of a semiconductor cavity QED system considerably, leading to asymmetries with respect to detuning in carrier lifetimes. This pronounced phonon effect originates from the pola......We show theoretically that the non-Markovian nature of the carrier-phonon interaction influences the dynamical properties of a semiconductor cavity QED system considerably, leading to asymmetries with respect to detuning in carrier lifetimes. This pronounced phonon effect originates from...... the polaritonic quasi-particle nature of the carrier-photon system interacting with the phonon reservoir....
Continued-fraction representation of the Kraus map for non-Markovian reservoir damping
van Wonderen, A. J.; Suttorp, L. G.
2018-04-01
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.
Non-Markovian quantum Brownian motion in one dimension in electric fields
Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.
2018-04-01
Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
International Nuclear Information System (INIS)
Palyulin, Vladimir V; Metzler, Ralf
2014-01-01
We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker–Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation. (fast track communications)
First Passage Moments of Finite-State Semi-Markov Processes
Energy Technology Data Exchange (ETDEWEB)
Warr, Richard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Cordeiro, James [Air Force Research Lab. (AFRL), Wright-Patterson AFB, OH (United States)
2014-03-31
In this paper, we discuss the computation of first-passage moments of a regular time-homogeneous semi-Markov process (SMP) with a finite state space to certain of its states that possess the property of universal accessibility (UA). A UA state is one which is accessible from any other state of the SMP, but which may or may not connect back to one or more other states. An important characteristic of UA is that it is the state-level version of the oft-invoked process-level property of irreducibility. We adapt existing results for irreducible SMPs to the derivation of an analytical matrix expression for the first passage moments to a single UA state of the SMP. In addition, consistent point estimators for these first passage moments, together with relevant R code, are provided.
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
We solve the Nakajima–Zwanzig (NZ) non-Markovian master equation to study the dynamics of different types of three-level atomic systems interacting with bosonic Lorentzian reservoirs at zero temperature. Von Neumann entropy (S) is used to show the evolution of the degree of entanglement of the subsystems.
Simple non-Markovian microscopic models for the depolarizing channel of a single qubit
International Nuclear Information System (INIS)
Fonseca Romero, K M; Lo Franco, R
2012-01-01
The archetypal one-qubit noisy channels - depolarizing, phase-damping and amplitude-damping channels - describe both Markovian and non-Markovian evolution. Simple microscopic models for the depolarizing channel, both classical and quantum, are considered. Microscopic models that describe phase-damping and amplitude-damping channels are briefly reviewed.
Non-Markovian dynamics in the theory of full counting statistics
DEFF Research Database (Denmark)
Flindt, Christian; Braggio, A.; Novotny, Tomas
2007-01-01
generating function corresponding to the resulting non-Markovian rate equation and find that the measured current cumulants behave significantly differently compared to those of a Markovian transport process. Our findings provide a novel interpretation of noise suppression found in a number of systems....
Large deviation estimates for a Non-Markovian Lévy generator of big order
International Nuclear Information System (INIS)
Léandre, Rémi
2015-01-01
We give large deviation estimates for a non-markovian convolution semi-group with a non-local generator of Lévy type of big order and with the standard normalisation of semi-classical analysis. No stochastic process is associated to this semi-group. (paper)
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 5. Evolution of entropy in different types of non-Markovian three-level systems: Single reservoir vs. two independent reservoirs. JAGHOURI HAKIMEH SARBISHAEI MOHSEN JAVIDAN KUROSH. Regular Volume 86 Issue 5 May 2016 pp 997-1008 ...
International Nuclear Information System (INIS)
Rufeil-Fiori, E.; Pastawski, H.M.
2009-01-01
The decay dynamics of a local excitation interacting with a non-Markovian environment, modeled by a semi-infinite tight-binding chain, is exactly evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i) early quadratic decay of the initial-state survival probability, up to a spreading time t S , (ii) exponential decay described by a self-consistent Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion through the return processes, leading to an inverse power law decay. At this last cross-over time t R a survival collapse becomes possible. This could reduce the survival probability by several orders of magnitude. The cross-over times t S and t R allow to assess the range of applicability of the Fermi Golden Rule and give the conditions for the observation of the Zeno and anti-Zeno effect.
The first-passage area for drifted Brownian motion and the moments of the Airy distribution
International Nuclear Information System (INIS)
Kearney, Michael J; Majumdar, Satya N; Martin, Richard J
2007-01-01
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. (fast track communication)
Statistical Analysis of the First Passage Path Ensemble of Jump Processes
von Kleist, Max; Schütte, Christof; Zhang, Wei
2018-02-01
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.
Nonstationary Narrow-Band Response and First-Passage Probability
DEFF Research Database (Denmark)
Krenk, Steen
1979-01-01
The notion of a nonstationary narrow-band stochastic process is introduced without reference to a frequency spectrum, and the joint distribution function of two consecutive maxima is approximated by use of an envelope. Based on these definitions the first passage problem is treated as a Markov po...
Universality for first passage percolation on sparse random graphs
Bhamidi, S.; Hofstad, van der R.W.; Hooghiemstra, G.
2014-01-01
We consider first passage percolation on the conguration model with n vertices, and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X2 logX-condition, we analyze the asymptotic distribution for the
Universality for first passage percolation on sparse random graphs
Bhamidi, S.; Van Der Hofstad, R.W.; Hooghiemstra, G.
2017-01-01
We consider first passage percolation on the configuration model with n vertices, and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X2 logX-condition, we analyze the asymptotic distribution for the
Non-Markovian dynamics of quantum systems: decay rate, capture and pure states
International Nuclear Information System (INIS)
Kanokov, Z.; Palchikov, Yu.V.; Antonenko, N.V.; Adamian, G.G.; Kanokov, Z.; Adamian, G.G.; Scheid, W.
2004-01-01
Full text: With the exact numerical solution of the equation for the reduced density matrix we found a minor role of the time dependence of the friction and diffusion coefficients in the escape rate from a potential well [1]. Since the used friction and diffusion coefficients were self- consistently under certain approximations derived, they preserve the positivity of the density matrix at any time. The mixed diffusion coefficient leads to a decrease of the escape rate. Since the used value of quantum diffusion coefficient in momentum is larger than the one following from a 'classic' treatment, the obtained escape rate is close to the rate calculated with the 'classic' set of diffusion coefficients. If the regime of motion is close to the under damped case or the temperature is small, the quasi-stationary escape rate can increase with friction. This is explained by the larger role of the increasing diffusion in the decay process. The agreement of the escape rate obtained with the analytical expressions in comparison to numerically calculated data depends on the characteristics of the considered system. The agreement is better in the overdamped regime. However, for any regime the deviations are not larger than in the case of the classical Kramers formula. Therefore, the analytical expressions can be applied in a large range of parameters for the potential and diffusion coefficients. We demonstrated that the uncertainty function is related to the linear entropy. The diffusion coefficients supplying the purity of states were elaborated for the non-Markovian dynamics. The obtained dependences of the capture probability on the friction proves that the quantum nature of this process should be taken into consideration when one calculates the capture cross section in nucleus-nucleus collisions
Li, Chuang; Yang, Sen; Song, Jie; Xia, Yan; Ding, Weiqiang
2017-05-15
In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is revealed that, by manipulating the detunings of classical field, the long-living stationary entanglement between two atoms can be generated in the presence of dissipation.
Energy Technology Data Exchange (ETDEWEB)
Hoerhammer, C.
2007-11-26
In this thesis, non-Markovian dynamics, decoherence and entanglement in dissipative quantum systems are studied. In particular, applications to quantum information theory of continuous variable systems are considered. The non-Markovian dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. In this context the focus is on non-Markovian effects on decoherence and separability time scales of various single- mode and two-mode continuous variable states. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial recurrence of coherence can occur in case of non-Lindblad-type dynamics. The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir and two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian and non-Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Therefore, new quantum correlations may emerge between the two modes. Below a critical bath temperature entanglement is preserved even in the steady state. A separability criterion is derived, which depends
Non-Markovian effect on the geometric phase of a dissipative qubit
International Nuclear Information System (INIS)
Chen Juanjuan; Tong Qingjun; An Junhong; Luo Honggang; Oh, C. H.
2010-01-01
We studied the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit, the lowest order correction to the geometric phase is derived analytically and the general case is calculated numerically. It was found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact on the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result is significant to the quantum information processing based on the geometric phase.
Shot-noise at a Fermi-edge singularity: Non-Markovian dynamics
Energy Technology Data Exchange (ETDEWEB)
Ubbelohde, N.; Maire, N.; Haug, R. J. [Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover (Germany); Roszak, K. [Institute of Physics, Wrocław University of Technology, PL-50370 Wrocław (Poland); Hohls, F. [Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig (Germany); Novotný, T. [Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, CZ-12116 Prague (Czech Republic)
2013-12-04
For an InAs quantum dot we study the current shot noise at a Fermi-edge singularity in low temperature cross-correlation measurements. In the regime of the interaction effect the strong suppression of noise observed at zero magnetic field and the sequence of enhancement and suppression in magnetic field go beyond a Markovian master equation model. Qualitative and quantitative agreement can however be achieved by a generalized master equation model taking non-Markovian dynamics into account.
The simulation of the non-Markovian behaviour of a two-level system
Semina, I.; Petruccione, F.
2016-05-01
Non-Markovian relaxation dynamics of a two-level system is studied with the help of the non-linear stochastic Schrödinger equation with coloured Ornstein-Uhlenbeck noise. This stochastic Schrödinger equation is investigated numerically with an adapted Platen scheme. It is shown, that the memory effects have a significant impact to the dynamics of the system.
Pseudothermalization in driven-dissipative non-Markovian open quantum systems
Lebreuilly, José; Chiocchetta, Alessio; Carusotto, Iacopo
2018-03-01
We investigate a pseudothermalization effect, where an open quantum system coupled to a nonequilibrated environment consisting of several non-Markovian reservoirs presents an emergent thermal behavior. This thermal behavior is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudothermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in low-temperature exciton-polariton experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudothermalization effect.
Quantum measurements in spin-boson model under non-Markovian environment
Berrada, K.; Aldaghri, O.
2017-07-01
We propose a control approach of the parameter estimation for a two-level quantum system interacting with a bosonic reservoir considering non-Markovian open, dissipative quantum system. We show that the precision of the estimation significantly affected and behaves differently within the framework of the markovian and non-Markovian regimes. The influence of memory effects for an Ohmic reservoir with Lorentz-Drude regularization on the estimation-parameter precision are numerically demonstrated under the following three conditions: ω0 ≪ωc , ω0 ≈ωc or ω0 ≫ωc , where ω0 is the characteristic frequency of the two-level system, and ωc is the cut-off frequency of Ohmic reservoir. We investigate the precision rate in high temperature, intermediate temperature, and low temperature reservoirs for various values of the ratio r =ωc /ω0 considering manifold external fields. We reveal that the enhancement and preservation of the measurement precision, highly depend on the combination of the external control field, reservoir parameters, and non-Markovian effects.
Data-driven non-Markovian closure models
Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael
2015-03-01
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model's parameter
Extreme and First-Passage Time of Ship Collision Loads
DEFF Research Database (Denmark)
Nielsen, Søren R. K.; Thoft-Christensen, Palle
1983-01-01
The paper outlines a general theory from which the distribution function of the extreme peak collision load encountered during a certain intended lifetime can be cal culated assuming the arrival of ship collisions to be specified by a Poisson counting proces s.......The paper outlines a general theory from which the distribution function of the extreme peak collision load encountered during a certain intended lifetime can be cal culated assuming the arrival of ship collisions to be specified by a Poisson counting proces s....
Error Distributions on Large Entangled States with Non-Markovian Dynamics
DEFF Research Database (Denmark)
McCutcheon, Dara; Lindner, Netanel H.; Rudolph, Terry
2014-01-01
We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten...... of errors occurs has a bound of Markovian form, and thus, accuracy threshold theorems based on Markovian models should be just as effective. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model....
Energy Technology Data Exchange (ETDEWEB)
Ding, Zhi-yong [School of Physics & Material Science, Anhui University, Hefei 230039 (China); School of Physics & Electronic Engineering, Fuyang Normal University, Fuyang 236037 (China); He, Juan, E-mail: juanhe78@163.com [School of Physics & Electronic Engineering, Fuyang Normal University, Fuyang 236037 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics & Material Science, Anhui University, Hefei 230039 (China)
2017-02-15
A feasible scheme for protecting the Greenberger–Horne–Zeilinger (GHZ) entanglement state in non-Markovian environments is proposed. It consists of prior weak measurement on each qubit before the interaction with decoherence environments followed by post quantum measurement reversals. It is shown that both the fidelity and concurrence of the GHZ state can be effectively improved. Meanwhile, we also verified that our scenario can enhance tripartite nonlocality remarkably. In addition, the result indicates that the larger the weak measurement strength, the better the effectiveness of the scheme with the lower success probability.
International Nuclear Information System (INIS)
Mineo, H.; Lin, S. H.; Fujimura, Y.; Xu, J.; Xu, R. X.; Yan, Y. J.
2013-01-01
Results of a theoretical study on non-Markov response for femtosecond laser-driven coherent ring currents in chiral aromatic molecules embedded in a condensed phase are presented. Coherent ring currents are generated by coherent excitation of a pair of quasi-degenerated π-electronic excited states. The coherent electronic dynamical behaviors are strongly influenced by interactions between the electronic system and phonon bath in a condensed phase. Here, the bath correlation time is not instantaneous but should be taken to be a finite time in ultrashort time-resolved experiments. In such a case, Markov approximation breaks down. A hierarchical master equation approach for an improved semiclassical Drude dissipation model was adopted to examine the non-Markov effects on ultrafast coherent electronic ring currents of (P)-2,2 ′ -biphenol in a condensed phase. Time evolution of the coherent ring current derived in the hierarchical master equation approach was calculated and compared with those in the Drude model in the Markov approximation and in the static limit. The results show how non-Markovian behaviors in quantum beat signals of ring currents depend on the Drude bath damping constant. Effects of temperatures on ultrafast coherent electronic ring currents are also clarified
Chakraborty, Ahana; Sensarma, Rajdeep
2018-03-01
The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
Bilayer graphene lattice-layer entanglement in the presence of non-Markovian phase noise
Bittencourt, Victor A. S. V.; Blasone, Massimo; Bernardini, Alex E.
2018-03-01
The evolution of single particle excitations of bilayer graphene under effects of non-Markovian noise is described with focus on the decoherence process of lattice-layer (LL) maximally entangled states. Once the noiseless dynamics of an arbitrary initial state is identified by the correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer graphene and the Dirac equation—which includes pseudovectorlike and tensorlike field interactions—the noisy environment is described as random fluctuations on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the Ornstein-Uhlenbeck processes: A non-Markovian noise model with a well-defined Markovian limit. Considering that an initial amount of entanglement shall be dissipated by the noise, two profiles of dissipation are identified. On one hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of entanglement are identified along the oscillation pattern for long interaction periods. On the other hand, for departing LL Werner and Cat states, the entanglement is suppressed although, for both cases, some identified memory effects compete with the pure noise-induced decoherence in order to preserve the the overall profile of a given initial state.
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction
Some remarks on first passage of Levy processes, the American put and pasting principles
Alili, L.; Kyprianou, A. E.
2005-01-01
The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskiǐ [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan a...
Entanglement backflow under the composite effect of two non-Markovian reservoirs
International Nuclear Information System (INIS)
Li, Jun-Gang; Zou, Jian; Shao, Bin
2012-01-01
The entanglement backflow of two qubits coupled to two independent reservoirs is investigated. It is found that under the collective effects of the two independent reservoirs, the entanglement backflow of the qubits does not always increase with the increase of the non-Markovianity of one of the reservoirs but demonstrates an intricate behavior. Interestingly, the action of one reservoir can affect the other reservoir's contribution to the entanglement backflow even when the two reservoirs are independent. -- Highlights: ► We study entanglement backflow of two qubits coupled to two independent reservoirs. ► We find that the entanglement backflow demonstrates an intricate behavior. ► The action of one reservoir can affect the contribution of the other reservoir.
Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors
Bülte, Johannes; Bednorz, Adam; Bruder, Christoph; Belzig, Wolfgang
2018-04-01
The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.
Directory of Open Access Journals (Sweden)
V.V.Ignatyuk
2004-01-01
Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.
Gross, Markus
2018-03-01
A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards–Wilkinson equation with non-conserved noise and the Mullins–Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This ‘renormalization’ of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.
International Nuclear Information System (INIS)
Hahm, Dae-Gi; Park, Kwan-Soon; Koh, Hyun-Moo
2008-01-01
The awareness of a seismic hazard and risk is being increased rapidly according to the frequent occurrences of the huge earthquakes such as the 2008 Sichuan earthquake which caused about 70,000 confirmed casualties and a 20 billion U.S. dollars economic loss. Since an earthquake load contains various uncertainties naturally, the safety of a structural system under an earthquake excitation has been assessed by probabilistic approaches. In many structural applications for a probabilistic safety assessment, it is often regarded that the failure of a system will occur when the response of the structure firstly crosses the limit barrier within a specified interval of time. The determination of such a failure probability is usually called the 'first-passage problem' and has been extensively studied during the last few decades. However, especially for the structures which show a significant nonlinear dynamic behavior, an effective and accurate method for the estimation of such a failure probability is not fully established yet. In this study, we presented a new approach to evaluate the first-passage probability of an earthquake response of seismically isolated structures. The proposed method is applied to the seismic isolation system for the containment buildings of a nuclear power plant. From the numerical example, we verified that the proposed method shows accurate results with more efficient computational efforts compared to the conventional approaches
Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation
International Nuclear Information System (INIS)
Dorda, A; Sorantin, M; Linden, W von der; Arrigoni, E
2017-01-01
We present a general scheme to address correlated nonequilibrium quantum impurity problems based on a mapping onto an auxiliary open quantum system of small size. The infinite fermionic reservoirs of the original system are thereby replaced by a small number N B of noninteracting auxiliary bath sites whose dynamics are described by a Lindblad equation, which can then be exactly solved by numerical methods such as Lanczos or matrix-product states. The mapping becomes exponentially exact with increasing N B , and is already quite accurate for small N B . Due to the presence of the intermediate bath sites, the overall dynamics acting on the impurity site is non-Markovian. While in previous work we put the focus on the manybody solution of the associated Lindblad problem, here we discuss the mapping scheme itself, which is an essential part of the overall approach. On the one hand, we provide technical details together with an in-depth discussion of the employed algorithms, and on the other hand, we present a detailed convergence study. The latter clearly demonstrates the above-mentioned exponential convergence of the procedure with increasing N B . Furthermore, the influence of temperature and an external bias voltage on the reservoirs is investigated. The knowledge of the particular convergence behavior is of great value to assess the applicability of the scheme to certain physical situations. Moreover, we study different geometries for the auxiliary system. On the one hand, this is of importance for advanced manybody solution techniques such as matrix product states which work well for short-ranged couplings, and on the other hand, it allows us to gain more insights into the underlying mechanisms when mapping non-Markovian reservoirs onto Lindblad-type impurity problems. Finally, we present results for the spectral function of the Anderson impurity model in and out of equilibrium and discuss the accuracy obtained with the different geometries of the auxiliary system
Non-Markovian decay of a three-level cascade atom in a structured reservoir
International Nuclear Information System (INIS)
Dalton, B.J.; Garraway, B.M.
2003-01-01
The dynamics of a three-level atom in a cascade (or ladder) configuration with both transitions coupled to a single structured reservoir of quantized electromagnetic field modes is treated using Laplace transform methods applied to the coupled amplitude equations. In this system two-photon excitation of the reservoir occurs, and both sequences for emitting the two photons are allowed and included in the theory. An integral equation is found to govern the complex amplitudes of interest. It is shown that the dynamics of the atomic system is completely determined in terms of reservoir structure functions, which are products of the mode density with the coupling constant squared. This dependence on reservoir structure functions rather than on the mode density or coupling constants alone, shows that it may be possible to extend pseudomode theory to treat multiphoton excitation of a structured reservoir--pseudomodes being introduced in one-one correspondence with the poles of reservoir structure functions in the complex frequency plane. A general numerical method for solving the integral equations based on discretizing frequency space, and applicable to different structured reservoirs such as high-Q cavities and photonic band-gap systems, is presented. An application to a high-Q-cavity case with identical Lorentzian reservoir structure functions is made, and the non-Markovian decay of the excited state shown. A formal solution to the integral equations in terms of right and left eigenfunctions of a non-Hermitian kernel is also given. The dynamics of the cascade atom, with the two transitions coupled to two separate structured reservoirs of quantized electromagnetic field modes, is treated similarly to the single structured reservoir situation. Again the dynamics only depends on reservoir structure functions. As only one sequence of emitting the two photons now occurs, the integral equation for the amplitudes can be solved analytically. The non-Markovian decay of the
Energy Technology Data Exchange (ETDEWEB)
Hughes, Keith H., E-mail: keith.hughes@bangor.ac.uk [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Cahier, Benjamin [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom); Martinazzo, Rocco [Dipartimento di Chimica Università degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Tamura, Hiroyuki [WPI-Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt/Main (Germany)
2014-10-17
Highlights: • Quantum dynamical study of exciton dissociation at a heterojunction interface. • The non-Markovian quantum dynamics involves a highly structured spectral density. • Spectral density is reconstructed from an effective mode transformation of the Hamiltonian. • The dynamics is studied using the hierarchical equations of motion approach. • It was found that the temperature has little effect on the charge transfer. - Abstract: We extend our recent quantum dynamical study of the exciton dissociation and charge transfer at an oligothiophene–fullerene heterojunction interface (Tamura et al., 2012) [6] by investigating the process using the non-perturbative hierarchical equations of motion (HEOM) approach. Based upon an effective mode reconstruction of the spectral density the effect of temperature on the charge transfer is studied using reduced density matrices. It was found that the temperature had little effect on the charge transfer and a coherent dynamics persists over the first few tens of femtoseconds, indicating that the primary charge transfer step proceeds by an activationless pathway.
Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism
Parish, Eric J.; Duraisamy, Karthik
2017-01-01
This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.
Bhamidi, S.; Van der Hofstad, R.; Hooghiemstra, G.
2010-01-01
We study first passage percolation (FPP) on the configuration model (CM) having power-law degrees with exponent ? ? [1, 2) and exponential edge weights. We derive the distributional limit of the minimal weight of a path between typical vertices in the network and the number of edges on the
Kalgin, Igor V; Chekmarev, Sergei F; Karplus, Martin
2014-04-24
Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed "streamlines", the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.
2015-01-01
Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations. PMID:24669953
First Passage Probability Estimation of Wind Turbines by Markov Chain Monte Carlo
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events...... of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal...... to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of the accuracy of the first passage probability estimation by the SS methods....
Iotti, Rita Claudia; Rossi, Fausto
2017-12-01
Microscopic modeling of electronic phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this context, non-Markovian density-matrix approaches are widely used simulation strategies. Here we show that such methods, along with valuable virtues, in some circumstances may exhibit potential limitations that need to be taken into account for a reliable description of quantum materials and related devices. More specifically, extending the analysis recently proposed in [EPL 112, 67005 (2015)] to high temperatures and degenerate conditions, we show that the usual mean-field treatment - employed to derive quantum-kinetic equations - in some cases may lead to anomalous results, characterized by decoherence suppression and positivity violations. By means of a simple two-level model, we show that such unexpected behaviors may affect zero-dimensional electronic systems coupled to dispersionless phonon modes, while such anomalies are expected to play a negligible role in nanosystems with higher dimensionality; these limitations are found to be significant in the low-density and low-temperature limit, while in the degenerate and/or finite-temperature regime - typical of many state-of-the-art quantum devices - their impact is strongly reduced.
An improved non-Markovian degradation model with long-term dependency and item-to-item uncertainty
Xi, Xiaopeng; Chen, Maoyin; Zhang, Hanwen; Zhou, Donghua
2018-05-01
It is widely noted in the literature that the degradation should be simplified into a memoryless Markovian process for the purpose of predicting the remaining useful life (RUL). However, there actually exists the long-term dependency in the degradation processes of some industrial systems, including electromechanical equipments, oil tankers, and large blast furnaces. This implies the new degradation state depends not only on the current state, but also on the historical states. Such dynamic systems cannot be accurately described by traditional Markovian models. Here we present an improved non-Markovian degradation model with both the long-term dependency and the item-to-item uncertainty. As a typical non-stationary process with dependent increments, fractional Brownian motion (FBM) is utilized to simulate the fractal diffusion of practical degradations. The uncertainty among multiple items can be represented by a random variable of the drift. Based on this model, the unknown parameters are estimated through the maximum likelihood (ML) algorithm, while a closed-form solution to the RUL distribution is further derived using a weak convergence theorem. The practicability of the proposed model is fully verified by two real-world examples. The results demonstrate that the proposed method can effectively reduce the prediction error.
Joint Probability Distributions for a Class of Non-Markovian Processes
Baule, A.; Friedrich, R.
2004-01-01
We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fr...
Kraus map for non-Markovian quantum dynamics driven by a thermal reservoir
van Wonderen, A.J.; Suttorp, L.G.
2013-01-01
Starting from unitary dynamics we study the evolution in time of a non-relativistic quantum system that exchanges energy with a thermal reservoir of harmonic oscillators. System and reservoir are assumed to be initially decorrelated. Reservoir correlation functions are factorized by means of a Kraus
Amplification of non-Markovian decay due to bound state absorption into continuum
International Nuclear Information System (INIS)
Garmon, S.; Simine, L.; Segal, D.; Petrosky, T.
2013-01-01
It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time 'near zone' and long time 'far zone'. In the near zone the survival probability falls off according to a t -1 power law, and in the far zone i t falls off as t -3 . We show that the timescale T Q separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale T Q diverges and the survival probability follows the t -1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t -1 power law dominates precisely at the point of ejection. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Non-Markovian effects on the dynamics of bubble growth in hot asymmetric nuclear matter
International Nuclear Information System (INIS)
Kolomietz, V.M.; Sanzhur, A.I.; Shlomo, S.
2003-01-01
We study the conditions for the generation and the dynamical evolution of embryonic overcritical vapor bubbles in an overheated asymmetric nuclear matter. We show that the Fermi-surface distortion and memory effects significantly hinder the growth of the bubbles. Moreover, the growth of the bubble is accompanied by characteristic oscillations of its radius R. The characteristic energy E, the damping parameter Γ, and the instability growth rate parameter ζ, depend on the relaxation time τ. The characteristic oscillations disappear in the short relaxation time limit τ→0. Our approach ignores the fluctuations of the particle numbers in the bubble region and the finite diffuse layer of the bubble. The minimum size of the critical radius R * for which our approach applies is determined by the condition a/R * <<1, where a=0.5-1 fm is the temperature-dependent surface thickness of the bubble
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Chaudhury, Srabanti; Chatterjee, Debarati; Cherayil, Binny J
2008-01-01
A harmonic oscillator that evolves under the action of both a systematic time-dependent force and a random time-correlated force can do work w. This work is a random quantity, and Mai and Dhar have recently shown, using the generalized Langevin equation (GLE) for the oscillator's position x, that it satisfies a fluctuation theorem. In principle, the same result could have been derived from the Fokker–Planck equation (FPE) for the probability density function, P(x,w,t), for the oscillator being at x at time t, having done work w. Although the FPE equivalent to the above GLE is easily constructed and solved, one finds, unexpectedly, that its predictions for the mean and variance of w do not agree with the fluctuation theorem. We show that to resolve this contradiction, it is necessary to construct an FPE that includes the velocity of the oscillator, v, as an additional variable. The FPE for P(x,v,w,t) does indeed yield expressions for the mean and variance of w that agree with the fluctuation theorem
Licata, Nicholas; Clark, Aaron
2014-03-01
Aquatic microorganisms face a variety of challenges in the course of development. One central challenge is efficiently regulating the export of toxic molecules inside the developing embryo. The strategies employed should be robust with respect to the variable ocean environment and limit the chances that exported toxins are reabsorbed. In this talk we consider the first-passage problem for the uptake of exported toxins by a spherical embryo. A perturbative solution of the advection-diffusion equation reveals that a concentration boundary layer forms in the vicinity of the embryo, and that fluid flow enhances the effectiveness of toxin export. We highlight connections between the model results and recent experiments on the development of sea urchin embryos. We acknowledge financial support from the University of Michigan-Dearobrn CASL Faculty Summer Research Grant.
A singular perturbation approach to non-Markovian escape rate problems
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Dygas, M.M.; Matkowsky, B.J.; Schuss, Z.
1986-01-01
The authors employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, they consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. They compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined
Ishizaki, Akihito; Tanimura, Yoshitaka
2008-05-01
Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.
Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation
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Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt (Germany); Martinazzo, Rocco [Dipartimento di Chimica, Universita degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Hughes, Keith H. [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom)
2012-10-14
A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
Flegg, Mark B.; Rüdiger, Sten; Erban, Radek
2013-01-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While
On perpetual American put valuation and first-passage in a regime-switching model with jumps
Jiang, Z.; Pistorius, M. R.
2008-01-01
In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching L\\'{e}vy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem under a state-dependent level rests on a path transformation and a new matrix Wiener-Hopf factorization result for this class of processes.
Lu, Shih-Yuan; Yen, Yi-Ming
2002-02-01
A first-passage scheme is devised to determine the overall rate constant of suspensions under the non-diffusion-limited condition. The original first-passage scheme developed for diffusion-limited processes is modified to account for the finite incorporation rate at the inclusion surface by using a concept of the nonzero survival probability of the diffusing entity at entity-inclusion encounters. This nonzero survival probability is obtained from solving a relevant boundary value problem. The new first-passage scheme is validated by an excellent agreement between overall rate constant results from the present development and from an accurate boundary collocation calculation for the three common spherical arrays [J. Chem. Phys. 109, 4985 (1998)], namely simple cubic, body-centered cubic, and face-centered cubic arrays, for a wide range of P and f. Here, P is a dimensionless quantity characterizing the relative rate of diffusion versus surface incorporation, and f is the volume fraction of the inclusion. The scheme is further applied to random spherical suspensions and to investigate the effect of inclusion coagulation on overall rate constants. It is found that randomness in inclusion arrangement tends to lower the overall rate constant for f up to the near close-packing value of the regular arrays because of the inclusion screening effect. This screening effect turns stronger for regular arrays when f is near and above the close-packing value of the regular arrays, and consequently the overall rate constant of the random array exceeds that of the regular array. Inclusion coagulation too induces the inclusion screening effect, and leads to lower overall rate constants.
Moix, Jeremy M.; Cao, Jianshu
2013-10-01
The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.
Default risk modeling beyond the first-passage approximation: Extended Black-Cox model
Katz, Yuri A.; Shokhirev, Nikolai V.
2010-07-01
We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm’s ability to avoid default even if company’s liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company’s default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity.
On a first passage problem in general queueing systems with multiple vacations
Directory of Open Access Journals (Sweden)
Jewgeni H. Dshalalow
1992-01-01
Full Text Available The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1 in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing process explicitly. Various examples and applications are discussed.
International Nuclear Information System (INIS)
Sharma, Ajeet K; Chowdhury, Debashish
2013-01-01
A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. However, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an in vitro experiment where single-stranded DNA, subjected to a mechanical tension F, is converted to double-stranded DNA by a single DNAP. The F-dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce nine novel distinct conditional dwell times of a DNAP. Using the method of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted F-dependences of these distributions are, in principle, accessible to single-molecule experiments. (paper)
International Nuclear Information System (INIS)
Bougioukas, G.
1982-01-01
14 patients (age 49.6 ± 13.3 years) with pure mitral insufficiency of the second to fourth degree underwent an operative intervention on the mitral valve, whereby in 12 cases the valve was replaced and two times the insufficiency could be cleared up with a plastic reconstruction. On the average of 21.6 ± 11 months after the operation a non-invasive study was done with the help of heart scintigraphy 'first passage technique' with Tc 99m pertechnetate at rest and at maximum ergometeric stress. With this method pre- and postoperative end-diastolic volumes (227/ 114 ml), end-systolic volumes (69/ 46 ml), heart minute volumes (4.5/ 5.7 l/min), total output fraction of the left ventricle (61/ 69%), diastolic filling speed and emptying speed of the ventricle were determined as well as the measuring of the lung flow time. The speed of the rapid filling phase gave no indication of a hindrance as a result of an implanted valve or a plastic reconstruction. The changes under stress indicate a normal reaction of the ventricle. This ability to react corresponds clinically to the improvement of the patients on the average of 1.1 degrees according to the NYHA classification. (orig./TRV) [de
Zilla, P; Fasol, R; Dudeck, U; Siedler, S; Preiss, P; Fischlein, T; Müller-Glauser, W; Baitella, G; Sanan, D; Odell, J
1990-08-01
A rapid and reliable harvest and culture technique was developed to provide a sufficient number of autologous endothelial cells for the confluent in vitro lining of cardiovascular prostheses. Enzymatic endothelial cell detachment was achieved by the in situ application of collagenase to short vessel segments. This harvest technique resulted in a complete lack of contaminating smooth muscle cells in all of 124 cultures from nonhuman primates and 13 cultures from human adults. The use of a microgrid technique enabled the daily in situ quantification of available endothelial cells. To assess ideal plating densities after passage the population doubling time was continuously related to the cell density. Surprisingly, a low plating density of 1.5 X 10(3) endothelial cells/cm2 achieved 43% shorter cell cycles than the usual plating density of 1.0 X 10(4) endothelial cells/cm2. Moreover, low density plating enabled mass cultures after one single cell passage, thereby reducing the cell damaging effect of trypsin. When the growth characteristics of endothelial cells from five anatomically different vessel sites were compared, the external jugular vein--which would be easily accessible and dispensable in each patient--proved to be an excellent source for endothelial cell cultures. By applying in situ administration of collagenase, low density plating and microgrid follow-up to adult human saphenous vein endothelial cells, 14,000,000 first passage endothelial cells--sufficient for the in vitro lining of long vascular prostheses--were obtained 26.2 days after harvest. (95% confidence interval:22.3 to 32.2 days).
Directory of Open Access Journals (Sweden)
Naiwei Lu
2017-01-01
Full Text Available Long-span bridges suffer from higher traffic loads and the simultaneous presence of multiple vehicles, which in conjunction with the steady traffic growth may pose a threat to the bridge safety. This study presents a methodology for first-passage probability evaluation of long-span bridges subject to stochastic heavy traffic loading. Initially, the stochastic heavy traffic loading was simulated based on long-term weigh-in-motion measurements of a highway bridge in China. A computational framework was presented integrating Rice’s level-crossing theory and the first-passage criterion. The effectiveness of the computational framework was demonstrated through a case study of a cable-stayed bridge. Numerical results show that the upper tail fitting of the up-crossing rate is an appropriate description of probability characteristics of the extreme traffic load effects of long-span bridges. The average daily truck traffic growth increases the probability of exceedance due to an intensive heavy traffic flow and results in a higher first-passage probability, but this increased trend is weakening as the continuous increase of the traffic volume. Since the sustained growth of gross vehicle weight has a constant impact on the probability of failure, setting a reasonable threshold overload ratio is an effective scheme as a traffic management to ensure the bridge serviceability.
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
Taillefumier, Thibaud; Magnasco, Marcelo O.
2013-01-01
Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss–Markov process will...
Taillefumier, Thibaud; Magnasco, Marcelo O
2013-04-16
Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its Hölder exponent H. The critical value occurs when the roughness of the boundary equals the roughness of the process, so for diffusive processes the critical value is Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous function of time. For rougher boundaries, H probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infinity. The critical point Hc = 1/2 corresponds to a widely studied case in the theory of neural coding, in which the external input integrated by a model neuron is a white-noise process, as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue that this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply defined times regardless of the intensity of internal noise.
Non-Markovian reservoir-dependent squeezing
International Nuclear Information System (INIS)
Paavola, J
2010-01-01
The squeezing dynamics of a damped harmonic oscillator are studied for different types of environment without making the Markovian approximation. The squeezing dynamics of a coherent state depend on the reservoir spectrum in a unique way that can, in the weak coupling approximation, be analysed analytically. Comparison of squeezing dynamics for ohmic, sub-ohmic and super-ohmic environments is done, showing a clear connection between the squeezing-non-squeezing oscillations and reservoir structure. Understanding the effects occurring due to structured reservoirs is important both from a purely theoretical point of view and in connection with evolving experimental techniques and future quantum computing applications.
Dynamics of non-Markovian exclusion processes
International Nuclear Information System (INIS)
Khoromskaia, Diana; Grosskinsky, Stefan; Harris, Rosemary J
2014-01-01
Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has a non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems. (paper)
Dynamics of non-Markovian exclusion processes
Khoromskaia, Diana; Harris, Rosemary J.; Grosskinsky, Stefan
2014-12-01
Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has a non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.
Tripartite nonlocality for an open Dirac system in the background of Schwarzschild space-time
Ding, Zhi-Yong; Shi, Jia-Dong; Wu, Tao; He, Juan
2017-12-01
In this paper, the behavior of the tripartite nonlocality for a Dirac system in the background of Schwarzschild space-time is studied. It is shown that the nonlocality of the ultimate physical accessible state always decreases as the Hawking effect increases monotonically, which is independent of the number of particles located near the event horizon. Besides, the more particles there are located near the event horizon, the more difficult the violation of the Svetlichny inequality becomes. Furthermore, we investigate the property of these particles suffering from a non-Markovian environment, and derive that the nonlocality decreases quickly with the increasing decoherence time accompanied by damping revivals. To preserve tripartite nonlocality in the non-Markovian environment, we propose a scheme by means of prior weak measurement and post measurement reversal. It is worth noticing that the effect is better for larger measurement strengths, while it induces smaller success probability.
Price Formation Modelling by Continuous-Time Random Walk: An Empirical Study
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Frédéric Délèze
2015-01-01
Full Text Available Markovian and non-Markovian\tmodels are presented to\tmodel the futures\tmarket price formation.\tWe show that\tthe\twaiting-time\tand\tthe\tsurvival\tprobabilities\thave\ta\tsignificant\timpact\ton\tthe\tprice\tdynamics.\tThis\tstudy tests\tanalytical\tsolutions\tand\tpresent\tnumerical\tresults for the\tprobability\tdensity function\tof the\tcontinuoustime random\twalk\tusing\ttick-by-tick\tquotes\tprices\tfor\tthe\tDAX\t30\tindex\tfutures.
The population and decay evolution of a qubit under the time-convolutionless master equation
International Nuclear Information System (INIS)
Huang Jiang; Fang Mao-Fa; Liu Xiang
2012-01-01
We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
The stretch to stray on time: Resonant length of random walks in a transient
Falcke, Martin; Friedhoff, Victor Nicolai
2018-05-01
First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν = - N / ( N + 1 ) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.
Non-Markovian State-Dependent Networks in Critical Loading
2015-02-04
Under suitable moment and mixing conditions which imply the invariance principle (cf. Herrndorf[8], Peligrad[17], Jacod and Shiryaev[9]), Corollary 4.1...volume 288 of Grundlehren der Mathema- tischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag: Berlin, second...arrival rate control policy on throughput and work-in-process in production systems with workload dependent processing rates. Int. J. Prod. Econ . 2003, 85
Non-Markovian dynamics of entanglement for multipartite systems
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Zhou Jiang; Wu Chengjun; Zhu Mingyi; Guo Hong, E-mail: hongguo@pku.edu.c [CREAM Group, State Key Laboratory of Advanced Optical Communication Systems and Networks (Peking University) and Institute of Quantum Electronics, School of Electronics Engineering and Computer Science, and Center for Computational Science and Engineering (CCSE), Peking University, Beijing 100871 (China)
2009-11-14
Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. To give a more physically intuitive insight, the quasimode Hamiltonian method is applied. Our quantitative analysis is helpful for the practical engineering of entanglement.
Simulations of a non-Markovian description of nucleation
Kuipers, J.; Barkema, G.T.
2010-01-01
In most nucleation theories, the state of a nucleating system is described by a distribution of droplet masses and this distribution evolves as a memoryless stochastic process. This is incorrect for a large class of nucleating systems. In a recent paper [ J. Kuipers and G. T. Barkema, Phys. Rev. E
Stabilizing strongly correlated photon fluids with non-Markovian reservoirs
Lebreuilly, José; Biella, Alberto; Storme, Florent; Rossini, Davide; Fazio, Rosario; Ciuti, Cristiano; Carusotto, Iacopo
2017-09-01
We introduce a frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a nonequilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or noninteger densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic nonequilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero-temperature many-body physics is highlighted.
International Nuclear Information System (INIS)
Seke, J.; Adam, G.; Soldatov, A.V.; Bogolubov, N.N.
2002-01-01
Full text: The dynamics of a discretized atom-field interaction model with a physically relevant form factor is analyzed. It is shown that after some short time interval only a small fraction of eigenvalues and eigenstates (belonging to the close vicinity of the excited atomic state energy E=ω 0 /2) contributes to the nondecay probability amplitudes in the long-time regime, whereas the contribution of all other eigenstates and eigenvalues is negligible. Nevertheless, to describe correctly the non-Markovian dynamics in the short-time regime the contribution of all eigenstates and eigenvalues must be taken into account. (author)
International Nuclear Information System (INIS)
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-01-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-06-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production.
Anomalous transport in turbulent plasmas and continuous time random walks
International Nuclear Information System (INIS)
Balescu, R.
1995-01-01
The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW's) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW's is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem: transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to t 1/2 is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW
Memory-induced acceleration and slowdown of barrier crossing
Kappler, Julian; Daldrop, Jan O.; Brünig, Florian N.; Boehle, Moritz D.; Netz, Roland R.
2018-01-01
We study the mean first-passage time τMFP for the barrier crossing of a single massive particle with non-Markovian memory by Langevin simulations in one dimension. In the Markovian limit of short memory time τΓ, the expected Kramers turnover between the overdamped (high-friction) and the inertial (low-friction) limits is recovered. Compared to the Markovian case, we find barrier crossing to be accelerated for intermediate memory time, while for long memory time, barrier crossing is slowed down and τMFP increases with τΓ as a power law τM F P˜τΓ2. Both effects are derived from an asymptotic propagator analysis: while barrier crossing acceleration at intermediate memory can be understood as an effective particle mass reduction, slowing down for long memory is caused by the slow kinetics of energy diffusion. A simple and globally accurate heuristic formula for τMFP in terms of all relevant time scales of the system is presented and used to establish a scaling diagram featuring the Markovian overdamped and the Markovian inertial regimes, as well as the non-Markovian intermediate memory time regime where barrier crossing is accelerated and the non-Markovian long memory time regime where barrier crossing is slowed down.
The spreading time in SIS epidemics on networks
He, Zhidong; Van Mieghem, Piet
2018-03-01
In a Susceptible-Infected-Susceptible (SIS) process, we investigate the spreading time Tm, which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time Tm resembles a lognormal-like distribution, though with different deep tails, both for the Markovian and the non-Markovian infection process, which implies that the spreading time can be very long with a relatively high probability. In addition, we show that a stronger virus, with a higher effective infection rate τ or an earlier timing of the infection attempts, does not always lead to a shorter average spreading time E [Tm ] . We numerically demonstrate that the average spreading time E [Tm ] in the complete graph and the star graph scales logarithmically as a function of the network size N for a fixed fraction of infected nodes in the metastable state.
Passage times of asymmetric anomalous walks with multiple paths
International Nuclear Information System (INIS)
Caceres, Manuel O; Insua, G Liliana
2005-01-01
We investigate the transient and the long-time behaviour of asymmetric anomalous walks in heterogeneous media. Two types of disorder are worked out explicitly: weak and strong disorder; in addition, the occurrence of disordered multiple paths is considered. We calculate the first passage time distribution of the associated stochastic transport process. We discuss the occurrence of the crossover from a power law to an exponential decay for the long-time behaviour of the distribution of the first passage times of disordered biased walks
Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.
Vestergaard, Christian L; Génois, Mathieu
2015-10-01
Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.
Parameter inference from hitting times for perturbed Brownian motion
Czech Academy of Sciences Publication Activity Database
Tamborrino, M.; Ditlevsen, S.; Lánský, Petr
2015-01-01
Roč. 21, č. 3 (2015), s. 331-352 ISSN 1380-7870 Institutional support: RVO:67985823 Keywords : first passage times * maximum likelihood estimation * Wiener proces * degradation proces * effect of intervention * survival analysis Subject RIV: BD - Theory of Information Impact factor: 0.810, year: 2015
Finite-difference time-domain simulation of thermal noise in open cavities
International Nuclear Information System (INIS)
Andreasen, Jonathan; Cao Hui; Taflove, Allen; Kumar, Prem; Cao Changqi
2008-01-01
A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes
Effect of two-qutrit entanglement on quantum speed limit time of a bipartite V-type open system
Energy Technology Data Exchange (ETDEWEB)
Behzadi, N., E-mail: n.behzadi@tabrizu.ac.ir [Research Institute for Fundamental Sciences, University of Tabriz (Iran, Islamic Republic of); Ahansaz, B.; Ektesabi, A.; Faizi, E. [Physics Department, Azarbaijan Shahid Madani University, Tabriz (Iran, Islamic Republic of)
2017-03-15
In the present paper, quantum speed limit (QSL) time of a bipartite V-type three-level atomic system under the effect of two-qutrit entanglement is investigated. Each party interacts with own independent reservoir. By considering two local unitarily equivalent Werner states and the Horodecki PPT state, as initial states, the QSL time is evaluated for each of them in the respective entangled regions. It is counterintuitively observed that the effect of entanglement on the QSL time driven from each of the initial Werner states are completely different when the degree of non-Markovianity is considerable. In addition, it is interesting that the effect of entanglement of the non-equivalent Horodecki state on the calculated QSL time displays an intermediate behavior relative to the cases obtained for the Werner states.
Time rescaling and Gaussian properties of the fractional Brownian motions
International Nuclear Information System (INIS)
Maccone, C.
1981-01-01
The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)
Chemical Continuous Time Random Walks
Aquino, T.; Dentz, M.
2017-12-01
Traditional methods for modeling solute transport through heterogeneous media employ Eulerian schemes to solve for solute concentration. More recently, Lagrangian methods have removed the need for spatial discretization through the use of Monte Carlo implementations of Langevin equations for solute particle motions. While there have been recent advances in modeling chemically reactive transport with recourse to Lagrangian methods, these remain less developed than their Eulerian counterparts, and many open problems such as efficient convergence and reconstruction of the concentration field remain. We explore a different avenue and consider the question: In heterogeneous chemically reactive systems, is it possible to describe the evolution of macroscopic reactant concentrations without explicitly resolving the spatial transport? Traditional Kinetic Monte Carlo methods, such as the Gillespie algorithm, model chemical reactions as random walks in particle number space, without the introduction of spatial coordinates. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. In real systems, transport limitations lead to incomplete mixing and decreased reaction efficiency. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical Master equation and formulate a generalized Gillespie algorithm. We then determine the modified chemical rate laws for different inter-reaction time distributions. We trace Michaelis-Menten-type kinetics back to finite-mean delay times, and predict time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium.
Suppression of thermal noise in a non-Markovian random velocity field
International Nuclear Information System (INIS)
Ueda, Masahiko
2016-01-01
We study the diffusion of Brownian particles in a Gaussian random velocity field with short memory. By extending the derivation of an effective Fokker–Planck equation for the Lanvegin equation with weakly colored noise to a random velocity-field problem, we find that the effect of thermal noise on particles is suppressed by the existence of memory. We also find that the renormalization effect for the relative diffusion of two particles is stronger than that for single-particle diffusion. The results are compared with those of molecular dynamics simulations. (paper: classical statistical mechanics, equilibrium and non-equilibrium)
Non-Markovian phonon dephasing of a quantum dot in a photonic-crystal nanocavity
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Nielsen, Per Kær; Kreiner-Møller, Asger
2012-01-01
this model, we are able to explain the broadband enhancement in an L3 cavity, and the quantitative difference compared to the AL-cavity arises from a larger background decay rate in the AL-cavity due to the presence of leaky radiation modes. The concept of the effective phonon density of states (DOS...
Dynamics of non-Markovianity in the presence of a driving field
Indian Academy of Sciences (India)
In some conditions, it is shown that in the presence of a driving field, the $N_{\\rm BLP} increases in the resonance and non-resonance limits. We have also found the exact solution of the master equation in order to investigate the effect of temperature- and environment excited states. We have shown that the behaviour of ...
Deterministic quantum controlled-PHASE gates based on non-Markovian environments
Zhang, Rui; Chen, Tian; Wang, Xiang-Bin
2017-12-01
We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atom-cavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.
Quantum coherence and non-Markovianity of an atom in a dissipative cavity under weak measurement
Liu, Yu; Zou, Hong-Mei; Fang, Mao-Fa
2018-01-01
Not Available Project supported by the Scientific Research Project of Hunan Provincial Education Department, China (Grant No. 16C0949), the Hunan Provincial Innovation Foundation for Postgraduate, China (Grant No. CX2017B177), the National Natural Science Foundation of China (Grant No. 11374096), and the Doctoral Science Foundation of Hunan Normal University, China.
Human mobility and time spent at destination: impact on spatial epidemic spreading.
Poletto, Chiara; Tizzoni, Michele; Colizza, Vittoria
2013-12-07
Host mobility plays a fundamental role in the spatial spread of infectious diseases. Previous theoretical works based on the integration of network theory into the metapopulation framework have shown that the heterogeneities that characterize real mobility networks favor the propagation of epidemics. Nevertheless, the studies conducted so far assumed the mobility process to be either Markovian (in which the memory of the origin of each traveler is lost) or non-Markovian with a fixed traveling time scale (in which individuals travel to a destination and come back at a constant rate). Available statistics however show that the time spent by travelers at destination is characterized by wide fluctuations, ranging from a single day up to several months. Such varying length of stay crucially affects the chance and duration of mixing events among hosts and may therefore have a strong impact on the spread of an emerging disease. Here, we present an analytical and a computational study of epidemic processes on a complex subpopulation network where travelers have memory of their origin and spend a heterogeneously distributed time interval at their destination. Through analytical calculations and numerical simulations we show that the heterogeneity of the length of stay alters the expression of the threshold between local outbreak and global invasion, and, moreover, it changes the epidemic behavior of the system in case of a global outbreak. Additionally, our theoretical framework allows us to study the effect of changes in the traveling behavior in response to the infection, by considering a scenario in which sick individuals do not leave their home location. Finally, we compare the results of our non-Markovian framework with those obtained with a classic Markovian approach and find relevant differences between the two, in the estimate of the epidemic invasion potential, as well as of the timing and the pattern of its spatial spread. These results highlight the importance of
Susceptible-infected-susceptible epidemics on networks with general infection and cure times
Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.
2013-06-01
The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.
Analyzing a stochastic time series obeying a second-order differential equation.
Lehle, B; Peinke, J
2015-06-01
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.
A lattice-model representation of continuous-time random walks
International Nuclear Information System (INIS)
Campos, Daniel; Mendez, Vicenc
2008-01-01
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied
A lattice-model representation of continuous-time random walks
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es
2008-02-29
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.
Karmeshu; Gupta, Varun; Kadambari, K V
2011-06-01
A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.
Time-fractional particle deposition in porous media
Xu, Jianping
2017-05-01
In the percolation process where fluids carry small solid particles, particle deposition causes a real-time permeability change of the medium as the swarm of particles propagates along the medium. Then the permeability change influences percolation and deposition behaviors as a feedback. This fact triggers memory effect in the deposition dynamics, which means the particulate transport and deposition behaviors become history-dependent. In this paper, we conduct the time-fractional generalization of the classical phenomenological model of particle deposition in porous media to incorporate the memory effect. We tested and compared the effects of employing different types of fractional operators, i.e. the Riemann-Liouville type, the Hadamard type and the Prabhakar type. Numerical simulation results show that the system behaviors vary according to the change of distinct memory kernels in an expected way. We then discuss the physical meaning of the time-fractional generalization. It is shown that different types of fractional operators unanimously ground themselves on the local-Newtonian time transformation in a complex system, which is equivalent to a class of history integrals. By the introduction of various memory kernels, it enables the model to more powerfully fit and approximate observed data. Further, the fundamental meaning of this work is not to show which fractional operator is ‘better’, but to argue collectively the legitimacy and practicality of a non-Markovian particle deposition dynamics in porous media, and in fact it is admissible to a bunch of memory kernels which differ greatly from each other in functional forms. Hopefully the presented generalized mass conservation formalism offers a broader framework to investigate transport problems in porous media.
Time-fractional particle deposition in porous media
International Nuclear Information System (INIS)
Xu, Jianping
2017-01-01
In the percolation process where fluids carry small solid particles, particle deposition causes a real-time permeability change of the medium as the swarm of particles propagates along the medium. Then the permeability change influences percolation and deposition behaviors as a feedback. This fact triggers memory effect in the deposition dynamics, which means the particulate transport and deposition behaviors become history-dependent. In this paper, we conduct the time-fractional generalization of the classical phenomenological model of particle deposition in porous media to incorporate the memory effect. We tested and compared the effects of employing different types of fractional operators, i.e. the Riemann–Liouville type, the Hadamard type and the Prabhakar type. Numerical simulation results show that the system behaviors vary according to the change of distinct memory kernels in an expected way. We then discuss the physical meaning of the time-fractional generalization. It is shown that different types of fractional operators unanimously ground themselves on the local-Newtonian time transformation in a complex system, which is equivalent to a class of history integrals. By the introduction of various memory kernels, it enables the model to more powerfully fit and approximate observed data. Further, the fundamental meaning of this work is not to show which fractional operator is ‘better’, but to argue collectively the legitimacy and practicality of a non-Markovian particle deposition dynamics in porous media, and in fact it is admissible to a bunch of memory kernels which differ greatly from each other in functional forms. Hopefully the presented generalized mass conservation formalism offers a broader framework to investigate transport problems in porous media. (paper)
Kramer, Tobias; Noack, Matthias; Reinefeld, Alexander; Rodríguez, Mirta; Zelinskyy, Yaroslav
2018-06-11
Time- and frequency-resolved optical signals provide insights into the properties of light-harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the complex. The hierarchical equations of motion (HEOM) provide a unifying theory, which allows one to study the combined effects of system-environment dissipation and non-Markovian memory without making restrictive assumptions about weak or strong couplings or separability of vibrational and electronic degrees of freedom. With increasing system size the exact solution of the open quantum system dynamics requires memory and compute resources beyond a single compute node. To overcome this barrier, we developed a scalable variant of HEOM. Our distributed memory HEOM, DM-HEOM, is a universal tool for open quantum system dynamics. It is used to accurately compute all experimentally accessible time- and frequency-resolved processes in light-harvesting molecular complexes with arbitrary system-environment couplings for a wide range of temperatures and complex sizes. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field
Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra
2017-10-01
In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.
International Nuclear Information System (INIS)
Haba, Z.
1981-01-01
In the usual models of Euclidean field theory the Schwinger functions are moments of a positive measure. In this paper the author discusses the basic properties of the measure μ, i.e. properties of the sample paths of the random field. (Auth.)
A multiscale view on inverse statistics and gain/loss asymmetry in financial time series
International Nuclear Information System (INIS)
Siven, Johannes; Lins, Jeffrey; Hansen, Jonas Lundbek
2009-01-01
Researchers have studied the first-passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to show that this is a long, rather than short, timescale phenomenon—if enough low frequency content of the price process is removed, the asymmetry disappears. We also propose a model which explains the asymmetry in terms of prolonged, correlated downward movements of individual stocks
Simple relations between mean passage times and Kramers' stationary rate
International Nuclear Information System (INIS)
Boilley, David; Jurado, Beatriz; Schmitt, Christelle
2004-01-01
The classical problem of the escape time of a metastable potential well in a thermal environment is generally studied by various quantities like Kramers' stationary escape rate, mean first passage time, nonlinear relaxation time, or mean last passage time. In addition, numerical simulations lead to the definition of other quantities as the long-time limit escape rate and the transient time. In this paper, we propose some simple analytical relations between all these quantities. In particular, we point out the hypothesis used to evaluate these various times in order to clarify their comparison and applicability, and show how average times include the transient time and the long-time limit of the escape rate
Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases.
Chou, Tom; Wang, Yu
2015-05-07
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a "wild-type" state to a given "terminally differentiated," "resistant," or "cancerous" state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be "nonlinear" (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times. Published by Elsevier Ltd.
Heterogeneous continuous-time random walks
Grebenkov, Denis S.; Tupikina, Liubov
2018-01-01
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
Sojourn time distributions in a Markovian G-queue with batch arrival and batch removal
Directory of Open Access Journals (Sweden)
Yang Woo Shin
1999-01-01
Full Text Available We consider a single server Markovian queue with two types of customers; positive and negative, where positive customers arrive in batches and arrivals of negative customers remove positive customers in batches. Only positive customers form a queue and negative customers just reduce the system congestion by removing positive ones upon their arrivals. We derive the LSTs of sojourn time distributions for a single server Markovian queue with positive customers and negative customers by using the first passage time arguments for Markov chains.
A simple exposure-time theory for all time-nonlocal transport formulations and beyond.
Ginn, T. R.; Schreyer, L. G.
2016-12-01
-differential equations, and so on. Because the exposure-time approach is both simple and localized, it provides a promising platform for launching forays into non-Markovian and/or nonlinear processes and into upscaling age-dependent multicomponent reaction systems.
Quantum trajectories: Memory and continuous observation
Barchielli, Alberto; Pellegrini, Clément; Petruccione, Francesco
2012-12-01
Starting from a generalization of the quantum trajectory theory [based on the stochastic Schrödinger equation (SSE)], non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows a consistent theory of quantum measurement in continuous time to be developed for these non-Markovian quantum trajectory models. In this context, the notions of “instrument,” “a priori,” and “a posteriori” states can be introduced. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non-Markovian effects come from the random environment, colored noises, randomness in the stimulating light, and delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied, and we show how these quantities are sensitive to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescent light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.
De Simone, Andrea; Riotto, Antonio
2011-01-01
The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter halos such as halo bias, accretion rate, formation time, merging rate and the formation history of halos. This is achieved by computing conditional probabilities with non-trivial initial conditions, and the conditional two-barrier first-crossing rate. In this paper we use the recently-developed path integral formulation of the excursion set theory to calculate analytically these conditional probabilities in the presence of a generic moving barrier, including the one describing the ellipsoidal collapse, and for both Gaussian and non-Gaussian initial conditions. The non-Markovianity of the random walks induced by non-Gaussi...
Computation of transit times using the milestoning method with applications to polymer translocation
Hawk, Alexander T.; Konda, Sai Sriharsha M.; Makarov, Dmitrii E.
2013-08-01
Milestoning is an efficient approximation for computing long-time kinetics and thermodynamics of large molecular systems, which are inaccessible to brute-force molecular dynamics simulations. A common use of milestoning is to compute the mean first passage time (MFPT) for a conformational transition of interest. However, the MFPT is not always the experimentally observed timescale. In particular, the duration of the transition path, or the mean transit time, can be measured in single-molecule experiments, such as studies of polymers translocating through pores and fluorescence resonance energy transfer studies of protein folding. Here we show how to use milestoning to compute transit times and illustrate our approach by applying it to the translocation of a polymer through a narrow pore.
Trapping time statistics and efficiency of transport of optical excitations in dendrimers
Heijs, Dirk-Jan; Malyshev, Victor A.; Knoester, Jasper
2004-09-01
We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and nonradiative decay of the excitations while diffusing across the dendrimer. We derive exact expressions for the Laplace transform of the trapping time distribution and the efficiency of trapping, and analyze those for various realizations of the energy bias, number of dendrimer generations, and relative rates for decay and hopping. We show that the essential parameter that governs the trapping efficiency is the product of the on-site excitation decay rate and the trapping time (mean first passage time) in the absence of decay.
Reaction time for trimolecular reactions in compartment-based reaction-diffusion models
Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang
2018-05-01
Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.
International Nuclear Information System (INIS)
Shu Chang-Zheng; Nie Lin-Ru; Zhou Zhong-Rao
2012-01-01
Stochastic resonance (SR)-like and resonance suppression (RS)-like phenomena in a time-delayed bistable system driven by additive white noise are investigated by means of stochastic simulations of the power spectrum, the quality factor of the power spectrum, and the mean first-passage time (MFPT) of the system. The calculative results indicate that: (i) as the system is driven by a small periodic signal, the quality factor as a function delay time exhibits a maximal value at smaller noise intensities, i.e., an SR-like phenomenon. With the increment in additive noise intensity, the extremum gradually disappears and the quality factor decreases monotonously with delay time. (ii) As the additive noise intensity is smaller, the curve of the MFPT with respect to delay time displays a peak, i.e., an RS-like phenomenon. At higher levels of noise, however, the non-monotonic behavior is lost. (general)
Continuous-time random walks with reset events. Historical background and new perspectives
Montero, Miquel; Masó-Puigdellosas, Axel; Villarroel, Javier
2017-09-01
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.
DEFF Research Database (Denmark)
Nielsen, Per Kær; Lodahl, Peter; Jauho, Antti-Pekka
2013-01-01
We study the fundamental limit on single-photon indistinguishability imposed by decoherence due to phonon interactions in semiconductor quantum dot-cavity quantum electrodynamics systems. Employing an exact diagonalization approach we find large differences compared to standard methods...
DEFF Research Database (Denmark)
Nielsen, Per Kær; Nielsen, Torben Roland; Lodahl, Peter
2010-01-01
treatments. A pronounced consequence is the emergence of a phonon induced spectral asymmetry when detuning the cavity from the quantum-dot resonance. The asymmetry can only be explained when considering the polaritonic quasiparticle nature of the quantum-dot-cavity system. Furthermore, a temperature induced...
Krimer, Dmitry O.; Hartl, Benedikt; Mintert, Florian; Rotter, Stefan
2017-10-01
Ensembles of quantum-mechanical spins offer a promising platform for quantum memories, but proper functionality requires accurate control of unavoidable system imperfections. We present an efficient control scheme for a spin ensemble strongly coupled to a single-mode cavity based on a set of Volterra equations relying solely on weak classical control pulses. The viability of our approach is demonstrated in terms of explicit storage and readout sequences that will serve as a starting point towards the realization of more demanding full quantum-mechanical optimal control schemes.
Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue
Directory of Open Access Journals (Sweden)
Charles Knessl
1996-01-01
Full Text Available We consider the GI/G/1 queue described by either the workload U(t (unfinished work or the number of customers N(t in the system. We compute the mean time until U(t reaches excess of the level K, and also the mean time until N(t reaches N0. For the M/G/1 and GI/M/1 models, we obtain exact contour integral representations for these mean first passage times. We then compute the mean times asymptotically, as K and N0→∞, by evaluating these contour integrals. For the general GI/G/1 model, we obtain asymptotic results by a singular perturbation analysis of the appropriate backward Kolmogorov equation(s. Numerical comparisons show that the asymptotic formulas are very accurate even for moderate values of K and N0.
On discrete stochastic processes with long-lasting time dependence in the variance
Queirós, S. M. D.
2008-11-01
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of qm-exponencial, form (eqm=1 x=ex). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.
Coherencia y entrelazamiento en dinámica no Markoviana de qubits
Directory of Open Access Journals (Sweden)
Cristian Edwin Susa Quintero
2013-06-01
Full Text Available We provide a thorough analysis of the entanglement dynamics of an interacting two-qubit systemin the non-Markovian regime. In such a regime, the time scale on which the reservoir degrees offreedom evolve is either of the same order of magnitude or less than that on which the systemevolves.We used an exact numerical method; the Quasi-Adiabatic Path Integral (QUAPI technique,to describe the corresponding qubit dissipative dynamics in such a non-Markovian regime. Wecomputed the time evolution of the density operator for the quibits, from which we quantified thecoherences and population dynamics, as well as the qubit-bath coupling effects. Using negativityas a metric, we calculated the dynamics of non-local quantum correlations (entanglement, andindentified a non-Markovian quantum phenomena in terms of early stage disentanglement, and thecollapse and revival of entanglement.
The timing statistics of spontaneous calcium release in cardiac myocytes.
Directory of Open Access Journals (Sweden)
Mesfin Asfaw
Full Text Available A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some cases it is known that these excitations are due to calcium (Ca release from the sarcoplasmic reticulum (SR via propagating subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine the timing statistics of spontaneous Ca release (SCR in a simplified model of a cardiac myocyte. In particular, we compute the mean first passage time (MFPT to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.
Takeover times for a simple model of network infection.
Ottino-Löffler, Bertrand; Scott, Jacob G; Strogatz, Steven H
2017-07-01
We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N≫1, the takeover time T is distributed as a Gumbel distribution for the star graph, as the convolution of two Gumbel distributions for a complete graph and an Erdős-Rényi random graph, as a normal for a one-dimensional ring and a two-dimensional lattice, and as a family of intermediate skewed distributions for d-dimensional lattices with d≥3 (these distributions approach the convolution of two Gumbel distributions as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.
Stochastic Resonance and First Arrival Time for Excitable Systems
Duki, Solomon Fekade; Taye, Mesfin Asfaw
2018-06-01
We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η ) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ =Be^{-A T}) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).
Extinction Time of a Metapopulation Driven by Colored Correlated Noises
International Nuclear Information System (INIS)
Li Jiangcheng
2010-01-01
The simplified incidence function model which is driven by the colored correlated noises is employed to investigate the extinction time of a metapopulation perturbed by environments. The approximate Fokker-Planck Equation and the mean first passage time which denotes the extinction time (T ex ) are obtained by virtue of the Novikov theorem and the Fox approach. After introducing a noise intensity ratio and a dimensionless parameter R = D/α (D and α are the multiplicative and additive colored noise intensities respectively), and then performing numerical computations, the results indicate that: (i) The absolute value of correlation strength Λ and its correlation time τ 3 play opposite roles on the T ex ; (ii) For the case of 0 2 play opposite roles on the T ex in which R > 1 is the best condition, and there is one-peak structure on the T ex - D plot; (iii) For the case of -1 1 play opposite roles on the T ex in which R ex - τ 2 plot. (general)
Dynamics of Quantum Entanglement in Reservoir with Memory Effects
International Nuclear Information System (INIS)
Hao Xiang; Sha Jinqiao; Sun Jian; Zhu Shiqun
2012-01-01
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants. (general)
International Nuclear Information System (INIS)
Doktorov, Alexander B; Kipriyanov, Alexey A
2007-01-01
In considering the irreversible chemical reaction A+B→ C+B in liquid solutions two many-particle approaches to the derivation of binary non-Markovian kinetic equations are compared: simple superposition decoupling and a method of extracting 'pair' channels from three-particle correlation evolution. It is shown that both methods provide an almost identical description of this reaction. However, in studies of reversible reactions in liquid solutions only the channel extraction method gives a correct physically clear description of the reaction though it consists of a sequence of steps: the development of integral encounter theory (IET), effective pairs approximation (EPA), modified encounter theory (MET), and the final regular form (RF) of kinetic equations. It is shown that the rate equations often encountered in the literature correspond to the independence of transient channels of 'scattering' in the bimolecular reversible reaction (A+B -B), while the independent transient channel of 'decay' in the reversible reactionA+B -C is defined solely by time integral convolution. In the general case transient channels in non-Markovian theory are not independent, and their interference manifests itself as a non-Markovian inhomogeneous source in binary non-Markovian kinetic equations in regular form. Based on the derived equations new universal kinetics (independent of models) of chemical equilibrium attainment have been obtained. It is shown that these kinetics can differ essentially from the kinetics corresponding to the kinetic law of mass action of formal chemical kinetics
Directory of Open Access Journals (Sweden)
Vicente Navarro, Eduardo
2006-05-01
Full Text Available The present essay is designed to be a general introduction to the philosophical problem of time from its very different forms and ways of approaching. In this sense, the article covers the problem from different perspectives and gives a brief account of the plurality and diversity of the time found in the different philosophical definitions, in the different layers of knowledge, in different periods and cultures and also in the different instruments used to measure time itself
Spin-resolved electron waiting times in a quantum-dot spin valve
Tang, Gaomin; Xu, Fuming; Mi, Shuo; Wang, Jian
2018-04-01
We study the electronic waiting-time distributions (WTDs) in a noninteracting quantum-dot spin valve by varying spin polarization and the noncollinear angle between the magnetizations of the leads using the scattering matrix approach. Since the quantum-dot spin valve involves two channels (spin up and down) in both the incoming and outgoing channels, we study three different kinds of WTDs, which are two-channel WTD, spin-resolved single-channel WTD, and cross-channel WTD. We analyze the behaviors of WTDs in short times, correlated with the current behaviors for different spin polarizations and noncollinear angles. Cross-channel WTD reflects the correlation between two spin channels and can be used to characterize the spin-transfer torque process. We study the influence of the earlier detection on the subsequent detection from the perspective of cross-channel WTD, and define the influence degree quantity as the cumulative absolute difference between cross-channel WTDs and first-passage time distributions to quantitatively characterize the spin-flip process. We observe that influence degree versus spin-transfer torque for different noncollinear angles as well as different polarizations collapse into a single curve showing universal behaviors. This demonstrates that cross-channel WTDs can be a pathway to characterize spin correlation in spintronics system.
Time scale of diffusion in molecular and cellular biology
International Nuclear Information System (INIS)
Holcman, D; Schuss, Z
2014-01-01
Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function. (topical review)
Time scale of diffusion in molecular and cellular biology
Holcman, D.; Schuss, Z.
2014-05-01
Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function.
Wang, Lei; Xiong, Chuang; Wang, Xiaojun; Li, Yunlong; Xu, Menghui
2018-04-01
Considering that multi-source uncertainties from inherent nature as well as the external environment are unavoidable and severely affect the controller performance, the dynamic safety assessment with high confidence is of great significance for scientists and engineers. In view of this, the uncertainty quantification analysis and time-variant reliability estimation corresponding to the closed-loop control problems are conducted in this study under a mixture of random, interval, and convex uncertainties. By combining the state-space transformation and the natural set expansion, the boundary laws of controlled response histories are first confirmed with specific implementation of random items. For nonlinear cases, the collocation set methodology and fourth Rounge-Kutta algorithm are introduced as well. Enlightened by the first-passage model in random process theory as well as by the static probabilistic reliability ideas, a new definition of the hybrid time-variant reliability measurement is provided for the vibration control systems and the related solution details are further expounded. Two engineering examples are eventually presented to demonstrate the validity and applicability of the methodology developed.
Directory of Open Access Journals (Sweden)
Ubiratan Paiva de Oliveira
2008-04-01
Full Text Available In Pinter: A Study of His Plays, Martin Esslin mentions three levels of possible interpretation for Old Times. According to him, Pinter's play could be interpreted on a realistic level, or either representing the male character's dream or a ritual game. He correctly remarks, though, that none of those levels excludes the others, because "... they must co-exist to create the atmosphere of poetic ambivalence on which the image of the play rests..1 In Pinter: A Study of His Plays, Martin Esslin mentions three levels of possible interpretation for Old Times. According to him, Pinter's play could be interpreted on a realistic level, or either representing the male character's dream or a ritual game. He correctly remarks, though, that none of those levels excludes the others, because "... they must co-exist to create the atmosphere of poetic ambivalence on which the image of the play rests..1
Ubiratan Paiva de Oliveira
2008-01-01
In Pinter: A Study of His Plays, Martin Esslin mentions three levels of possible interpretation for Old Times. According to him, Pinter's play could be interpreted on a realistic level, or either representing the male character's dream or a ritual game. He correctly remarks, though, that none of those levels excludes the others, because "... they must co-exist to create the atmosphere of poetic ambivalence on which the image of the play rests..1 In Pinter: A Study of His Plays, Martin Esslin ...
International Nuclear Information System (INIS)
Jia Zhenglin; Mei Dongcheng
2011-01-01
We numerically investigate the influences of the time delay τ simultaneously existing in both the deterministic and fluctuating forces, the time delay τ r existing only in the fluctuating force and the cross-correlation strength λ on the enhancement of the mean first-passage time (MFPT) as a function of the additive D and the multiplicative α noise intensities in a metastable system. The results indicate that both the multiplicative and additive noises can induce the noise-enhanced stability (NES) effect. An increase of λ can enhance or weaken the NES effect induced by the additive noise, depending on the value of τ. However, it weakens the NES effect induced by the multiplicative noise with a suppression of the effect of λ caused by increasing τ. The τ-induced critical behavior on both NES effects can be observed, i.e. an increase of τ can enhance or restrain the NES effects induced by the two kinds of noises. With an increase of λ and τ, MFPT versus D shows a transition from one peak to two peaks and finally one peak, implying the multiple NES effect caused by λ and τ. An increase of τ r can enhance the NES effect induced by the additive noise and weaken the NES effect induced by the multiplicative noise.
International Nuclear Information System (INIS)
Jia, Zheng-Lin; Mei, Dong-Cheng
2011-01-01
We investigate numerically the effects of time delay on the phenomenon of noise-enhanced stability (NES) in a periodically modulated bistable system. Three types of time-delayed feedback, including linear delayed feedback, nonlinear delayed feedback and global delayed feedback, are considered. We find a non-monotonic behaviour of the mean first-passage time (MFPT) as a function of the delay time τ, with a maximum in the case of linear delayed feedback and with a minimum in the case of nonlinear delayed feedback. There are two peculiar values of τ around which the NES phenomenon is enhanced or weakened. For the case of global delayed feedback, the increase of τ always weakens the NES phenomenon. Moreover, we also show that the amplitude A and the frequency Ω of the periodic forcing play an opposite role in the NES phenomenon, i.e. the increase of A weakens the NES effect while the increase of Ω enhances it. These observations demonstrate that the time-delayed feedback can be used as a feasible control scheme for the NES phenomenon
Exact decoherence dynamics of a single-mode optical field
International Nuclear Information System (INIS)
An, J.-H.; Yeo Ye; Oh, C.H.
2009-01-01
We apply the influence-functional method of Feynman and Vernon to the study of a single-mode optical field that interacts with an environment at zero temperature. Using the coherent-state formalism of the path integral, we derive a generalized master equation for the single-mode optical field. Our analysis explicitly shows how non-Markovian effects manifest in the exact decoherence dynamics for different environmental correlation time scales. Remarkably, when these are equal to or greater than the time scale for significant change in the system, the interplay between the backaction-induced coherent oscillation and the dissipative effect of the environment causes the non-Markovian effect to have a significant impact not only on the short-time behavior but also on the long-time steady-state behavior of the system.
Decoherence suppression of excitons by bang-bang control
International Nuclear Information System (INIS)
Kishimoto, T.; Hasegawa, A.; Mitsumori, Y.; Ishi-Hayase, J.; Sasaki, M.; Minami, F.
2007-01-01
We report the demonstration of decoherence control of excitons on a layered compound semiconductor GaSe by using successive three femtosecond pulses, i.e., the six-wave mixing configuration. The second pulse acts as a π pulse which reverses the time evolution of non-Markovian dynamics. By changing the pulse interval conditions, we confirmed for the first time the suppression of exciton decoherence by π pulse irradiation
Memory effects on stochastic resonance
Neiman, Alexander; Sung, Wokyung
1996-02-01
We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory.
... this page: //medlineplus.gov/ency/patientinstructions/000756.htm Time outs To use the sharing features on this ... children, 2 to 12 years old. Why Does Time out Work? When you put children in time ...
Three-dimensional photodissociation in strong laser fields: Memory-kernel effective-mode expansion
International Nuclear Information System (INIS)
Li Xuan; Thanopulos, Ioannis; Shapiro, Moshe
2011-01-01
We introduce a method for the efficient computation of non-Markovian quantum dynamics for strong (and time-dependent) system-bath interactions. The past history of the system dynamics is incorporated by expanding the memory kernel in exponential functions thereby transforming in an exact fashion the non-Markovian integrodifferential equations into a (larger) set of ''effective modes'' differential equations (EMDE). We have devised a method which easily diagonalizes the EMDE, thereby allowing for the efficient construction of an adiabatic basis and the fast propagation of the EMDE in time. We have applied this method to three-dimensional photodissociation of the H 2 + molecule by strong laser fields. Our calculations properly include resonance-Raman scattering via the continuum, resulting in extensive rotational and vibrational excitations. The calculated final kinetic and angular distribution of the photofragments are in overall excellent agreement with experiments, both when transform-limited pulses and when chirped pulses are used.
Kinetics of the Dynamical Information Shannon Entropy for Complex Systems
International Nuclear Information System (INIS)
Yulmetyev, R.M.; Yulmetyeva, D.G.
1999-01-01
Kinetic behaviour of dynamical information Shannon entropy is discussed for complex systems: physical systems with non-Markovian property and memory in correlation approximation, and biological and physiological systems with sequences of the Markovian and non-Markovian random noises. For the stochastic processes, a description of the information entropy in terms of normalized time correlation functions is given. The influence and important role of two mutually dependent channels of the entropy change, correlation (creation or generation of correlations) and anti-correlation (decay or annihilation of correlation) is discussed. The method developed here is also used in analysis of the density fluctuations in liquid cesium obtained from slow neutron scattering data, fractal kinetics of the long-range fluctuation in the short-time human memory and chaotic dynamics of R-R intervals of human ECG. (author)
Time Operators and Time Crystals
Nakatsugawa, K.; Fujii, T.; Saxena, A.; Tanda, S.
2017-01-01
We investigate time operators in the context of quantum time crystals in ring systems. We demonstrate that a self-adjoint time operator with a periodic time evolution can be derived for a free particle on a ring system: The conventional Aharonov-Bohm time operator is obtained by taking the infinite-radius limit. We also reveal the relationship between our time operator and a $\\mathcal PT$-symmetric time operator. We find that both time operators indeed describe the periodic time evolution of ...
DEFF Research Database (Denmark)
Bødker, Mads; Gimpel, Gregory; Hedman, Jonas
2014-01-01
time-in and time-out use. Time-in technology use coincides and co-exists within the flow of ordinary life, while time-out use entails ‘taking time out’ of everyday life to accomplish a circumscribed task or engage reflectively in a particular experience. We apply a theoretically informed grounded...
Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics
Iannuzzi, Marcella; Laio, Alessandro; Parrinello, Michele
2003-01-01
The possibility of observing chemical reactions in ab initio molecular dynamics runs is severely hindered by the short simulation time accessible. We propose a new method for accelerating the reaction process, based on the ideas of the extended Lagrangian and coarse-grained non-Markovian metady- namics. We demonstrate that by this method it is possible to simulate reactions involving complex atomic rearrangements and very large energy barriers in runs of a few picoseconds.
DEFF Research Database (Denmark)
Veraart, Almut; Winkel, Matthias
2010-01-01
The mathematical operation of time-changing continuous-time stochastic processes can be regarded as a standard method for building financial models. We briefly review the theory on time-changed stochastic processes and relate them to stochastic volatility models in finance. Popular models......, including time-changed Lévy processes, where the time-change process is given by a subordinator or an absolutely continuous time change, are presented. Finally, we discuss the potential and the limitations of using such processes for constructing multivariate financial models....
From a stochastic to a macroscopic approach to brownian motion
International Nuclear Information System (INIS)
Bocquet, L.
1998-01-01
In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)
DEFF Research Database (Denmark)
Nielsen, Morten
2017-01-01
This is a proposed special issue with six thematic articles by different contributors on 'urban times' edited by me.......This is a proposed special issue with six thematic articles by different contributors on 'urban times' edited by me....
A. van den Broek; W.P. Knulst; K. Breedveld
1999-01-01
Original title: Naar andere tijden? The report Different times? Time use and time structuring in the Netherlands, 1975-1995 (Naar andere tijden? Tijdsbesteding en tijdsordening in Nederland, 1975-1995) paints a picture of the way in which the Dutch spend the 168 hours that are available each
Newman, William L.
One of a series of general interest publications on science topics, the booklet provides those interested in geologic time with an introduction to the subject. Separate sections discuss the relative time scale, major divisions in geologic time, index fossils used as guides for telling the age of rocks, the atomic scale, and the age of the earth.…
Song, Ya-Ju; Tan, Qing-Shou; Kuang, Le-Man
2017-03-08
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).
Purcell, Conor
2018-05-01
Carlo Rovelli, best-selling author of Seven Brief Lessons on Physics, is back with a new book, The Order of Time. This latest venture offers insight into the notion of time, including narratives on how our understanding of the concept has changed from antiquity to the present, as well as a concise update on how time is understood today through the lens of quantum mechanics.
Collapse–revival of squeezing of two atoms in dissipative cavities
International Nuclear Information System (INIS)
Zou Hong-Mei; Fang Mao-Fa
2016-01-01
Based on the time-convolutionless master-equation approach, we investigate the squeezing dynamics of two atoms in dissipative cavities. We find that the atomic squeezing is related to initial atomic states, atom–cavity couplings, non-Markovian effects and resonant frequencies of an atom and its cavity. The results show that a collapse–revival phenomenon will occur in the atomic squeezing and this process is accompanied by the buildup and decay of entanglement between two atoms. Enhancing the atom–cavity coupling can increase the frequency of the collapse–revival of the atomic squeezing. The stronger the non-Markovian effect is, the more obvious the collapse–revival phenomenon is. In particular, if the atom–cavity coupling or the non-Markovian effect is very strong, the atomic squeezing will tend to a stably periodic oscillation in a long time. The oscillatory frequency of the atomic squeezing is dependent on the resonant frequency of the atom and its cavity. (paper)
Estimation of temperature in micromaser-type systems
Farajollahi, B.; Jafarzadeh, M.; Rangani Jahromi, H.; Amniat-Talab, M.
2018-06-01
We address the estimation of the number of photons and temperature in a micromaser-type system with Fock state and thermal fields. We analyze the behavior of the quantum Fisher information (QFI) for both fields. In particular, we show that in the Fock state field model, the QFI for non-entangled initial state of the atoms increases monotonously with time, while for entangled initial state of the atoms, it shows oscillatory behavior, leading to non-Markovian dynamics. Moreover, it is observed that the QFI, entropy of entanglement and fidelity have collapse and revival behavior. Focusing on each period that the collapses and revivals occur, we see that the optimal points of the QFI and entanglement coincide. In addition, when one of the subsystems evolved state fidelity becomes maximum, the QFI also achieves its maximum. We also address the evolved fidelity versus the initial state as a good witness of non-Markovianity. Moreover, we interestingly find that the entropy of the composite system can be used as a witness of non-Markovian evolution of the subsystems. For the thermal field model, we similarly investigate the relation among the QFI associated with the temperature, von Neumann entropy, and fidelity. In particular, it is found that at the instants when the maximum values of the QFI are achieved, the entanglement between the two-qubit system and the environment is maximized while the entanglement between the probe and its environment is minimized. Moreover, we show that the thermometry may lead to optimal estimation of practical temperatures. Besides, extending our computation to the two-qubit system, we find that using a two-qubit probe generally leads to more effective estimation than the one-qubit scenario. Finally, we show that initial state entanglement plays a key role in the advent of non-Markovianity and determination of its strength in the composite system and its subsystems.
Annemarie Wennekers; Frank Huysmans; Jos de Haan
2018-01-01
Original title: Lees:Tijd The amount of time that Dutch people spend reading has been declining steadily since the 1950s. This decline in reading time contrasts starkly with the positive personal and social benefits that can be derived from reading, according to lots of research. The Reading:
Prosser, Simon
2018-01-01
Our engagement with time is a ubiquitous feature of our lives. We are aware of time on many scales, from the briefest flicker of change to the way our lives unfold over many years. But to what extent does this encounter reveal the true nature of temporal reality? To the extent that temporal reality is as it seems, how do we come to be aware of it? And to the extent that temporal reality is not as it seems, why does it seem that way? These are the central questions addressed by Simon Prosser in Experiencing Time. These questions take on a particular importance in philosophy for two reasons. Firstly, there is a view concerning the metaphysics of time, known as the B-theory of time, according to which the apparently dynamic quality of change, the special status of the present, and even the passage of time are all illusions. Instead, the world is a four-dimensional space-time block, lacking any of the apparent dynamic features of time. If the B-theory is correct, as the book argues, then it must be explained why ...
Stoilov, Todor, Ed.
2012-01-01
The time management is worthy goal of many human activities. It concerns variety problems related to goals definition, assessment of available resources, control of management policies, scheduling of decisions. This book is an attempt to illustrate the decision making process in time management for different success stories, which can be used as…
DEFF Research Database (Denmark)
Thomsen, Bodil Marie Stavning
2011-01-01
The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations.......The article analyses some of artist Søren Lose's photographic installations in which time, history and narration is reflected in the creation of allegoric, spatial relations....
Ecosystems contain energy and materials such as carbon, nitrogen, phosphorus, and water, and are open to their flow-through. Turnover time refers to the amount of time required for replacement by flow-through of the energy or substance of interest contained in the system, and is ...
Directory of Open Access Journals (Sweden)
Luca Poncellini
2010-06-01
Full Text Available The analysis of natural phenomena applied to architectural planning and design is facing the most fascinating and elusive of the four dimensions through which man attempts to define life within the universe: time. We all know what time is, said St. Augustine, but nobody knows how to describe it. Within architectural projects and representations, time rarely appears in explicit form. This paper presents the results of a research conducted by students of NABA and of the Polytechnic of Milan with the purpose of representing time considered as a key element within architectural projects. Student investigated new approaches and methodologies to represent time using the two-dimensional support of a sheet of paper.
Age-dependent decay in the landscape
International Nuclear Information System (INIS)
Winitzki, Sergei
2008-01-01
The picture of the 'multiverse' arising in diverse cosmological scenarios involves transitions between metastable vacuum states. It was pointed out by Krauss and Dent that the transition rates decrease at very late times, leading to a dependence of the transition probability between vacua on the age of each vacuum region. I investigate the implications of this non-Markovian, age-dependent decay on the global structure of the spacetime in landscape scenarios. I show that the fractal dimension of the eternally inflating domain is precisely equal to 3, instead of being slightly below 3, which is the case in scenarios with purely Markovian, age-independent decay. I develop a complete description of a non-Markovian landscape in terms of a nonlocal master equation. Using this description I demonstrate by an explicit calculation that, under some technical assumptions about the landscape, the probabilistic predictions of our position in the landscape are essentially unchanged, regardless of the measure used to extract these predictions. I briefly discuss the physical plausibility of realizing non-Markovian vacuum decay in cosmology in view of the possible decoherence of the metastable quantum state.
Frank, Adam
2012-01-01
From Stonehenge to beyond the Big Bang, an exhilarating scientific exploration of how we make time Time is the grandest conception of the universe that we humans have been able to imagine and its most intimate, the very frame of human life. In About Time, astrophysicist and award-winning writer Adam Frank tells the scientific story of this wonderful and tyrannical invention. A Palaeolithic farmer moved through the sun-fuelled day and star-steered night in a radically different way than the Elizabethan merchants who set their pace to the clocks newly installed in their town squares. Since th
Energy Technology Data Exchange (ETDEWEB)
Kudaka, Shoju [Department of Physics, University of the Ryukyus, Okinawa 903-0129 (Japan); Matsumoto, Shuichi, E-mail: shuichi@edu.u-ryukyu.ac.jp [Department of Mathematics, University of the Ryukyus, Okinawa 903-0129 (Japan)
2012-10-01
The idea of a Larmor clock is reexamined in the relativistic regime. We propose a concept of proper time for quantum theoretical particles. The Larmor clock can measure, under some relevant conditions, the proper time that passes while the particle stays in a space region. Our approach to Larmor clock is different than those of other researchers in the following two aspects: our concept of Larmor clock does not distinguish whether the particle is transmitted or reflected at the end of its stay, and pointer of our Larmor clock is not the spin but the total angular momentum. -- Highlights: ► The idea of a Larmor clock is reexamined in the relativistic regime. ► We propose a concept of proper time for quantum theoretical particles. ► The Larmor clock measures the passage of this quantum theoretical proper time.
Directory of Open Access Journals (Sweden)
Populizio Ivan
2002-06-01
Full Text Available According to Einstein’s renowned declaration, for those who believe in physics – or, more precisely, in its capability to offer a “scientific” representation of the world – the distinction between present, past and future is just “an illusion, though obstinate”. If we consider an effective analogy by Mauro Dorato, we can state that those who agree with the famous German scientist will recognize in the present, past and future a relationship very similar to that between “here” and “somewhere else” – in other words, the present is just a located moment and has no privileged status. In other conceptual universes, some of which are explored by philosophy, or imagined by art, as well as in other scientific disciplines like biology, the need for a strong distinction between “what has happened”, “what will happen” and “what is happening” seems to be unavoidable. At the macroscopic level of living beings there does not seem to be a way out of the “eternal present”, which cannot be escaped even by the desire of some well-developed mammals to understand reality or such an apparently primary experience as the “passing of time”. Even the “timeless” description of reality offered by physics is immersed in time and changes with it. This paradox seems to contain the core of the irreducibility between two cultural constructions which we will be calling “the time of the soul” and “the time of the world”, after Ricoeur. The main thesis of this essay is that there are two fundamentally different ways of facing the mystery of time, which have a precise relationship with the mentioned contrast between the subjective and the objective conception of time – mental, qualitative and experienced in the first case; physical, quantitative and measurable in the second. Considering Ricoeur’s research on time and stories, we can conclude that this dichotomy may give rise to another similarly radical difference between
DEFF Research Database (Denmark)
Kothari, Ninad B.; Wohlgemuth, Melville J.; Hulgard, Katrine
2014-01-01
To successfully negotiate a cluttered environment, an echolocating bat must control the timing of motor behaviors in response to dynamic sensory information. Here we detail the big brown bat's adaptive temporal control over sonar call production for tracking prey, moving predictably or unpredicta...
Gabbert, Silke; Hilber, Isabel
2016-01-01
A core aim of the European chemicals legislation REACH is to ensure that the risks caused by substances of very high concern (SVHC) are adequately controlled. Authorisation – i.e. the formal approval of certain uses of SVHC for a limited time - is a key regulatory instrument in order to achieve
DEFF Research Database (Denmark)
Brichet, Nathalia Sofie
2018-01-01
Based on anthropological fieldwork in Greenland, I explore how rubies as a natural resource create and organise forms of temporality in order for the stones to appear as a valuable good. I suggest that a circular argument is at play with regard to the Greenlandic rubies, namely that time creates ...... embedded in and generated through social practices. Accordingly, time in relation to mining does not so much present a philosophical challenge, but is rather just a “thing” that happens to be good to think a Greenlandic resource landscape through – as are rubies.......Based on anthropological fieldwork in Greenland, I explore how rubies as a natural resource create and organise forms of temporality in order for the stones to appear as a valuable good. I suggest that a circular argument is at play with regard to the Greenlandic rubies, namely that time creates...... valuable rubies and rubies create time. I further argue that this interdependence is an important self-fulfilling driver in creating a viable mining industry for gemstones in Greenland. A focus on temporality enables me to engage in this circularity and thereby explore one component in the work of making...
DEFF Research Database (Denmark)
Andreasen, Karen Egedal; Rasmussen, Annette
such as the PISA studies, and tendencies in educational politics and schoolsystems in Europe, USA, Australia and Asia. This spring (2011) all danish pupils in grade 6. has been tested nationally for the first time in reading skills and mathematics. The argumentation behind the initiative points to both economical...
Hanus, Filip
2016-01-01
The diploma thesis applies to issues and methods of time management at work of ČSOB, a.s. managers in western area of the Czech Republic. The thesis is devided into two basic parts. First part is theoretical and methodological, second part contains of impractical research using questionnaires investigation and controlled conversation. First part of the thesis describes theoretical anchoring of the topic including methods of gathering data. Second part shortly introduces particular company and...
Lušina, Barbara
2011-01-01
Leisure is an important part of our lives that we are left with after completing commitments - school, vocational, social, family. It is important because it gives us happiness, freedom, relaxation, helps us to feel better and allows personal growth and development. In the theoretical part well-defined leisure is presented, with its main functions, various activities, principles of exploitation and factors that affect leisure. The thesis also includes description of ranking free time in the ...
2015-06-01
13 published papers , and 8 technical reports. All of these publications are available through password-protected access at: http...additional Ph.D. thesis on hardware hiding has been completed, together with an additional paper ; thesis preparation is in progress. In addition, this...employing microcontrollers and other real-time processors. These devices typically lack memory management and make little to no use of cache. • Dynamic
Dutton, Michael; Lo, Hsiu-ju Stacy; Wu, Dong Dong
2010-01-01
“Where is the market?” inquires the tourist one dark, chilly morning. “Follow the ghosts,” responds the taxi driver, indicating a shadowy parade of overloaded tricycles. “It’s not called the ghost market for nothing!” And indeed, Beijing is nothing if not haunted. Among the soaring skyscrapers, choking exhaust fumes, nonstop traffic jams, and towering monuments, one discovers old Beijing—newly styled, perhaps, but no less present and powerful than in its ancient incarnation. Beijing Time cond...
Gryb, Sean; Thebault, Karim
2014-01-01
On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of change as relative variation leads to a fundamentally timeless formalism for quantum gravity. Here, we will show how one may avoid this acute 'problem of time'. Under our view, duration is still regarded as relative, but te...
Schnell, J D
2006-01-01
L'unité a pour but de normaliser en signe, en largeur et en amplitude les signaux de timing destinés à être acquis par les DPRAM. Les signaux d'origine, reçus en format blocking (30V), ou TTL (logique positive ou négative) sont transmis en mode différentiel au DPRAM. En option, ils peuvent être transmis parallèlement sur un tiroir auxiliaire lequel redistribue ces signaux aux fins de tests sur son panneau avant.
Lockwood, Dean
2012-01-01
The âCloudâ, hailed as a new digital commons, a utopia of collaborative expression and constant connection, actually constitutes a strategy of vitalist post-hegemonic power, which moves to dominate immanently and intensively, organizing our affective political involvements, instituting new modes of enclosure, and, crucially, colonizing the future through a new temporality of control. The virtual is often claimed as a realm of invention through which capitalism might be cracked, but it is precisely here that power now thrives. Cloud time, in service of security and profit, assumes all is knowable. We bear witness to the collapse of both past and future virtuals into a present dedicated to the exploitation of the spectres of both.
Yang, Suzanne; Kadouri, Alane; Révah-Lévy, Anne; Mulvey, Edward P.; Falissard, Bruno
2009-01-01
Once convicted, the perpetrator of serious crime embarks upon a new journey: the challenge of adjusting to long-term imprisonment. Prisoners’ views of incarceration and the meaning of this experience may affect their later adjustment to life in the community. On the basis of brief narrative responses collected during an epidemiological survey of the psychological health of prisoners in France, this study examined the impact of incarceration on psychological state in a group of 59 inmates serving long sentences. Qualitative content analysis and computer-assisted linguistic analysis (using ALCESTE software) were performed on the textual data of open responses to three standard questions. Using a combination of these two approaches, seven categories of the subjective experience of prisoners in the sample were identified: the Outside World, Others, Punishment, Time, Affects and Impulses, Self-Concept, and Speech. Further qualitative analyses were then performed to compare the responses of Severely Mentally Ill (SMI) subjects and subjects with no psychiatric disorder. These analyses revealed contrasting attitudes towards incarceration. SMI subjects spoke in more hostile and persecutory terms about their experience in prison, attributing suffering to external circumstances, while subjects with no psychiatric disorder evoked similar themes, but with an introspective attitude. The themes evoked by mentally ill individuals in our sample suggest that their reactions to the prison environment arise in part from aspects of their psychiatric symptoms, and this may have relevance to future mental health policy and practices in criminal corrections. PMID:19619895
Process algebra with timing : real time and discrete time
Baeten, J.C.M.; Middelburg, C.A.; Bergstra, J.A.; Ponse, A.J.; Smolka, S.A.
2001-01-01
We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point is a new real time version with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete
Process algebra with timing: Real time and discrete time
Baeten, J.C.M.; Middelburg, C.A.
1999-01-01
We present real time and discrete time versions of ACP with absolute timing and relative timing. The startingpoint is a new real time version with absolute timing, called ACPsat , featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete
Probability of Failure in Random Vibration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
1988-01-01
Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out......-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passage probability...
Plasma production and thermalisation in a strong field
International Nuclear Information System (INIS)
Vinnik, D.V.; Schmidt, S.M.; Prozorkevich, A.V.; Smolyansky, S.A.; Toneev, V.D.; Hecht, M.B.; Roberts, C.D.
2001-01-01
Aspects of the formation and equilibration of a quark-gluon plasma are explored using a quantum kinetic equation, which involves a non-Markovian, Abelian source term for quark and antiquark production and, for the collision term, a relaxation time approximation that defines a time-dependent quasi-equilibrium temperature and collective velocity. The strong Abelian field is determined via the simultaneous solution of Maxwell's equation. A particular feature of this approach is the appearance of plasma oscillations in all thermodynamic observables. Their presence can lead to a sharp increase in the time-integrated dilepton yield, although a rapid expansion of the plasma may eliminate this signal. (orig.)
Revealing virtual processes of a quantum Brownian particle in phase space
International Nuclear Information System (INIS)
Maniscalco, S
2005-01-01
The short-time dynamics of a quantum Brownian particle in a harmonic potential is studied in phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analysed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short-time dynamics where system-reservoir correlations are not negligible, show up in phase space
Temporal organization of cellular self-replication
Alexandrov, Victor; Pugatch, Rami
Recent experiments demonstrate that single cells grow exponentially in time. A coarse grained model of cellular self-replication is presented based on a novel concept - the cell is viewed as a self-replicating queue. This allows to have a more fundamental look into various temporal organizations and, importantly, the inherent non-Markovianity of noise distributions. As an example, the distribution of doubling times can be inferred and compared to single cell experiments in bacteria. We observe data collapse upon scaling by the average doubling time for different environments and present an inherent task allocation trade-off. Support from the Simons Center for Systems Biology, IAS, Princeon.
Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.
2011-09-01
A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.
Memory effects in single-molecule spectroscopy
International Nuclear Information System (INIS)
Schmitt, Daniel T.; Schulz, Michael; Reineker, Peter
2007-01-01
From the time series of LH2 optical single-molecule fluorescence excitation spectra of Rhodospirillum molischianum the memory function of the Mori-Zwanzig equation for the optical intensity is derived numerically. We show that the time dependence of the excited states is determined by at least three different non-Markovian stochastic processes with decay constants for the Mori-Zwanzig kernel on the order of 1-5min -1 . We suggest that this decay stems from the conformational motion of the protein scaffold of LH2
Energy Technology Data Exchange (ETDEWEB)
Uchiyama, Yusuke, E-mail: r1230160@risk.tsukuba.ac.jp; Konno, Hidetoshi
2014-04-01
Defect turbulence described by the one-dimensional complex Ginzburg–Landau equation is investigated and analyzed via a birth–death process of the local structures composed of defects, holes, and modulated amplitude waves (MAWs). All the number statistics of each local structure, in its stationary state, are subjected to Poisson statistics. In addition, the probability density functions of interarrival times of defects, lifetimes of holes, and MAWs show the existence of long-memory and some characteristic time scales caused by zigzag motions of oscillating traveling holes. The corresponding stochastic process for these observations is fully described by a non-Markovian master equation.
International Nuclear Information System (INIS)
Doering, C.R.; Bagley, R.J.; Hagan, P.S.; Levermore, C.D.
1988-01-01
A reply to the comment on bistability driven by weakly colored gaussian noise is presented.The fokker-planck boundary layer and mean first-passage times are evaluated.It is agreed that there is a difference between the two first-passage times, and that alternative may be more appropriate for quantitative comparison with the low lying spectrum of the Fokker-Planck operator
Time in contemporary cosmology
International Nuclear Information System (INIS)
Mavrides, Stamatia
1980-01-01
Cosmological time is defined, as is coordinated universal time against local times of special relativity. The problems of time and matter, age of the universe, Goedel models, arrow of time, are also discussed [fr
... sharing on social media links Babies Need Tummy Time! Page Content Tummy Time is not only an ... of your baby’s normal growth. What Is Tummy Time? Tummy Time describes the times when you place ...
Continuous-variable quantum teleportation in bosonic structured environments
Energy Technology Data Exchange (ETDEWEB)
He Guangqiang; Zhang Jingtao; Zhu Jun; Zeng Guihua [State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240 (China)
2011-09-15
The effects of dynamics of continuous-variable entanglement under the various kinds of environments on quantum teleportation are quantitatively investigated. Only under assumption of the weak system-reservoir interaction, the evolution of teleportation fidelity is analytically derived and is numerically plotted in terms of environment parameters including reservoir temperature and its spectral density, without Markovian and rotating wave approximations. We find that the fidelity of teleportation is a monotonically decreasing function for Markovian interaction in Ohmic-like environments, while it oscillates for non-Markovian ones. According to the dynamical laws of teleportation, teleportation with better performances can be implemented by selecting the appropriate time.
Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process
International Nuclear Information System (INIS)
Skorobogatov, G.A.; Svertilov, S.I.
1999-01-01
The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru
Amnestically Induced Persistence in Random Walks
Cressoni, J. C.; da Silva, Marco Antonio Alves; Viswanathan, G. M.
2007-02-01
We study how the Hurst exponent α depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker’s position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer’s disease and other dementias.
Correlation effects in a discrete quantum random walk
International Nuclear Information System (INIS)
Stang, J B; Rezakhani, A T; Sanders, B C
2009-01-01
We introduce memory-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying the Hamiltonian of the walker to include couplings with memory-keeping agents. We next study numerically the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence non-Markovian) effects. Our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms
Transcriptional delay stabilizes bistable gene networks.
Gupta, Chinmaya; López, José Manuel; Ott, William; Josić, Krešimir; Bennett, Matthew R
2013-08-02
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner.
One- and two-body dissipation in peripheral heavy ion collisions
International Nuclear Information System (INIS)
Bartel, J.; Feldmeier, H.
1980-01-01
For peripheral collisions of heavy ions we solve the man-body Schroedinger equation in second order time-dependent perturbation theory. The two nuclei interact via a two-body interaction of finite range. With controllable approximations we get to a sensible comparison between 1p-1h excitations caused by the coherent Hartree part and direct 2p-2h excitations both created by the same two-body interaction. The results of the calculation show that for peripheral collisions almost all excitation energy originates from one-body dissipation. Furthermore we encounter large virtual excitations during the collision indicating a non Markovian process. (orig.)
'Stutter timing' for charge decay time measurement
International Nuclear Information System (INIS)
Chubb, John; Harbour, John; Pavey, Ian
2011-01-01
The paper describes the approach of 'stutter timing' that has been developed to improve the accuracy of measuring charge decay times in the presence of noise in compact and portable charge decay test instrumentation. The approach involves starting and stopping the timing clock as the noisy signal rises above and falls below the target threshold voltage level.
Scheduling with time-dependent execution times
Woeginger, G.J.
1995-01-01
We consider systems of tasks where the task execution times are time-dependent and where all tasks have some common deadline. We describe how to compute in polynomial time a schedule that minimizes the number of late tasks. This answers a question raised in a recent paper by Ho, Leung and Wei.
Multiplexing real-time timed events
Holenderski, M.J.; Cools, W.A.; Bril, R.J.; Lukkien, J.J.
2009-01-01
This paper presents the design and implementation of RELTEQ, a timed event management algorithm based on relative event times, supporting long event interarrival time, long lifetime of the event queue, no drift and low overhead. It is targeted at embedded operating systems. RELTEQ has been conceived
PT; Pro-time; Anticoagulant-prothrombin time; Clotting time: protime; INR; International normalized ratio ... PT is measured in seconds. Most of the time, results are given as what is called INR ( ...
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
Directory of Open Access Journals (Sweden)
Richard P Mann
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
Multi-scale inference of interaction rules in animal groups using Bayesian model selection.
Directory of Open Access Journals (Sweden)
Richard P Mann
2012-01-01
Full Text Available Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis. We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.
Badr, Salah M.; Bruztman, Donald P.; Nelson, Michael L.; Byrnes, Ronald Benton
1992-01-01
This paper presents an introduction to the basic issues involved in real-time systems. Both real-time operating sys and real-time programming languages are explored. Concurrent programming and process synchronization and communication are also discussed. The real-time requirements of the Naval Postgraduate School Autonomous Under Vehicle (AUV) are then examined. Autonomous underwater vehicle (AUV), hard real-time system, real-time operating system, real-time programming language, real-time sy...
Evaluating Distributed Timing Constraints
DEFF Research Database (Denmark)
Kristensen, C.H.; Drejer, N.
1994-01-01
In this paper we describe a solution to the problem of implementing time-optimal evaluation of timing constraints in distributed real-time systems.......In this paper we describe a solution to the problem of implementing time-optimal evaluation of timing constraints in distributed real-time systems....
Zeng, Lunwu; Xu, Jin; Wang, Chengen; Zhang, Jianhua; Zhao, Yuting; Zeng, Jing; Song, Runxia
2017-12-07
When space (time) translation symmetry is spontaneously broken, the space crystal (time crystal) forms; when permittivity and permeability periodically vary with space (time), the photonic crystal (photonic time crystal) forms. We proposed the concept of photonic time crystal and rewritten the Maxwell's equations. Utilizing Finite Difference Time Domain (FDTD) method, we simulated electromagnetic wave propagation in photonic time crystal and photonic space-time crystal, the simulation results show that more intensive scatter fields can obtained in photonic time crystal and photonic space-time crystal.
Gap timing and the spectral timing model.
Hopson, J W
1999-04-01
A hypothesized mechanism underlying gap timing was implemented in the Spectral Timing Model [Grossberg, S., Schmajuk, N., 1989. Neural dynamics of adaptive timing and temporal discrimination during associative learning. Neural Netw. 2, 79-102] , a neural network timing model. The activation of the network nodes was made to decay in the absence of the timed signal, causing the model to shift its peak response time in a fashion similar to that shown in animal subjects. The model was then able to accurately simulate a parametric study of gap timing [Cabeza de Vaca, S., Brown, B., Hemmes, N., 1994. Internal clock and memory processes in aminal timing. J. Exp. Psychol.: Anim. Behav. Process. 20 (2), 184-198]. The addition of a memory decay process appears to produce the correct pattern of results in both Scalar Expectancy Theory models and in the Spectral Timing Model, and the fact that the same process should be effective in two such disparate models argues strongly that process reflects a true aspect of animal cognition.
Shackle in time - time in Shackle
DEFF Research Database (Denmark)
Madsen, Mogens Ove
2015-01-01
GLS Shackle got much and the crucial inspiration from John Maynard Keynes. But that's not all. He took a number of further consequences of Keynes’ thoughts. This implies for example ideal claims to economists - having to deal with both mechanical time and expectational time. In consequence the idea...
Intelligence, Inspection Time, and Decision Time.
Bates, Timothy C.; Eysenck, Hans J.
1993-01-01
Relationships among Multidimensional Aptitude Battery scores, inspection time, choice reaction time, and the odd-man procedure were investigated for 63 female and 25 male adults. No significant relationships were found for these mental speed measures and the Eysenck Personality Questionnaire-Revised dimensions of extraversion, neuroticism, and…
Choosing between his time and her time?
DEFF Research Database (Denmark)
Deding, Mette; Lausten, Mette
When adding up market work and non-market work, Danish men and women work about the same number of hours per day. While men do the major share of the market work, women do the major share of the non-market work. In this paper, we investigate the interaction between the different time use activities...... spouses. This is especially the case for market work and housework, while childcare is different. Thus, when considering labour supply the total workload must be taken into account. Furthermore, the interdependence between the spouses’ working hours suggests that bargaining is taking place...... for Danish working couples. The analysis is based on the Danish Time Use Survey from 2001, which contains detailed time use information for both spouses. We analyse the time used by each spouse on market work and non-market work, taking the endogeneity of time regressors into account. Non-market work...
Sacha, Krzysztof; Zakrzewski, Jakub
2018-01-01
Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals—the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek’s idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.
... page: //medlineplus.gov/ency/patientinstructions/000355.htm Screen time and children To use the sharing features on ... videos is considered unhealthy screen time. Current Screen Time Guidelines Children under age 2 should have no ...
Is Time Predictability Quantifiable?
DEFF Research Database (Denmark)
Schoeberl, Martin
2012-01-01
Computer architects and researchers in the realtime domain start to investigate processors and architectures optimized for real-time systems. Optimized for real-time systems means time predictable, i.e., architectures where it is possible to statically derive a tight bound of the worst......-case execution time. To compare different approaches we would like to quantify time predictability. That means we need to measure time predictability. In this paper we discuss the different approaches for these measurements and conclude that time predictability is practically not quantifiable. We can only...... compare the worst-case execution time bounds of different architectures....
Raju, C. K.
1991-01-01
A study of time in Newtonian physics is presented. Newton's laws of motion, falsifiability and physical theories, laws of motion and law of gravitation, and Laplace's demon are discussed. Short bibliographic sketches of Laplace and Karl Popper are included. (KR)
Time flies faster under time pressure.
Rattat, Anne-Claire; Matha, Pauline; Cegarra, Julien
2018-04-01
We examined the effects of time pressure on duration estimation in a verbal estimation task and a production task. In both temporal tasks, participants had to solve mazes in two conditions of time pressure (with or without), and with three different target durations (30 s, 60 s, and 90 s). In each trial of the verbal estimation task, participants had to estimate in conventional time units (minutes and seconds) the amount of time that had elapsed since they started to solve the maze. In the production task, they had to press a key while solving the maze when they thought that the trial's duration had reached a target value. Results showed that in both tasks, durations were judged longer with time pressure than without it. However, this temporal overestimation under time pressure did not increase with the length of the target duration. These results are discussed within the framework of scalar expectancy theory. Copyright © 2018 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Wheeler, J.A.
1979-01-01
The author discusses the double-slit experiment and the problem of whether one can choose whether the photon shall have come through both of the slits, or only one of them, after it has already transversed the screen. A proper quantum concept of correlation is formalised as it depends on time. It takes the existence of the dynamic entity under study and the concept of time for granted, and does not transcend the concept of time. Time is absolute and universal in Newtonian physics and in special relativity successive times correspond to successive slices through space-time. Many fingured time is discussed in this context. The concepts of transcending time, causal order without causal order, asymmetry in time and the expansion of the universe, memory and the arrow of time, and the gates of time are all considered. (Auth./C.F.)
Directory of Open Access Journals (Sweden)
Johann-Albrecht Meylahn
2015-06-01
Full Text Available Maybe, before we speak of time, or maybe whilst we are speaking of time, or maybe after we have spoken of time, in the various modes of time’s insistence to exist, one should give time to the talk of time. There are various different modes of time’s insistence to exist, such as quantum physics in conversation with relativity theory where time is constructed as a fourth dimension of space. Or there are the modes of time in history, religion, psychology and philosophy, and each of these modes is composed, and composes its own specific object called time, and a particular subject who understands and interprets time in that particular mode. Yet, before, whilst or after these modes of time’s insistence to exist, one should maybe give time to time’s time. Give time for the various times to articulate themselves in the various modes of existence, thereby creating both a whole plurality of differing subjects, as well as plurality of differing objects, all called ‘time’. Once time has been given time to talk its talk, to articulate itself within the various modes, it will be interrupted by the articulations of time in various modes of time still to come. These disruptions of time by time always still to come opens the door for a theological narrative – a narrative on time, but created by the coming of messianic times, interpreted in the mode of hope but also in the mode of a promise from the past.
McEwan, Anna E.
2012-01-01
This essay invites reflection on the phenomena of time as it impacts the day-to-day life of teachers. It also explores assumptions about time and teaching in three areas: first, beliefs about the force of time and the teacher's struggle to control it; second, beliefs about the potential of time and the benefits of its passing for teachers and…
Perceptions of Time and Long Time Intervals
Energy Technology Data Exchange (ETDEWEB)
Drottz-Sjoeberg, Britt-Marie [Norwegian Univ. of Science and Technology, Trondheim (Norway). Dept. of Psychology
2006-09-15
There are certainly many perspectives presented in the literature on time and time perception. This contribution has focused on perceptions of the time frames related to risk and danger of radiation from a planned Swedish repository for spent nuclear fuel. Respondents from two municipalities judged SSI's reviews of the entrepreneur's plans and work of high importance, and more important the closer to our time the estimate was given. Similarly were the consequences of potential leakage from a repository perceived as more serious the closer it would be to our time. Judgements of risks related to the storage of spent nuclear fuel were moderately large on the used measurement scales. Experts are experts because they have more knowledge, and in this context they underlined e.g. the importance of reviews of the radiation situation of time periods up to 100,000 years. It was of interest to note that 55% of the respondents from the municipalities did not believe that the future repository would leak radioactivity. They were much more pessimistic with respect to world politics, i.e. a new world war. However, with respect to the seriousness of the consequences given a leakage from the repository, the public group consistently gave high risk estimates, often significantly higher than those of the expert group. The underestimations of time estimates, as seen in the tasks of pinpointing historic events, provide examples of the difficulty of making estimations involving long times. Similar results showed that thinking of 'the future' most often involved about 30 years. On average, people reported memories of about 2.5 generations back in time, and emotional relationships stretching approximately 2.5 generations into the future; 94% of the responses, with respect to how many future generations one had an emotional relationship, were given in the range of 1-5 generations. Similarly, Svenson and Nilsson found the opinion that the current generations
Perceptions of Time and Long Time Intervals
International Nuclear Information System (INIS)
Drottz-Sjoeberg, Britt-Marie
2006-01-01
There are certainly many perspectives presented in the literature on time and time perception. This contribution has focused on perceptions of the time frames related to risk and danger of radiation from a planned Swedish repository for spent nuclear fuel. Respondents from two municipalities judged SSI's reviews of the entrepreneur's plans and work of high importance, and more important the closer to our time the estimate was given. Similarly were the consequences of potential leakage from a repository perceived as more serious the closer it would be to our time. Judgements of risks related to the storage of spent nuclear fuel were moderately large on the used measurement scales. Experts are experts because they have more knowledge, and in this context they underlined e.g. the importance of reviews of the radiation situation of time periods up to 100,000 years. It was of interest to note that 55% of the respondents from the municipalities did not believe that the future repository would leak radioactivity. They were much more pessimistic with respect to world politics, i.e. a new world war. However, with respect to the seriousness of the consequences given a leakage from the repository, the public group consistently gave high risk estimates, often significantly higher than those of the expert group. The underestimations of time estimates, as seen in the tasks of pinpointing historic events, provide examples of the difficulty of making estimations involving long times. Similar results showed that thinking of 'the future' most often involved about 30 years. On average, people reported memories of about 2.5 generations back in time, and emotional relationships stretching approximately 2.5 generations into the future; 94% of the responses, with respect to how many future generations one had an emotional relationship, were given in the range of 1-5 generations. Similarly, Svenson and Nilsson found the opinion that the current generations' general responsibility for
Mayato, R; Egusquiza, I
2002-01-01
The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.
Directory of Open Access Journals (Sweden)
Balbi Amedeo
2013-09-01
Full Text Available Time has always played a crucial role in cosmology. I review some of the aspects of the present cosmological model which are more directly related to time, such as: the definition of a cosmic time; the existence of typical timescales and epochs in an expanding universe; the problem of the initial singularity and the origin of time; the cosmological arrow of time.
MARES VALERICA; MARES MARIUS DANIEL
2014-01-01
The efficient management of time is essential in any profession and in any activity domain. Anybody can increase his capacity to organize his time and get important benefits from it. The way in which one organizes his time will always have a direct impact on the objects of his work (resources and activities), so that it is worth allocating time for developing some instruments and techniques that could help planning and organizing time efficiently and attaining the objectives while meeting the...
Iliopoulos, Nikos; Thanopulos, Ioannis; Yannopapas, Vassilios; Paspalakis, Emmanuel
2018-03-01
We study the spontaneous emission of a two-level quantum emitter next to a plasmonic nanoparticle beyond the Markovian approximation and the rotating-wave approximation (RWA) by combining quantum dynamics and classical electromagnetic calculations. For emitters with decay times in the picosecond to nanosecond time regime, as well as located at distances from the nanoparticle up to its radius, the dynamics with and without the RWA and the transition from the non-Markovian to the Markovian regime are investigated. For emitters with longer decay times, the Markov approximation proves to be adequate for distances larger than half the nanoparticle radius. However, the RWA is correct for all distances of the emitter from the nanoparticle. For short decay time emitters, the Markov approximation and RWA are both inadequate, with only the RWA becoming valid again at a distance larger than half the nanoparticle radius. We also show that the entanglement dynamics of two initially entangled qubits interacting independently with the nanoparticle may have a strong non-Markovian character when counter-rotating effects are included. Interesting effects such as entanglement sudden death, periodic entanglement revival, entanglement oscillations, and entanglement trapping are further observed when different initial two-qubit states and different distances between the qubit and the nanoparticle are considered.
Atomic theory of viscoelastic response and memory effects in metallic glasses
Cui, Bingyu; Yang, Jie; Qiao, Jichao; Jiang, Minqiang; Dai, Lanhong; Wang, Yun-Jiang; Zaccone, Alessio
2017-09-01
An atomic-scale theory of the viscoelastic response of metallic glasses is derived from first principles, using a Zwanzig-Caldeira-Leggett system-bath Hamiltonian as a starting point within the framework of nonaffine linear response to mechanical deformation. This approach provides a generalized Langevin equation (GLE) as the average equation of motion for an atom or ion in the material, from which non-Markovian nonaffine viscoelastic moduli are extracted. These can be evaluated using the vibrational density of states (DOS) as input, where the boson peak plays a prominent role in the mechanics. To compare with experimental data for binary ZrCu alloys, a numerical DOS was obtained from simulations of this system, which also take electronic degrees of freedom into account via the embedded-atom method for the interatomic potential. It is shown that the viscoelastic α -relaxation, including the α -wing asymmetry in the loss modulus, can be very well described by the theory if the memory kernel (the non-Markovian friction) in the GLE is taken to be a stretched-exponential decaying function of time. This finding directly implies strong memory effects in the atomic-scale dynamics and suggests that the α -relaxation time is related to the characteristic time scale over which atoms retain memory of their previous collision history. This memory time grows dramatically below the glass transition.
Time and timing in vehicle routing problems
Jabali, O.
2010-01-01
The distribution of goods to a set of geographically dispersed customers is a common problem faced by carrier companies, well-known as the Vehicle Routing Problem (VRP). The VRP consists of finding an optimal set of routes that minimizes total travel times for a given number of vehicles with a fixed
Reichenbach, Hans
1999-01-01
Ever a source of philosophical conjecture and debate, the concept of time represents the beating heart of physics. This final work by the distinguished physicist Hans Reichenbach represents the culmination and integration of a lifetime's philosophical contributions and inquiries into the analysis of time. The result is an outstanding overview of such qualitative, or topological, attributes of time as order and direction.Beginning with a discussion of the emotive significance of time, Reichenbach turns to an examination of the time order of mechanics, the time direction of thermodynamics and m
Revealing electronic open quantum systems with subsystem TDDFT
Krishtal, Alisa; Pavanello, Michele
2016-03-01
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
Revealing electronic open quantum systems with subsystem TDDFT.
Krishtal, Alisa; Pavanello, Michele
2016-03-28
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
Perturbation expansions of stochastic wavefunctions for open quantum systems
Ke, Yaling; Zhao, Yi
2017-11-01
Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.
DEFF Research Database (Denmark)
Elkind, David; Rinaldi, Carla; Flemmert Jensen, Anne
Proceedings from the conference "Children, Time, and Play". Danish University of Education, January 30th 2003.......Proceedings from the conference "Children, Time, and Play". Danish University of Education, January 30th 2003....
Time Discretization Techniques
Gottlieb, S.; Ketcheson, David I.
2016-01-01
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include
International Nuclear Information System (INIS)
Winans, J.
1994-01-01
The purpose of this document is to augment Synchronized Time Stamp Support authored by Jim Kowalkowski. This document provides additional documentation to clarify and explain software involved in timing operations of the accelerator
International Nuclear Information System (INIS)
Wang, Z.S.; Lai, C.H.; Oh, C.H.; Kwek, L.C.
2004-01-01
We present a calculation of quantum tunneling time based on the transition duration of wave peak from one side of a barrier to the other. In our formulation, the tunneling time comprises a real and an imaginary part. The real part is an extension of the phase tunneling time with quantum corrections whereas the imaginary time is associated with energy derivatives of the probability amplitudes
Forsyth, Patrick
2016-01-01
Packed with tips and techniques, Successful Time Management serves as a guide to reviewing and assessing new work practices to improve time management. It includes great time-saving ideas, practical solutions, checklists, and advice on controlling paperwork, delegating and working with others, prioritizing to focus on key issues, and getting and staying organized. This new third edition contains new practical tips on using email in a time effective manner and dealing with other internet-based tools and apps to help productivity.
Time management and procrastination
van Eerde, W.; Mumford, M.D.; Frese, M.
2015-01-01
This chapter combines the topics time management and procrastination. Time management is an overarching term derived from popular notions on how to be effective at work. Procrastination has been mainly researched from a personality perspective, addressing the emotional and psychological issues of the phenomenon in more detail. First, I describe time management and procrastination, and next I address interventions that may help people in overcoming procrastination. Studies on time management s...
Measuring Business Cycle Time.
Stock, James H
1987-01-01
The business cycle analysis of Arthur F. Burns and Wesley C. Mitchell and the National Bureau of Economic Research presumed that aggregate economic variables evolve on a time scale defined by business cycle turning points rather than by months or quarters. Do macroeconomic variables appear to evolve on an economic rather than a calendar time scale? Evidence presented here suggests that they do. However, the estimated economic time scales are only weakly related to business cycle time scales, ...
Chiu, Chih-Hao; Lei, Kin Fong; Yeh, Wen-Ling; Chen, Poyu; Chan, Yi-Sheng; Hsu, Kuo-Yao; Chen, Alvin Chao-Yu
2017-10-16
Local injections of anesthetics, NSAIDs, and corticosteroids for tendinopathies are empirically used. They are believed to have some cytotoxicity toward tenocytes. The maximal efficacy dosages of local injections should be determined. A commercial 2D microfluidic xCELLigence system had been developed to detect real-time cellular proliferation and their responses to different stimuli and had been used in several biomedical applications. The purpose of this study is to determine if human tenocytes can successfully proliferate inside xCELLigence system and the result has high correlation with conventional cell culture methods in the same condition. First passage of human tenocytes was seeded in xCELLigence and conventional 24-well plates. Ketorolac tromethamine, bupivacaine, methylprednisolone, and betamethasone with different concentrations (100, 50, and 10% diluted of clinical usage) were exposed in both systems. Gene expression of type I collagen, type III collagen, tenascin-C, decorin, and scleraxis were compared between two systems. Human tenocytes could proliferate both in xCELLigence and conventional cell culture systems. Cytotoxicity of each drug revealed dose-dependency when exposed to tenocytes in both systems. Significance was found between groups. All the four drugs had comparable cytotoxicity in their 100% concentration. When 50% concentration was used, betamethasone had a relatively decreased cytotoxicity among them in xCELLigence but not in conventional culture. When 10% concentration was used, betamethasone had the least cytotoxicity. Strong and positive correlation was found between cell index of xCELLigence and result of WST-1 assay (Pearson's correlation [r] = 0.914). Positive correlation of gene expression between tenocytes in xCELLigence and conventional culture was also observed. Type I collagen: [r] = 0.823; type III collagen: [r] = 0.899; tenascin-C: [r] = 0.917; decorin: [r] = 0.874; and scleraxis: [r] = 0.965. Human
Buying time promotes happiness
Whillans, Ashley; Dunn, Elizabeth; Smeets, Paul M.; Bekkers, R.H.F.P.; Norton, M.I.
2017-01-01
Around the world, increases in wealth have produced an unintended consequence: a rising sense of time scarcity. We provide evidence that using money to buy time can provide a buffer against this time famine, thereby promoting happiness. Using large, diverse samples from the United States, Canada,
Geber, Beverly
1987-01-01
More employees are choosing to work part time. Although this trend started because of working women, some men are choosing part-time positions. Part-time employees forfeit salary and promotion potential, yet most feel the trade is fair and that they are more productive during their working hours. (CH)
2016-08-01
Knowingly or not, people generally place economic value on their time. Wage workers are paid a rate per hour, and service providers may charge per hour of their time. In the transportation realm, travelers place a value on their travel time and have ...
International Nuclear Information System (INIS)
Moreira, João M.L.; Gallinaro, Bruno; Carajilescov, Pedro
2013-01-01
The construction time of PWRs is studied considering published data about nuclear power plants in the world. For the 268 PWRs in operation in 2010, the mode of the construction time distribution is around 5–6 years, and 80% of the plants were built in less than 120 months. To circumvent the problem of comparing plants with different size we normalized the construction time to plants with 1 GW. We restricted the analysis to 201 PWRs which suffered less from external factors that were beyond the control of the management from 1965 to 2010. The results showed that the normalized construction time did not increase over the years and nor with the plants’ gross power level. The learning rate of the industry regarding normalized construction times showed a reduction with 95% confidence level of about 0.56±0.07 months for each 10 GW of installed capacity. Over the years the normalized construction time decreased and became more predictable. The data showed that countries with more centralized regulatory, construction and operation environments were able to build PWRs in shorter times. Countries less experienced with the nuclear technology built PWRs in longer times. - Highlights: ► The construction time of PWRs is analyzed based on historical data. ► Different factors affecting construction time are considered in the analyses. ► The normalized construction time of PWRs decreased with time and gross power level. ► Countries with more centralized institutions built PWRs more quickly
Time Management for Educators.
Burden, Paul R.
Time management principles can help teachers become more aware of ways in which time can be used to the greatest advantage. An exploration of personal time perspectives is a step toward establishing effective patterns of behavior. Productivity may be high in the morning and low in the late afternoon, for example, and organizing some activities to…
Zheng, F.
2011-01-01
Urban travel times are intrinsically uncertain due to a lot of stochastic characteristics of traffic, especially at signalized intersections. A single travel time does not have much meaning and is not informative to drivers or traffic managers. The range of travel times is large such that certain
International Nuclear Information System (INIS)
Strnad, J.
1983-01-01
A Thomas precession mechanism is described which would become effective in a symmetric six-dimensional space-time if the time vector of a particle would rotate uniformly. For the effect a discrepancy of the decay time of particles in flight, proportional to their kinetic energy would be characteristic
Directory of Open Access Journals (Sweden)
MARES VALERICA
2014-12-01
Full Text Available The efficient management of time is essential in any profession and in any activity domain. Anybody can increase his capacity to organize his time and get important benefits from it. The way in which one organizes his time will always have a direct impact on the objects of his work (resources and activities, so that it is worth allocating time for developing some instruments and techniques that could help planning and organizing time efficiently and attaining the objectives while meeting the deadlines.
Elton, L. R. B
1978-01-01
Time and Man focuses on the endeavors of humans to probe the mysteries of time and to elucidate its properties. The discussions are both philosophical and factual in nature and encompass science as well as the physical sciences, biology and related disciplines (for example, evolution), and the humanities (for example, religion). Factual information is presented to help the reader gain a better understanding of the concepts associated with time.Comprised of nine chapters, this volume first considers the passage of time and the experiences which humans associate with the concept of time before r
A Risk-Based Approach for Asset Allocation with A Defaultable Share
Directory of Open Access Journals (Sweden)
Yang Shen
2018-02-01
Full Text Available This paper presents a novel risk-based approach for an optimal asset allocation problem with default risk, where a money market account, an ordinary share and a defaultable security are investment opportunities in a general non-Markovian economy incorporating random market parameters. The objective of an investor is to select an optimal mix of these securities such that a risk metric of an investment portfolio is minimized. By adopting a sub-additive convex risk measure, which takes into account interest rate risk, as a measure for risk, the investment problem is discussed mathematically in a form of a two-player, zero-sum, stochastic differential game between the investor and the market. A backward stochastic differential equation approach is used to provide a flexible and theoretically sound way to solve the game problem. Closed-form expressions for the optimal strategies of the investor and the market are obtained when the penalty function is a quadratic function and when the risk measure is a sub-additive coherent risk measure. An important case of the general non-Markovian model, namely the self-exciting threshold diffusion model with time delay, is considered. Numerical examples based on simulations for the self-exciting threshold diffusion model with and without time delay are provided to illustrate how the proposed model can be applied in this important case. The proposed model can be implemented using Excel spreadsheets.
Stochastic Wilson–Cowan models of neuronal network dynamics with memory and delay
International Nuclear Information System (INIS)
Goychuk, Igor; Goychuk, Andriy
2015-01-01
We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence. (paper)
Allen, Phillip G.
1985-12-01
The call for abolishing photo reconnaissance in favor of real time is once more being heard. Ten years ago the same cries were being heard with the introduction of the Charge Coupled Device (CCD). The real time system problems that existed then and stopped real time proliferation have not been solved. The lack of an organized program by either DoD or industry has hampered any efforts to solve the problems, and as such, very little has happened in real time in the last ten years. Real time is not a replacement for photo, just as photo is not a replacement for infra-red or radar. Operational real time sensors can be designed only after their role has been defined and improvements made to the weak links in the system. Plodding ahead on a real time reconnaissance suite without benefit of evaluation of utility will allow this same paper to be used ten years from now.
Buying time promotes happiness.
Whillans, Ashley V; Dunn, Elizabeth W; Smeets, Paul; Bekkers, Rene; Norton, Michael I
2017-08-08
Around the world, increases in wealth have produced an unintended consequence: a rising sense of time scarcity. We provide evidence that using money to buy time can provide a buffer against this time famine, thereby promoting happiness. Using large, diverse samples from the United States, Canada, Denmark, and The Netherlands ( n = 6,271), we show that individuals who spend money on time-saving services report greater life satisfaction. A field experiment provides causal evidence that working adults report greater happiness after spending money on a time-saving purchase than on a material purchase. Together, these results suggest that using money to buy time can protect people from the detrimental effects of time pressure on life satisfaction.
Simulating detectors dead time
International Nuclear Information System (INIS)
Rustom, Ibrahim Farog Ibrahim
2015-06-01
Nuclear detectors are used in all aspects of nuclear measurements. All nuclear detectors are characterized by their dead time i.e. the time needed by a detector to recover from a previous incident. A detector dead time influences measurements taken by a detector and specially when measuring high decay rate (>) where is the detector dead time. Two models are usually used to correct for the dead time effect: the paralayzable and the non-paralayzable models. In the current work we use Monte Carlo simulation techniques to simulate radioactivity and the effect of dead time and the count rate of a detector with a dead time =5x10 - 5s assuming the non-paralayzable model. The simulation indicates that assuming a non -paralayzable model could be used to correct for decay rate measured by a detector. The reliability of the non-paralayzable model to correct the measured decay rate could be gauged using the Monte Carlo simulation. (Author)
Directory of Open Access Journals (Sweden)
Theodore R. Schatzki
2005-01-01
Full Text Available This essay pursues two goals: (1 to argue that two fundamental types of time—the time of objective reality and “the time of the soul”—meet in human activity and history and (2 to defend the legitimacy of calling a particular version of the second type a kind of time. The essay begins by criticizing Paul Ricoeur’s version of the claim that times of these two sorts meet in history. It then presents an account of human activity based on Heidegger’s Being and Time, according to which certain times of the two types—existential temporality and succession—meet in human activity. The legitimacy of calling existential temporality a kind of time is then defended via an expanded analysis of activity that examines where the two times meet there. The concluding section briefly considers a conception of historical time due to David Carr before showing why history is a broader domain encompassing human activity where the two times meet.
Connell, Linda; Wichner, David; Jakey, Abegael
2013-01-01
Within many operations, the pressures for on-time performance are high. Each month, on-time statistics are reported to the Department of Transportation and made public. There is a natural tendency for employees under pressure to do their best to meet these objectives. As a result, pressure to get the job done within the allotted time may cause personnel to deviate from procedures and policies. Additionally, inadequate or unavailable resources may drive employees to work around standard processes that are seen as barriers. However, bypassing practices to enable on-time performance may affect more than the statistics. ASRS reports often highlight on-time performance pressures which may result in impact across all workgroups in an attempt to achieve on-time performance. Reporters often provide in-depth insights into their experiences which can be used by industry to identify and focus on the implementation of systemic fixes.
DEFF Research Database (Denmark)
Øhrstrøm, Peter
2011-01-01
Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can...... be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation can be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1......) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models....
Theadore, Jason C
2011-01-01
The most important organizational resource is energy. The most important resource in time management is energy. Managing energy, not time, can help create encouraging time management skills and appropriate work life balance. Once a leader understands that time should be spent on things that are important instead of everything that is urgent, you can begin to develop a balance that will support your values, your family, and your organization. When leaders find meaningful ways to add a sense of purpose to their work they can personally improve themselves and their organizations. If your personal values do not align with the values of your organization you will never work with a true sense of purpose. Make the time to manage your energy. You will be surprised how much free time you find.
Intrinsic Time Quantum Geometrodynamics
Ita III, Eyo Eyo; Soo, Chopin; Yu, Hoi-Lai
2015-01-01
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational `arrows of tim...
Fathi, Albert
2015-07-01
In this paper we revisit our joint work with Antonio Siconolfi on time functions. We will give a brief introduction to the subject. We will then show how to construct a Lipschitz time function in a simplified setting. We will end with a new result showing that the Aubry set is not an artifact of our proof of existence of time functions for stably causal manifolds.
Time Dependent Quantum Mechanics
Morrison, Peter G.
2012-01-01
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic ...
MacKinnon, Janice Christine
2017-07-01
A significant barrier to accessing healthcare in Canada is long waiting lists, which can be linked to the way that Medicare was structured. After significant pressure, provincial governments began to address wait times. An example of a successful strategy to reduce wait times for elective surgery is the Saskatchewan Surgical Initiative, which saw wait times in the province change from being among the longest in Canada to the shortest.
TIME MANAGEMENT FOR ACCOUNTANTS
Directory of Open Access Journals (Sweden)
Cristina Elena BIGIOI
2016-06-01
Full Text Available Time is money. Every accountant knows that. In our country, the taxes are changing frequently. The accountants have to update their fiscal knowledge. The purpose of the article is to find how the accountants manage their time, taking into consideration the number of fiscal declarations and the fiscal changes. In this article we present some ways to improve time management for accountants.
International Nuclear Information System (INIS)
Urakawa, Junji; Ishii, Kazuhiro; Kadokura, Eiichi; Kawamoto, Takashi; Kikuchi, Mitsuo; Kikutani, Eiji
1990-01-01
The TRISTAN accelerator complex comprises four accelerators: a 200 MeV electron linac for positron production, a 2.5 GeV linac, an 8 GeV accumulation ring (AR) and a 30 GeV main ring (MR). The TRISTAN timing system is divided into fast and slow timing systems. The fast timing system supplies timing signals (fast timing) for devices whose operation is synchronized with bunched beams from either the linac or the AR. These signals are also used in various beam monitors and beam feedback systems. The slow timing system generates trigger signals (slow timing) in order to achieve synchronization between the magnetic field and the rf accelerating voltage of the AR or MR. These triggers are also used for the automatic operation of machines. The TRISTAN timing system fulfills the following features with the required flexibility and extensibility while in the operation mode: (1) the linac gun trigger signals and the AR revolution clock are synchronized within ≅ 100 ps in timing accuracy, and a short pulse (≅ 1.5 ns) from the linac is injected and accumulated into an arbitrarily selected bucket of AR for a long time; (2) bucket matching between the AR and MR is achieved within ±6 ps in timing accuracy and a single bunched beam from the AR is injected into an arbitrarily selected bucket of the MR; (3) the slow timing system manages the operation mode of the AR and MR with both flexibility and extensibility; (4) the synchronization signals are transmitted through coaxial cables over a circumference of 3 km from the main control room. (orig.)
Sun, Bo; Sunkavalli, Kalyan; Ramamoorthi, Ravi; Belhumeur, Peter N; Nayar, Shree K
2007-01-01
The properties of virtually all real-world materials change with time, causing their bidirectional reflectance distribution functions (BRDFs) to be time varying. However, none of the existing BRDF models and databases take time variation into consideration; they represent the appearance of a material at a single time instance. In this paper, we address the acquisition, analysis, modeling, and rendering of a wide range of time-varying BRDFs (TVBRDFs). We have developed an acquisition system that is capable of sampling a material's BRDF at multiple time instances, with each time sample acquired within 36 sec. We have used this acquisition system to measure the BRDFs of a wide range of time-varying phenomena, which include the drying of various types of paints (watercolor, spray, and oil), the drying of wet rough surfaces (cement, plaster, and fabrics), the accumulation of dusts (household and joint compound) on surfaces, and the melting of materials (chocolate). Analytic BRDF functions are fit to these measurements and the model parameters' variations with time are analyzed. Each category exhibits interesting and sometimes nonintuitive parameter trends. These parameter trends are then used to develop analytic TVBRDF models. The analytic TVBRDF models enable us to apply effects such as paint drying and dust accumulation to arbitrary surfaces and novel materials.
Singh J P
2000-01-01
The paper examines various measures of time and argues that none of the measures meet the needs of commerce and law for transactions carried out in the cyberspace. It therefore suggests that a new measure of the time and epoch, called eTime be introduced. The paper further suggests that the assumed zero of eTime should be the epoch of signing ‘A Declaration of Independence of Cyberspace’, i.e. Fri, Feb 9, 1996 17:16:35 +0100 at Davos, Switzerland.
Minguzzi, E.
2010-09-01
Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K + relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K + (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques.
Liu, Quan-Hui; Wang, Wei; Tang, Ming; Zhang, Hai-Feng
2016-05-09
Information diffusion and disease spreading in communication-contact layered network are typically asymmetrically coupled with each other, in which disease spreading can be significantly affected by the way an individual being aware of disease responds to the disease. Many recent studies have demonstrated that human behavioral adoption is a complex and non-Markovian process, where the probability of behavior adoption is dependent on the cumulative times of information received and the social reinforcement effect of the cumulative information. In this paper, the impacts of such a non-Markovian vaccination adoption behavior on the epidemic dynamics and the control effects are explored. It is found that this complex adoption behavior in the communication layer can significantly enhance the epidemic threshold and reduce the final infection rate. By defining the social cost as the total cost of vaccination and treatment, it can be seen that there exists an optimal social reinforcement effect and optimal information transmission rate allowing the minimal social cost. Moreover, a mean-field theory is developed to verify the correctness of simulation results.
Application of quantum Darwinism to a structured environment
Pleasance, Graeme; Garraway, Barry M.
2017-12-01
Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual "pseudomode" components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.
Time Here, Time There, Time Everywhere: Teaching Young Children Time through Daily Routine
Lee, Joohi; Lee, Joo Ok; Fox, Jill
2009-01-01
According to Piaget, 5- or 6-year-old children gradually acquire the concept of time based on events (Piaget, 1969). In his experiment of investigating children's time concepts, Piaget found that children of these ages were able to place pictures based on sequential events with some errors; the younger children made more errors. The National…
Validating Timed Component Contracts
DEFF Research Database (Denmark)
Le Guilly, Thibaut; Liu, Shaoying; Olsen, Petur
2015-01-01
This paper presents a technique for testing software components with contracts that specify functional behavior, synchronization, as well as timing behavior. The approach combines elements from unit testing with model-based testing techniques for timed automata. The technique is implemented...... in an online testing tool, and we demonstrate its use on a concrete use case....
Pickover, Clifford A.
1999-09-01
"Bucky Fuller thought big," Wired magazine recently noted, "Arthur C. Clarke thinks big, but Cliff Pickover outdoes them both." In his newest book, Cliff Pickover outdoes even himself, probing a mystery that has baffled mystics, philosophers, and scientists throughout history--What is the nature of time?In Time: A Traveler's Guide , Pickover takes readers to the forefront of science as he illuminates the most mysterious phenomenon in the universe--time itself. Is time travel possible? Is time real? Does it flow in one direction only? Does it have a beginning and an end? What is eternity? Pickover's book offers a stimulating blend of Chopin, philosophy, Einstein, and modern physics, spiced with diverting side-trips to such topics as the history of clocks, the nature of free will, and the reason gold glitters. Numerous diagrams ensure readers will have no trouble following along.By the time we finish this book, we understand a wide variety of scientific concepts pertaining to time. And most important, we will understand that time travel is, indeed, possible.
DEFF Research Database (Denmark)
Madsen, Mogens Ove
2016-01-01
GLS Shackle got much and the crucial inspiration from John Maynard Keynes. But that’s not all. He took a number of further consequences of Keynes’ thoughts. This implies for example ideal claims to economists — having to deal with both mechanical time and expectational time. In consequence the idea...
DEFF Research Database (Denmark)
Dalsgård, Anne Line
2017-01-01
in the neighbourhood, as credit credit cards are locked in a punctuated time, where dates are crucial. Using an episode that I happened to be part of as point of departure, I argue that decepção is the estrangement experienced, when a moment of trust is thrown back upon you, distorted by the process of time....
Arias, Elisa Felicitas
2005-09-15
Measuring time is a continuous activity, an international and restless enterprise hidden in time laboratories spread all over the planet. The Bureau International des Poids et Mesures is charged with coordinating activities for international timekeeping and it makes use of the world's capacity to produce a remarkably stable and accurate reference time-scale. Commercial atomic clocks beating the second in national laboratories can reach a stability of one part in 10(14) over a 5 day averaging time, compelling us to research the most highly performing methods of remote clock comparison. The unit of the international time-scale is the second of the International System of Units, realized with an uncertainty of the order 10(-15) by caesium fountains. Physicists in a few time laboratories are making efforts to gain one order of magnitude in the uncertainty of the realization of the second, and more refined techniques of time and frequency transfer are in development to accompany this progress. Femtosecond comb technology will most probably contribute in the near future to enhance the definition of the second with the incorporation of optical clocks. We will explain the evolution of the measuring of time, current state-of-the-art measures and future challenges.
DEFF Research Database (Denmark)
Christensen, Knud Smed
2000-01-01
Describes fundamentals of parallel programming and a kernel for that. Describes methods for modelling and checking parallel problems. Real time problems.......Describes fundamentals of parallel programming and a kernel for that. Describes methods for modelling and checking parallel problems. Real time problems....
Zielinski, Theresa Julia; Brooks, David W.; Crippen, Kent J.; March, Joe L.
2001-06-01
Time management is an important issue for teachers and students. This article discusses teachers' use of time from the perspective of curriculum and instruction. Average high school students spend fewer than 5 hours per week in outside-of-class study; average college students spend about 20 hours. Procrastination, often viewed in a negative light by teachers, usually pays off so well for college students that seniors become better at it than freshmen. Three suggestions for designing instruction are: test early and often; do not waste the best students' time in an effort to improve overall performance; and use engaging activities that motivate students to give of their time. The impact of computers on curricula is a double-edged sword. Time must be devoted to teaching the use of applications, but the programs reduce busywork. Will this turn out to be a simple tradeoff, or will the programs make us much more efficient so that less time is required? Will computer programs ultimately lead to an expanded criterion for expertise, thus demanding even more time to become an expert? These issues are described and suggestions for controlling time during instruction are provided.
Time management and procrastination
van Eerde, W.; Mumford, M.D.; Frese, M.
2015-01-01
This chapter combines the topics time management and procrastination. Time management is an overarching term derived from popular notions on how to be effective at work. Procrastination has been mainly researched from a personality perspective, addressing the emotional and psychological issues of
International Nuclear Information System (INIS)
Blok, M. de; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-01-01
This report describes a time-interpolator with which time differences can be measured using digital and analog techniques. It concerns a maximum measuring time of 6.4 μs with a resolution of 100 ps. Use is made of Emitter Coupled Logic (ECL) and analogues of high-frequency techniques. The difficulty which accompanies the use of ECL-logic is keeping as short as possible the mutual connections and closing properly the outputs in order to avoid reflections. The digital part of the time-interpolator consists of a continuous running clock and logic which converts an input signal into a start- and stop signal. The analog part consists of a Time to Amplitude Converter (TAC) and an analog to digital converter. (author). 3 refs.; 30 figs
DEFF Research Database (Denmark)
Davis, Lee N.; Davis, Jerome D.; Hoisl, Karin
2013-01-01
the employee is away from the workplace. We build on existing theory in the fields of organizational creativity and knowledge recombination, especially work relating context to creativity. The paper’s main theoretical contribution is to extend our understanding of the boundaries of employee creativity......This paper studies the contextual factors that influence whether invention occurs during work time or leisure time. Leisure time invention, a potentially important but thus far largely unexplored source of employee creativity, refers to invention where the main underlying idea occurs while...... by adding to the discussion of how access to and exploitation of different types of resources—during work hours or during leisure time — may affect creativity. Based on survey data from more than 3,000 inventions from German employee inventors, we find that leisure time inventions are more frequently...
International Nuclear Information System (INIS)
Lo, C.C.
1977-01-01
The processing of pulses with very fast risetimes for timing purposes involves many problems because of the large equivalent bandwidths involved. For pulses with risetimes in the 150 ps range (and full widths at half maximum (FWHM) of 400 ps) bandwidths in excess of 1GHz are required. Furthermore, these very narrow pulses with current amplitudes as small as 1 mA carry very small charges ( -12 coulomb), therefore, requiring very sensitive trigger circuits. The difficulty increases when timing characteristics in the picosecond range are sought especially when a wide input signal amplitude range causes a time-walk problem. The fast timing discriminator described has a time-walk of approximately +-75 ps over the input signal range from 80 mV to 3V. A schematic of the discriminator is included, and operation and performance are discussed
Gino, Francesca; Mogilner, Cassie
2014-02-01
Money, a resource that absorbs much daily attention, seems to be involved in much unethical behavior, which suggests that money itself may corrupt. This research examined a way to offset such potentially deleterious effects-by focusing on time, a resource that tends to receive less attention than money but is equally ubiquitous in daily life. Across four experiments, we examined whether shifting focus onto time can salvage individuals' ethicality. We found that implicitly activating the construct of time, rather than money, leads individuals to behave more ethically by cheating less. We further found that priming time reduces cheating by making people reflect on who they are. Implications for the use of time primes in discouraging dishonesty are discussed.
Directory of Open Access Journals (Sweden)
Oleg Svatos
2013-01-01
Full Text Available In this paper we analyze complexity of time limits we can find especially in regulated processes of public administration. First we review the most popular process modeling languages. There is defined an example scenario based on the current Czech legislature which is then captured in discussed process modeling languages. Analysis shows that the contemporary process modeling languages support capturing of the time limit only partially. This causes troubles to analysts and unnecessary complexity of the models. Upon unsatisfying results of the contemporary process modeling languages we analyze the complexity of the time limits in greater detail and outline lifecycles of a time limit using the multiple dynamic generalizations pattern. As an alternative to the popular process modeling languages there is presented PSD process modeling language, which supports the defined lifecycles of a time limit natively and therefore allows keeping the models simple and easy to understand.
DEFF Research Database (Denmark)
Nøjgaard, Nikolai; Geiß, Manuela; Merkle, Daniel
2017-01-01
tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure...... of the event labeled reconciliation problem with horizontal transfer. Results: We investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations....... This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an O(|V (T)| log(|V (S)|))-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require...
International Nuclear Information System (INIS)
Reznik, B.
1999-01-01
Time plays an unusual role in quantum theory, and the measurement of time is very different from the measurement of other physical qualities associated with a particle. As an example, the measurability of when something occurred is conceptually fraught with difficulties within the theory. Time must be measured by clocks, and one must somehow cause the occurrence of the event of interest to interact with a clock to record when that event occurred. But that interaction carries with it an inevitable perturbation of the event itself. I will argue that in addition to the usual ΔtΔE > ℎ associated with the accuracy of any clock, there is an additional ΔtE > ℎ uncertainty in the measurement of the time of arrival of a particle. Furthermore this constraint arises because the timing device can itself prevent the event from ever occurring at all. I will compare time measurements involving physical clocks, with attempts to construct a time operator and describe new difficulties associated with the latter approach
International Nuclear Information System (INIS)
Asami, Tohru; Hashimoto, Kazuo; Yamamoto, Seiichi
1992-01-01
Recently, aiming at the application to the plant control for nuclear reactors and traffic and communication control, the research and the practical use of the expert system suitable to real time processing have become conspicuous. In this report, the condition for the required function to control the object that dynamically changes within a limited time is presented, and the technical difference between the real time expert system developed so as to satisfy it and the expert system of conventional type is explained with the actual examples and from theoretical aspect. The expert system of conventional type has the technical base in the problem-solving equipment originating in STRIPS. The real time expert system is applied to the fields accompanied by surveillance and control, to which conventional expert system is hard to be applied. The requirement for the real time expert system, the example of the real time expert system, and as the techniques of realizing real time processing, the realization of interruption processing, dispersion processing, and the mechanism of maintaining the consistency of knowledge are explained. (K.I.)
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Carajilescov, Pedro; Moreira, Joao M.L., E-mail: pedro.carajilescov@ufabc.edu.b, E-mail: joao.moreira@ufabc.edu.b [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil). Center of Engineering, Modeling and Applied Social Sciences
2011-07-01
The cost of electricity generated by nuclear power is greatly affected by the capital cost, which is dependent on the construction time of the plant. This work analyses the construction time of PWRs in several countries with different market structure and licensing experience. Countries which succeeded to establish a more collaborative environment among utilities, constructors, regulators, and energy planners through effective partnerships were able to build PWRs in shorter times. The construction time in Germany, France and Russia was around 80 months and in Japan, about 60 months. The envelope of 95% of the cases includes a range between 50 and 250 months of construction time. The evaluations show that construction time of PWRs has been longer for countries that did not hold the technology to build their own reactors, and depended on contracts with foreign suppliers. The nominal power of the reactors was considered a measure of plant size, technology complexity and standardization. Countries with standardized reactor designs (France, Japan and Russia) were able to build plants in shorter times. (author)
Heilmann, Conrad
2017-10-01
Controversies about time discounting loom large in decisions about climate change. Prominently, a particularly controversial debate about time discounting in climate change decision-making has been conducted within climate economics, between the authors of Stern et al. (Stern review on the economics of climate change, 2006) and their critics (most prominently Dasgupta in Comments on the Stern review's economics of climate change, 2006; Tol in Energy Environ 17(6):977-981, 2006; Weitzman in J Econ Lit XLV:703-724, 2007; Nordhaus in J Econ Lit XLV:686-702, 2007). The article examines the role of values in this debate. Firstly, it is shown that time discounting is a case in which values are key because it is at heart an ethical problem. Secondly, it is argued that time discounting in climate economics is a case of economists making frequent and routine references to ethical values and indeed conduct ethical debates with each other. Thirdly, it is argued that there is evidence for deep and pervasive entanglement between facts and values in the prevalent methodologies for time discounting. Finally, it is argued that this means that economists have given up the 'value-free ideal' concerning time discounting, and discussed how the current methodology of time discounting in economics can be improved.
International Nuclear Information System (INIS)
Carajilescov, Pedro; Moreira, Joao M.L.
2011-01-01
The cost of electricity generated by nuclear power is greatly affected by the capital cost, which is dependent on the construction time of the plant. This work analyses the construction time of PWRs in several countries with different market structure and licensing experience. Countries which succeeded to establish a more collaborative environment among utilities, constructors, regulators, and energy planners through effective partnerships were able to build PWRs in shorter times. The construction time in Germany, France and Russia was around 80 months and in Japan, about 60 months. The envelope of 95% of the cases includes a range between 50 and 250 months of construction time. The evaluations show that construction time of PWRs has been longer for countries that did not hold the technology to build their own reactors, and depended on contracts with foreign suppliers. The nominal power of the reactors was considered a measure of plant size, technology complexity and standardization. Countries with standardized reactor designs (France, Japan and Russia) were able to build plants in shorter times. (author)
Josephson comparator switching time
Energy Technology Data Exchange (ETDEWEB)
Herr, Quentin P; Miller, Donald L; Przybysz, John X [Northrop Grumman, Baltimore, MD (United States)
2006-05-15
Comparator performance can be characterized in terms of both sensitivity and decision time. Delta-sigma analogue-to-digital converters are tolerant of sensitivity errors but require short decision time due to feedback. We have analysed the Josephson comparator using the numerical solution of the Fokker-Planck equation, which describes the time evolution of the ensemble probability distribution. At balance, the result is essentially independent of temperature in the range 5-20 K. There is a very small probability, 1 x 10{sup -14}, that the decision time will be longer than seven single-flux-quantum pulse widths, defined as Phi{sub 0}/(I{sub c}R{sub n}). For junctions with a critical current density of 4.5 kA, this decision time is only 20 ps. Decision time error probability decreases rapidly with lengthening time interval, at a rate of two orders of magnitude per pulse width. We conclude that Josephson comparator performance is quite favourable for analogue-to-digital converter applications.
Eisemann, Elmar; Assarsson, Ulf; Wimmer, Michael
2011-01-01
Important elements of games, movies, and other computer-generated content, shadows are crucial for enhancing realism and providing important visual cues. In recent years, there have been notable improvements in visual quality and speed, making high-quality realistic real-time shadows a reachable goal. Real-Time Shadows is a comprehensive guide to the theory and practice of real-time shadow techniques. It covers a large variety of different effects, including hard, soft, volumetric, and semi-transparent shadows.The book explains the basics as well as many advanced aspects related to the domain
DEFF Research Database (Denmark)
David, A.; Larsen, K.G.; Legay, A.
2015-01-01
A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation, and a set of operators supporting stepwise design. We develop a specification framework for real-time systems using Timed I/O Automata as the specification formalism......, with the semantics expressed in terms of Timed I/O Transition Systems. We provide constructs for refinement, consistency checking, logical and structural composition, and quotient of specifications-all indispensable ingredients of a compositional design methodology. The theory is implemented in the new tool Ecdar...
2006-12-01
as the fundamental unit of time in the International System of Units. It was defined as ( Metrologia , 1968) “the duration of 9 192 631 770 periods of...atomic time equivalent to the second of ET in principle. The Comité Consultatif pour la Définition de la Seconde (CCDS) of the CIPM recommended...with the definition of the second, the unit of time of the Inter- national System of Units” ( Metrologia , 1971). The CCDS (BIPM Com. Cons. Déf. Seconde
Inglesfield, J. E.
2007-01-01
A method of solving the time-dependent Schr\\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\\"odinger equation. Results are presented for a one-dimensi...
Directory of Open Access Journals (Sweden)
Nancy J. Knauer
2013-09-01
Full Text Available This paper engages the unspoken fourth dimension of intersectionality—time. Using the construction of lesbian, gay, bisexual, and transgender (LGBT identities as an example, it establishes that identity, as it is lived and experienced, is not only multivalent, but also historically contingent. It then raises a number of points regarding the temporal locality of identity—the influence of time on issues of identity and understanding, its implications for legal interventions, social movement building, and paradigms of progressive change. As the title suggests, the paper asks us to consider the frame of identity over time.
The relaxation time approximation
International Nuclear Information System (INIS)
Gairola, R.P.; Indu, B.D.
1991-01-01
A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs
Stupar, Sandra
2017-01-01
One of the most important questions concerning the foundations of physics, especially since the discovery of relativity and quantum theory, is the nature and role of time. In this book we bring together researchers from different areas of physics, mathematics, computer science and philosophy to discuss the role time plays in physics. There have been few books on this topic to date, and two of the key aims of the workshop and this book are to encourage more researchers to explore this area, and to pique students’ interest in the different roles time plays in physics.
Time and frequency applications.
Hellwig, H
1993-01-01
An overview is given of the capabilities of atomic clocks and quartz crystal oscillators in terms of available precision of time and frequency signals. The generation, comparison, and dissemination of time and frequency is then discussed. The principal focus is to survey uses of time and frequency in navigation, communication, and science. The examples given include the Global Positioning System, a satellite-based global navigation system, and general and dedicated communication networks, as well as experiments in general relativity and radioastronomy. The number of atomic clocks and crystal oscillators that are in actual use worldwide is estimated.
DEFF Research Database (Denmark)
Behrmann, Gerd; Larsen, Kim Guldstrand; Rasmussen, Jacob Illum
2004-01-01
This contribution reports on the considerable effort made recently towards extending and applying well-established timed automata technology to optimal scheduling and planning problems. The effort of the authors in this direction has to a large extent been carried out as part of the European...... projects VHS [22] and AMETIST [17] and are available in the recently released UPPAAL CORA [12], a variant of the real-time verification tool UPPAAL [20,5] specialized for cost-optimal reachability for the extended model of priced timed automata....
DEFF Research Database (Denmark)
Svejvig, Per; Geraldi, Joana; Grex, Sara
Despite the ubiquitous pressure for speed, our approaches to accelerate projects remain constrained to the old-fashioned understanding of the project as a vehicle to deliver products and services, not value. This article explores an attempt to accelerate time to benefit. We describe and deconstruct...... of the time. Although all cases valued speed and speed to benefit, and implemented most practices proposed by the methodology, only three of the five projects were more successful in decreasing time to speed. Based on a multi-case study comparison between these five different projects and their respective...
DEFF Research Database (Denmark)
Holst-Christensen, Bo
interest in getting a degree, they prefer the educators to do the work for them. The focus of my experiments have therefore been to develop teaching techniques that ensures that the students study efficiently and at the same time moves the task of identifying which parts of the subjects that are giving...... the students problems from the educator to the students. By using techniques that put more weight on student participation, cooperation and preparation, I have been able to cut significantly down on the time used for lecturing, allowing more time for student work and reflection. As an example by getting...... the students to identify the parts of the subjects that need further explanation, I get the students to take ownership of the learning task and at the same time give me a more direct feedback. By creating teaching materials and exercises that can be used in a number of different ways, it is possible to involve...
International Nuclear Information System (INIS)
Kapuscik, E.
1992-02-01
Generalizing concepts of the Einstein radiolocation method and, as a consequence, special relativity transformation rules we get that the time flow in the moving system depends on the direction of motion. 3 refs. (author)
National Research Council Canada - National Science Library
Adler, Robert
1997-01-01
We describe how to take a stable, ARMA, time series through the various stages of model identification, parameter estimation, and diagnostic checking, and accompany the discussion with a goodly number...
Energy Technology Data Exchange (ETDEWEB)
Center for Human Reliability Studies
2007-05-01
The purpose of this monograph is to provide information on drug retention times in the human body. The information provided is based on plausible illegal drug use activities that might be engaged in by a recreational drug user.
Directory of Open Access Journals (Sweden)
Annett eSchirmer
2011-10-01
Full Text Available Experimental evidence suggests that emotions can both speed-up and slow-down the internal clock. Speeding-up has been observed for to-be-timed emotional stimuli that have the capacity to sustain attention, whereas slowing-down has been observed for to-be-timed neutral stimuli that are presented in the context of emotional distractors. These effects have been explained by mechanisms that involve changes in bodily arousal, attention or sentience. A review of these mechanisms suggests both merits and difficulties in the explanation of the emotion-timing link. Therefore, a hybrid mechanism involving stimulus-specific sentient representations is proposed as a candidate for mediating emotional influences on time. According to this proposal, emotional events enhance sentient representations, which in turn support temporal estimates. Emotional stimuli with a larger share in ones sentience are then perceived as longer than neutral stimuli with a smaller share.
... with friends. Get social. Try a dance club, hiking group or golf league. Encouragement from others can ... quickly alternating activity produces many of the same benefits of continuous moderate-intensity exercise in less time. ...
Multivariate Time Series Search
National Aeronautics and Space Administration — Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical...
DEFF Research Database (Denmark)
Kofod, Julie Lundbak
This master thesis examines the distinction between tense logic and first order logic concerning time. In particular it studies whether this distinction exists in physics or not. Firstly a general test is made: translating sentences concern- ing time from physics into the two logics. The results...... here are inconclusive, as it is possible for both logics to represent the sen- tences, so this experiment does not reveal a similar distinction in physics. However this test also reveals some properties of the logics: tense logic holds a local view on time while first order logic holds a global view...... logic and reversibility in physics and tense logic and irreversibility in physics. Through this study it is concluded that it is not possible to see this correspondence with the tested property; time symmetry, since symmetry seems to concern the underlying structures, not the logic itself. It is...
International Nuclear Information System (INIS)
Timmer, E.; Heine, E.
1985-01-01
Along the NIKHEF accelerator in Amsterdam (Netherlands), at several places a signal is needed for the sychronisation of all devices with the acceleration process. In this report, basic principles and arrangements of this timing system are described
Lippmann, C
2013-01-01
The Time Projection Chamber (TPC) is the main device in the ALICE 'central barrel' for the tracking and identification (PID) of charged particles. It has to cope with unprecedented densities of charges particles.
Monga, Ashwani; Zor, Ozum
2018-04-21
Consumers are known to spend both time and money. These two resources are often seen as economically comparable because the value of one's time can be equated to a monetary amount, such as one's wage rate. Recent research suggests that even when time and money are economically equivalent, they are psychologically different. We discuss how time (versus money) leads to decision making that is more heuristic rather than systematic, to an orientation that is more emotional rather than value-maximizing, to a thinking process that is more holistic rather than analytic, and to a mindset that is more abstract rather than concrete. Implications arise for a variety of domains such as consumer search, happiness, product evaluation, and charitable giving. Copyright © 2018 Elsevier Ltd. All rights reserved.
Time-predictable architectures
Rochange, Christine; Uhrig , Sascha
2014-01-01
Building computers that can be used to design embedded real-time systems is the subject of this title. Real-time embedded software requires increasingly higher performances. The authors therefore consider processors that implement advanced mechanisms such as pipelining, out-of-order execution, branch prediction, cache memories, multi-threading, multicorearchitectures, etc. The authors of this book investigate the timepredictability of such schemes.
LEADERSHIP AND TIME MANAGEMENT
NIKEZIC Srdan; BATAVELJIC Dragan; NIKEZIC Stefan; BATAVELJIC Branka
2014-01-01
When it comes to resources, it is primarily referred to material and financial and rarely human. It is assumed that human resources are used in the right way that their involvement, measured in time and intensity, is properly set to goals and tasks. Practice, unfortunately disproves this assumption. Employees spend too much time for unnecessary and low-priority activities, not realizing that the implementation of certain, key activities the requirement for achieving the ...
International Nuclear Information System (INIS)
Chang, S.S.; Kim, M.S.; Won, S.C.; Choi, S.J.
1991-01-01
The PLS timing system consists of a master oscillator, a repetition rate pulse generator, a storage ring rf synchronizing system, and a rf driver and kicker trigger system composed of a fixed delay module and variable delay modules. All the timing modules are installed in the VME crates and controlled by the 32 bit microprocessors, and communicating with the Host computer via Ethernet. This paper describes the architectural design of this system as well as the requirements of performance
DEFF Research Database (Denmark)
Hisdal, H.; Holmqvist, E.; Hyvärinen, V.
Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the......Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the...
Time management a prokrastinace
Šarmandžijeva, Cagan
2017-01-01
The theoretical part of this thesis is focused on time management, its history and importance of the goals and tools, which allow us to organize our time. It will also focus on the issue of procrastination, its origin and occurrence in the history, definition of analysis paralysis and people's attitude towards motivation and self-confrontation. It will also introduce us to several tools used in fight against procrastination. The methodological and practical parts will elaborate on a qualitati...
Kalan, Petra
2013-01-01
In this work I did a research about hygiene habits of people and their home environment. The work presents how the hygiene habits changed in people home environment through time. The work presents changes of the body hygiene standards adopted by people from the middle ages onward. Todays customs are quite different from the ones we had some time ago. Moreover, hygiene of living environment has also changes which resulted into lower death rate and death illness related to bad hygiene among pop...
2009-11-01
VNIIFTRI and the PTB [7]. GPS time transfer represents today about 85% of the time links for TAI; in this technique, we make use of different types...campaign visited the PTB, the VNIIFTRI , and the AOS [8]. Already in 1996, the use of GLONASS in standard CGGTTS Common-View mode was proposed, but...are compared on regular basis to GPS and TWSTFT methods [16]. Also, with the agreement of the CCTF (2009), the link between the PTB and VNIIFTRI
Dobbs-Dixon, Ian; Agol, Eric; Deming, Drake
2015-12-01
We utilize multi-dimensional simulations of varying equatorial jet strength to predict wavelength-dependent variations in the eclipse times of gas-giant planets. A displaced hot spot introduces an asymmetry in the secondary eclipse light curve that manifests itself as a measured offset in the timing of the center of eclipse. A multi-wavelength observation of secondary eclipse, one probing the timing of barycentric eclipse at short wavelengths and another probing at longer wavelengths, will reveal the longitudinal displacement of the hot spot and break the degeneracy between this effect and that associated with the asymmetry due to an eccentric orbit. The effect of time offsets was first explored in the IRAC wavebands by Williams et al. Here we improve upon their methodology, extend to a broad range of wavelengths, and demonstrate our technique on a series of multi-dimensional radiative-hydrodynamical simulations of HD 209458b with varying equatorial jet strength and hot-spot displacement. Simulations with the largest hot-spot displacement result in timing offsets of up to 100 s in the infrared. Though we utilize a particular radiative hydrodynamical model to demonstrate this effect, the technique is model independent. This technique should allow a much larger survey of hot-spot displacements with the James Webb Space Telescope than currently accessible with time-intensive phase curves, hopefully shedding light on the physical mechanisms associated with thermal energy advection in irradiated gas giants.
International Nuclear Information System (INIS)
Dobbs-Dixon, Ian; Agol, Eric; Deming, Drake
2015-01-01
We utilize multi-dimensional simulations of varying equatorial jet strength to predict wavelength-dependent variations in the eclipse times of gas-giant planets. A displaced hot spot introduces an asymmetry in the secondary eclipse light curve that manifests itself as a measured offset in the timing of the center of eclipse. A multi-wavelength observation of secondary eclipse, one probing the timing of barycentric eclipse at short wavelengths and another probing at longer wavelengths, will reveal the longitudinal displacement of the hot spot and break the degeneracy between this effect and that associated with the asymmetry due to an eccentric orbit. The effect of time offsets was first explored in the IRAC wavebands by Williams et al. Here we improve upon their methodology, extend to a broad range of wavelengths, and demonstrate our technique on a series of multi-dimensional radiative-hydrodynamical simulations of HD 209458b with varying equatorial jet strength and hot-spot displacement. Simulations with the largest hot-spot displacement result in timing offsets of up to 100 s in the infrared. Though we utilize a particular radiative hydrodynamical model to demonstrate this effect, the technique is model independent. This technique should allow a much larger survey of hot-spot displacements with the James Webb Space Telescope than currently accessible with time-intensive phase curves, hopefully shedding light on the physical mechanisms associated with thermal energy advection in irradiated gas giants
Energy Technology Data Exchange (ETDEWEB)
Dobbs-Dixon, Ian [Department of Physics, NYU Abu Dhabi P.O. Box 129188 Abu Dhabi (United Arab Emirates); Agol, Eric [Department of Astronomy, University of Washington, Seattle WA 98195 (United States); Deming, Drake [NASA Astrobiology Institute Virtual Planet Laboratory (United States)
2015-12-10
We utilize multi-dimensional simulations of varying equatorial jet strength to predict wavelength-dependent variations in the eclipse times of gas-giant planets. A displaced hot spot introduces an asymmetry in the secondary eclipse light curve that manifests itself as a measured offset in the timing of the center of eclipse. A multi-wavelength observation of secondary eclipse, one probing the timing of barycentric eclipse at short wavelengths and another probing at longer wavelengths, will reveal the longitudinal displacement of the hot spot and break the degeneracy between this effect and that associated with the asymmetry due to an eccentric orbit. The effect of time offsets was first explored in the IRAC wavebands by Williams et al. Here we improve upon their methodology, extend to a broad range of wavelengths, and demonstrate our technique on a series of multi-dimensional radiative-hydrodynamical simulations of HD 209458b with varying equatorial jet strength and hot-spot displacement. Simulations with the largest hot-spot displacement result in timing offsets of up to 100 s in the infrared. Though we utilize a particular radiative hydrodynamical model to demonstrate this effect, the technique is model independent. This technique should allow a much larger survey of hot-spot displacements with the James Webb Space Telescope than currently accessible with time-intensive phase curves, hopefully shedding light on the physical mechanisms associated with thermal energy advection in irradiated gas giants.
International Nuclear Information System (INIS)
Mills, D.M.
1992-01-01
When new or more powerful probes become available that offer both shorter data-collection times and the opportunity to apply innovative approaches to established techniques, it is natural that investigators consider the feasibility of exploring the kinetics of time-evolving systems. This stimulating area of research not only can lead to insights into the metastable or excited states that a system may populate on its way to a ground state, but can also lead to a better understanding of that final state. Synchrotron radiation, with its unique properties, offers just such a tool to extend X-ray measurements from the static to the time-resolved regime. The most straight-forward application of synchrotron radiation to the study of transient phenomena is directly through the possibility of decreased data-collection times via the enormous increase in flux over that of a laboratory X-ray system. Even further increases in intensity can be obtained through the use of novel X-ray optical devices. Widebandpass monochromators, e.g., that utilize the continuous spectral distribution of synchrotron radiation, can increase flux on the sample several orders of magnitude over conventional X-ray optical systems thereby allowing a further shortening of the data-collection time. Another approach that uses the continuous spectral nature of synchrotron radiation to decrease data-collection times is the open-quote parallel data collectionclose quotes method. Using this technique, intensities as a function of X-ray energy are recorded simultaneously for all energies rather than sequentially recording data at each energy, allowing for a dramatic decrease in the data-collection time
Smyth, L G; Martin, Z; Hall, B; Collins, D; Mealy, K
2012-09-01
Public and political pressures are increasing on doctors and in particular surgeons to demonstrate competence assurance. While surgical audit is an integral part of surgical practice, its implementation and delivery at a national level in Ireland is poorly developed. Limits to successful audit systems relate to lack of funding and administrative support. In Wexford General Hospital, we have a comprehensive audit system which is based on the Lothian Surgical Audit system. We wished to analyse the amount of time required by the Consultant, NCHDs and clerical staff on one surgical team to run a successful audit system. Data were collected over a calendar month. This included time spent coding and typing endoscopy procedures, coding and typing operative procedures, and typing and signing discharge letters. The total amount of time spent to run the audit system for one Consultant surgeon for one calendar month was 5,168 min or 86.1 h. Greater than 50% of this time related to work performed by administrative staff. Only the intern and administrative staff spent more than 5% of their working week attending to work related to the audit. An integrated comprehensive audit system requires a very little time input by Consultant surgeons. Greater than 90% of the workload in running the audit was performed by the junior house doctors and administrative staff. The main financial implications for national audit implementation would relate to software and administrative staff recruitment. Implementation of the European Working Time Directive in Ireland may limit the time available for NCHD's to participate in clinical audit.
Directory of Open Access Journals (Sweden)
Estrid Sørensen
2007-01-01
Full Text Available While time and space form a classic duality in social science, this article demonstrates a perspective on time, space and materiality as a core trinity. As a prominent figure in contemporary discussions on materiality in the social sciences Science and Technology Studies (STS emphasizes relational approaches. STS however lacks a clear relational definition of materiality and tends instead to focus on the agency of entities, on for instance material agency. The article suggests a relational definition of materiality and notes that this move implies turning the question of the time of materiality into an empirical question. It is argued that relational materiality must be studied spatially, and thus a spatial approach describing patterns of relations is presented. Based on field work in a primary school classroom and computer lab, three materials are analyzed: the blackboard, a bed-loft and an online 3D virtual environment. The empirical descriptions depict three different materialities, and it is shown how time is formed differently in each of them. Time, it is argued, is an emergent and characterizing aspect of materialities as spatial formations. URN: urn:nbn:de:0114-fqs070122
Gleick, James
2016-01-01
From the acclaimed author of The Information and Chaos, here is a mind-bending exploration of time travel: its subversive origins, its evolution in literature and science, and its influence on our understanding of time itself. The story begins at the turn of the previous century, with the young H. G. Wells writing and rewriting the fantastic tale that became his first book and an international sensation: The Time Machine. It was an era when a host of forces was converging to transmute the human understanding of time, some philosophical and some technological: the electric telegraph, the steam railroad, the discovery of buried civilizations, and the perfection of clocks. James Gleick tracks the evolution of time travel as an idea that becomes part of contemporary culture—from Marcel Proust to Doctor Who, from Jorge Luis Borges to Woody Allen. He investigates the inevitable looping paradoxes and examines the porous boundary between pulp fiction and modern physics. Finally, he delves into a temporal shift that...
SNS Diagnostics Timing Integration
Long, Cary D; Murphy, Darryl J; Pogge, James; Purcell, John D; Sundaram, Madhan
2005-01-01
The Spallation Neutron Source (SNS) accelerator systems will deliver a 1.0 GeV, 1.4 MW proton beam to a liquid mercury target for neutron scattering research. The accelerator complex consists of a 1 GeV linear accelerator, an accumulator ring and associated transport lines. The SNS diagnostics platform is PC-based running Windows XP Embedded for its OS and LabVIEW as its programming language. Coordinating timing among the various diagnostics instruments with the generation of the beam pulse is a challenging task that we have chosen to divide into three phases. First, timing was derived from VME based systems. In the second phase, described in this paper, timing pulses are generated by an in house designed PCI timing card installed in ten diagnostics PCs. Using fan-out modules, enough triggers were generated for all instruments. This paper describes how the Timing NAD (Network Attached Device) was rapidly developed using our NAD template, LabVIEW's PCI driver wizard, and LabVIEW Channel Access library. The NAD...
International Nuclear Information System (INIS)
Vajna, Szabolcs; Kertész, János; Tóth, Bálint
2013-01-01
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the non-trivial dynamics of the task list. The model is characterized by a priority distribution as an input parameter, which describes the choice procedure from the list. We give exact results on the asymptotic behaviour of the model and we show that the interevent time distribution is power-law decaying for any kind of input distributions that remain normalizable in the infinite list limit, with exponents tunable between 1 and 2. The model satisfies a scaling law between the exponents of interevent time distribution (β) and autocorrelation function (α): α + β = 2. This law is general for renewal processes with power-law decaying interevent time distribution. We conclude that slowly decaying autocorrelation function indicates long-range dependence only if the scaling law is violated. (paper)
Hoek, M.; Cardinali, M.; Corell, O.; Dickescheid, M.; Ferretti B., M. I.; Lauth, W.; Schlimme, B. S.; Sfienti, C.; Thiel, M.
2017-12-01
A prototype detector, called FLASH (Fast Light Acquiring Start Hodoscope), was built to provide precise Time-of-Flight (TOF) measurements and reference timestamps for detector setups at external beam lines. Radiator bars, made of synthetic fused silica, were coupled to a fast MCP-PMT with 64 channels and read out with custom electronics using Time-over-Threshold (TOT) for signal characterization. The TRB3 system, a high-precision TDC implemented in an FPGA, was used as data acquisition system. The performance of a system consisting of two FLASH units was investigated at a dedicated test experiment at the Mainz Microtron (MAMI) accelerator using its 855 MeV electron beam. The TOT measurement enabled time walk corrections and an overall TOF resolution of ∼70 ps could be achieved which translates into a resolution of ∼50 ps per FLASH unit. The intrinsic resolution of the frontend electronics including the TDC was measured to be less than 25 ps.
International Nuclear Information System (INIS)
Bossi, R.H.; Oien, C.T.
1981-01-01
Real-time radiography is used for imaging both dynamic events and static objects. Fluorescent screens play an important role in converting radiation to light, which is then observed directly or intensified and detected. The radiographic parameters for real-time radiography are similar to conventional film radiography with special emphasis on statistics and magnification. Direct-viewing fluoroscopy uses the human eye as a detector of fluorescent screen light or the light from an intensifier. Remote-viewing systems replace the human observer with a television camera. The remote-viewing systems have many advantages over the direct-viewing conditions such as safety, image enhancement, and the capability to produce permanent records. This report reviews real-time imaging system parameters and components
DEFF Research Database (Denmark)
Murakami, Kyoko
2012-01-01
This article is a continuous dialogue on memory triggered by Brockmeier’s (2010) article. I drift away from the conventionalization of the archive as a spatial metaphor for memory in order to consider the greater possibility of “time” for conceptualizing memory. The concept of time is central...... in terms of autobiographical memory. The second category of time is discussed, drawing on Augustine and Bergson amongst others. Bergson’s notion of duration has been considered as a promising concept for a better understanding of autobiographical memory. Psychological phenomena such as autobiographical...... memory should embrace not only spatial dimension, but also a temporal dimension, in which a constant flow of irreversible time, where multiplicity, momentarily, dynamic stability and becoming and emergence of novelty can be observed....
Energy Technology Data Exchange (ETDEWEB)
None, None
2007-05-01
The purpose of this monograph is to provide information on drug retention times in the human body. The information provided is based on plausible illegal drug use activities that might be engaged in by a recreational drug user. Based on anecdotal evidence, most people “party” during extended time away from the work environment. Therefore, the following scenarios were envisioned: (1) a person uses an illicit drug at a party on Saturday night (infrequent user); (2) a person uses a drug one time on Friday night and once again on Saturday night (infrequent user); and (3) a person uses a drug on Friday night, uses a drug twice on Saturday night, and once again on Sunday (frequent user).
Directory of Open Access Journals (Sweden)
Thomas eWidlok
2014-11-01
Full Text Available Cognitive Scientists interested in causal cognition increasingly search for evidence from non-WEIRD people but find only very few cross-cultural studies that specifically target causal cognition. This article suggests how information about causality can be retrieved from ethnographic monographs, specifically from ethnographies that discuss agency and concepts of time. Many apparent cultural differences with regard to causal cognition dissolve when cultural extensions of agency and personhood to non-humans are taken into account. At the same time considerable variability remains when we include notions of time, linearity and sequence. The article focuses on ethnographic case studies from Africa but provides a more general perspective on the role of ethnography in research on the diversity and universality of causal cognition.
DEFF Research Database (Denmark)
Fischer, Paul; Hilbert, Astrid
2012-01-01
We introduce a platform which supplies an easy-to-handle, interactive, extendable, and fast analysis tool for time series analysis. In contrast to other software suits like Maple, Matlab, or R, which use a command-line-like interface and where the user has to memorize/look-up the appropriate...... commands, our application is select-and-click-driven. It allows to derive many different sequences of deviations for a given time series and to visualize them in different ways in order to judge their expressive power and to reuse the procedure found. For many transformations or model-ts, the user may...... choose between manual and automated parameter selection. The user can dene new transformations and add them to the system. The application contains efficient implementations of advanced and recent techniques for time series analysis including techniques related to extreme value analysis and filtering...
DEFF Research Database (Denmark)
Berg Johansen, Christina
2018-01-01
I want to feel the temporalities I am theorizing and writing about. To feel, explore, be moved through, tugged under by my research subject, to not know where my explorations will take me. How does time appear when I take responsibility for it instead of placing it as and with the Other? Can my...... temporal research emerge in symbiotic play with other human and non-human entities? In this essay, I will share how a methodological breakdown opened to me a net of (auto-)ethnographic wo/anderings, dialogical interviews and performative time-laboratories. I do not know where I am headed, but every...... sensuous memory lies in store, waiting for its time....
Time Domain Induced Polarization
DEFF Research Database (Denmark)
Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest
2012-01-01
Time-domain-induced polarization has significantly broadened its field of reference during the last decade, from mineral exploration to environmental geophysics, e.g., for clay and peat identification and landfill characterization. Though, insufficient modeling tools have hitherto limited the use...... of time-domaininduced polarization for wider purposes. For these reasons, a new forward code and inversion algorithm have been developed using the full-time decay of the induced polarization response, together with an accurate description of the transmitter waveform and of the receiver transfer function......, to reconstruct the distribution of the Cole-Cole parameters of the earth. The accurate modeling of the transmitter waveform had a strong influence on the forward response, and we showed that the difference between a solution using a step response and a solution using the accurate modeling often is above 100...
DEFF Research Database (Denmark)
Sandvik, Kjetil; Refslund Christensen, Dorthe
referred to through accounts of ‘how death occurred’; second, a present time constituted by emotional and social stress and, thirdly, a wishful time or subjunctive mode articulating relational potentialities of these children and inventing memories with them (“I wish you would have lived to….”). We analyze......This paper explores relations between ritualized spatiality and the conceptions of time reflected in memorial websites such as the Danish site Mindet.dk, a narrowly framed, socially protective online community in which individuals can perform their grief through design of individual entries...... (‘memories’) for their deceased loved ones and get personal, social support in their mourning processes through communication with other mourners, through mutual appreciation of each other’s postings and through emotional labor reflected on the individual sites. The main focus in this paper is how online...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
DEFF Research Database (Denmark)
Christiansen, Steen Ledet
Time travel films necessarily fragment linear narratives, as scenes are revisited with differences from the first time we saw it. Popular films such as Back to the Future mine comedy from these visitations, but there are many different approaches. One extreme is Chris Marker's La Jetée - a film...... made almost completely of still images, recounting the end of the world. These stills can be viewed as fragments that have survived the end of the world and now provide the only access to the events that occured. Shane Carruth's Primer has a different approach to time travel, the narrative diegesis...... that is presented; how do we understand such films and to what extent is it even possible to make sense of a film that has no real beginning, middle or end?...
International Nuclear Information System (INIS)
Assis, A.K.T.
2011-01-01
Full text: Isaac Newton (1642-1727) defended in his book Mathematical Principles of Natural Philosophy, also know as Principia, published in 1687, the utilization of absolute time in physics. According to him 'absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external'. Leibniz (1646-1716), on the other hand, was against this concept and proposed relative time to replace it: 'As for my opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistence, as time is an order of successions'. Leibniz ideas were accepted and developed by Ernst Mach (1838-1916) in his book The Science of Mechanics, published in 1883. In this work we consider the implementation of relational time, as proposed by Leibniz and Mach, and the consequences this implementation will mean for physics as a whole. We consider some specific examples related to mechanics (Newton's bucket experiment, the flattening of the Earth, Foucault's pendulum experiment) and to electromagnetism (Ampere's force between current carrying wires, an electric charge describing a Larmor radius due to a nearby large magnet, two charges orbiting around one another). We generalize these ideas considering the principle of physical proportions (PPP), according to which no absolute magnitudes should appear in the laws of physics. We present some laws satisfying this principle and others which do not comply with it. The laws which do not satisfy the PPP should be based upon incomplete theories. We present the consequences of complete theories complying with this fundamental principle of nature. (author)