Non-Markovian stochastic processes: colored noise.
Łuczka, J
2005-06-01
We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.
Non-Markovian stochastic Liouville equation and its Markovian representation.
Shushin, A I
2003-06-01
The non-Markovian variant of the stochastic Liouville equation (SLE) is studied within the continuous time random walk approach (CTRWA). The CTRWA-based non-Markovian SLE is shown to be equivalently represented by the corresponding conventional Markovian SLE. This Markovian representation provides a rigorous method for deriving the non-Markovian SLE and allows for a physically clear interpretation of the specific features of this SLE. It also enables one to develop convenient non-Markovian models useful for applications, some of which are discussed in detail. Special attention is given to the discussion of anomalous long-tailed CTRW processes and non-Markovian SLE. The obtained results are applied to the analysis of the effect of rate fluctuations on chemical reaction kinetics. It is shown, in particular, that the anomalous fluctuations not only influence the reaction rate but also change the reaction kinetics itself.
Counting statistics of non-Markovian quantum stochastic processes.
Flindt, Christian; Novotný, Tomás; Braggio, Alessandro; Sassetti, Maura; Jauho, Antti-Pekka
2008-04-18
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 of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.
Stochastic theory of non-Markovian open quantum system
NASA Astrophysics Data System (ADS)
Zhao, Xinyu
In this thesis, a stochastic approach to solving non-Markovian open quantum system called "non-Markovian quantum state diffusion" (NMQSD) approach is discussed in details. The NMQSD approach can serve as an analytical and numerical tool to study the dynamics of the open quantum systems. We explore three main topics of the NMQSD approach. First, we extend the NMQSD approach to many-body open systems such as two-qubit system and coupled N-cavity system. Based on the exact NMQSD equations and the corresponding master equations, we investigate several interesting non-Markovian features due to the memory effect of the environment such as the entanglement generation in two-qubit system and the coherence and entanglement transfer between cavities. Second, we extend the original NMQSD approach to the case that system is coupled to a fermionic bath or a spin bath. By introducing the anti-commutative Grassmann noise and the fermionic coherent state, we derive a fermionic NMQSD equation and the corresponding master equation. The fermionic NMQSD is illustrated by several examples. In a single qubit dissipative example, we have explicitly demonstrated that the NMQSD approach and the ordinary quantum mechanics give rise to the exactly same results. We also show the difference between fermionic bath and bosonic bath. Third, we combine the bosonic and fermionic NMQSD approach to develop a unified NMQSD approach to study the case that an open system is coupled to a bosonic bath and a fermionic bath simultaneously. For all practical purposes, we develop a set of useful computer programs (NMQSD Toolbox) to implement the NMQSD equation in realistic computations. In particular, we develop an algorithm to calculate the exact O operator involved in the NMQSD equation. The NMQSD toolbox is designed to be user friendly, so it will be especially valuable for a non-expert who has interest to employ the NMQSD equation to solve a practical problem. Apart from the central topics on the NMQSD
An alternative realization of the exact non-Markovian stochastic Schrödinger equation.
Song, Kai; Song, Linze; Shi, Qiang
2016-06-14
Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performed to demonstrate the efficiency of the new method.
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
Gambetta, Jay; Wiseman, H.M.
2003-12-01
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.
Vega, Ines de; Alonso, Daniel; Gaspard, Pierre
2005-02-01
It is our aim to study the dynamics of a two-level atom immersed in the modified radiation field of a photonic band-gap material using non-Markovian stochastic Schroedinger equations. Up to now, such methodology has only been applied to toy models and not to physically realistic systems as the one presented here. In order to check its validity, we shall study several of the physical phenomena already described in the literature within non-Markovian master equations, such as the long-time-limit residual population in the excited level of the atom and the population inversion which occurs in the atomic system when applying an external laser field. In addition to the stochastic equation, we propose a non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity. We propose a correlation function for the radiation field (environment) that captures many of the physically relevant aspects of the problem and describes the short-time behavior in a more accurate way than previously proposed ones. This characteristic permits a correct description of the fluctuations of the electromagnetic field, which in the stochastic formalism are represented by the noise, and a better description of the non-Markovian effects in the atomic dynamics. The methodology presented in this paper to apply stochastic Schroedinger equations can be followed to study more complex systems, like many-level atoms embedded in more complicated photonic band-gap structures.
Stochastic Impulse Control of Non-Markovian Processes
Djehiche, Boualem; Hamadene, Said Hdhiri, Ibtissam
2010-02-15
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.
Stochastic simulation of dissipation and non-Markovian effects in open quantum systems.
Lacroix, Denis
2008-04-01
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation for the reduced density. The influence of the environment is incorporated through a mean field which is both stochastic and nonlocal in time and where the standard two-time correlation functions of the environment appear naturally. Since no approximation is made, the presented theory incorporates exactly dissipative and non-Markovian effects. Applications to the spin-boson model coupled to a heat bath with various coupling regimes and temperature show that the presented stochastic theory can be a valuable tool to simulate exactly the dynamics of open quantum systems. Links with the stochastic Schrödinger equation method and possible extensions to "imaginary time" propagation are discussed.
Shushin, A I
2008-03-01
Some specific features and extensions of the continuous-time random-walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR, CTRW processes are represented by multidimensional Markovian ones. In this representation the probability density function (PDF) W(t) of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on the relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on the statistical properties of noise. Some applications of the generalized non-Markovian SLE are discussed. In particular, it is applied to study two modifications of the CTRW approach. One of them considers cascaded CTRWs in which the controlling process is actually a CTRW-like one controlled by another CTRW process, controlled in turn by a third one, etc. Within the MR a simple expression for the PDF W(t) of the total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long-time tailed W(t) . The cascaded CTRWs can model the effect of the complexity of a system on the relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW modification describes the kinetics of processes governed by fluctuating W(t) . Within the MR the problem is analyzed in a general form without restrictive assumptions on the correlations of PDFs of consecutive renewals. The analysis shows that fluctuations of W(t) can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.
Alonso, Daniel; Vega, Ines de
2010-06-15
Open quantum systems are often encountered in many different physical situations. From quantum optics to statistical mechanics, they are fundamental in the understanding of a great variety of different phenomena. Some of the most common examples are the relaxation to equilibrium, the existence of nonequilibrium stationary states, and the dynamics of atoms in interaction with electromagnetic fields. A crucial step in the analysis is to consider the quantum open system and its environment as the two mutually interacting components of a larger isolated system. Thereafter, the so-called Markov approximation is often considered, which consists on assuming that the time scales associated to the dynamics of the quantum open system are larger than those of the environment. It is the interplay of the different time scales associated with the system and the environment what determines the validity of the different approximations made. In this paper we will discuss the dynamics of a open quantum system in contact with a reservoir when the Markov approximation is not valid, and we have to include some non-Markovian or memory effects.
Exact Closed Master Equation for Gaussian Non-Markovian Dynamics.
Ferialdi, L
2016-03-25
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
Non-Markovian dynamics without using a quantum trajectory
Wu Chengjun; Li Yang; Zhu Mingyi; Guo Hong
2011-05-15
Open quantum systems interacting with structured environments is important and manifests non-Markovian behavior, which was conventionally studied using a quantum trajectory stochastic method. In this paper, by dividing the effects of the environment into two parts, we propose a deterministic method without using a quantum trajectory. This method is more efficient and accurate than the stochastic method in most Markovian and non-Markovian cases. We also extend this method to the generalized Lindblad master equation.
Closing the hierarchy for non-Markovian magnetization dynamics
NASA Astrophysics Data System (ADS)
Tranchida, J.; Thibaudeau, P.; Nicolis, S.
2016-04-01
We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau-Lifshitz-Gilbert and the Landau-Lifshitz-Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.
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.
Quantum measurements in continuous time, non-Markovian evolutions and feedback.
Barchielli, Alberto; Gregoratti, Matteo
2012-11-28
In this article, we reconsider a version of quantum trajectory theory based on the stochastic Schrödinger equation with stochastic coefficients, which was mathematically introduced in the 1990s, and we develop it in order to describe the non-Markovian evolution of a quantum system continuously measured and controlled, thanks to a measurement-based feedback. Indeed, realistic descriptions of a feedback loop have to include delay and thus need a non-Markovian theory. The theory allows us to put together non-Markovian evolutions and measurements in continuous time, in agreement with the modern axiomatic formulation of quantum mechanics. To illustrate the possibilities of such a theory, we apply it to a two-level atom stimulated by a laser. We introduce closed loop control too, via the stimulating laser, with the aim of enhancing the 'squeezing' of the emitted light, or other typical quantum properties. Note that here we change the point of view with respect to the usual applications of control theory. In our model, the 'system' is the two-level atom, but we do not want to control its state, to bring the atom to a final target state. Our aim is to control the 'Mandel Q-parameter' and the spectrum of the emitted light; in particular, the spectrum is not a property at a single time, but involves a long interval of times (a Fourier transform of the autocorrelation function of the observed output is needed).
Non-Markovianity in Randomized Benchmarking
NASA Astrophysics Data System (ADS)
Ball, Harrison; Stace, Tom M.; Biercuk, Michael J.
2015-03-01
Randomized benchmarking is routinely employed to recover information about the fidelity of a quantum operation by exploiting probabilistic twirling errors over an implementation of the Clifford group. Standard assumptions of Markovianity in the underlying noise environment, however, remain at odds with realistic, correlated noise encountered in real systems. We model single-qubit randomized benchmarking experiments as a sequence of ideal Clifford operations interleaved with stochastic dephasing errors, implemented as unitary rotations about σz. Successive error rotations map to a sequence of random variables whose correlations introduce non-Markovian effects emulating realistic colored-noise environments. The Markovian limit is recovered by turning off all correlations, reducing each error to an independent Gaussian-distributed random variable. We examine the dependence of the statistical distribution of fidelity outcomes on these noise correlations, deriving analytic expressions for probability density functions and related statistics for relevant fidelity metrics. This enables us to characterize and bear out the distinction between the Markovian and non-Markovian cases, with implications for interpretation and handling of experimental data.
Experimental observation of weak non-Markovianity
Bernardes, Nadja K.; Cuevas, Alvaro; Orieux, Adeline; Monken, C. H.; Mataloni, Paolo; Sciarrino, Fabio; Santos, Marcelo F.
2015-01-01
Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the so-called weak non-Markovian dynamics. Through full process tomography, we experimentally demonstrate that the dynamics of a qubit can be non-Markovian despite an always increasing correlation between the system and its environment which, in our case, denotes no information backflow. We also show the transition from the weak to the strong regime by changing a single parameter in the environmental state, leading us to a better understanding of the fundamental features of non-Markovianity. PMID:26627910
Exact non-Markovian dynamics of qubits coupled to two interacting environments
NASA Astrophysics Data System (ADS)
Shen, H. Z.; Li, D. X.; Su, Shi-Lei; Zhou, Y. H.; Yi, X. X.
2017-09-01
As the memory effect may be helpful in quantum information processing, non-Markovian dynamics plays an important role in the description of many-body open systems. Among these topics, the system consisting of independent qubits interacting with several coupled environments is of particular interest. In this paper, we study the exact non-Markovian dynamics of two independent qubits. Each of the qubits interacts individually with its environment, and these two environments coupled with each other. We investigate the non-Markovianity measure of the system for the whole parameter regime without the rotating-wave approximation (RWA) and compare the results with that under the RWA. We find that the non-Markovianity measure for two qubits manifests a transition from a non-Markovian to Markovian regime regardless of the coupling strength between the environments. The physical origin of this transition is revealed, and a possible observation of the prediction in superconducting quantum interference devices is discussed.
Non-Markovian open quantum systems: Input-output fields, memory, and monitoring
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2012-03-01
Principles of monitoring non-Markovian open quantum systems are analyzed. We use a field representation of the environment [C. W. Gardiner and M. J. Collett, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.31.3761 31, 3761 (1985)] for the separation of its memory and detector part, respectively. We claim that the system-plus-memory compound becomes Markovian; the detector part is tractable by standard Markovian monitoring. Because of non-Markovianity, only the mixed state of the system can be predicted; the pure state of the system can be retrodicted. We present the corresponding non-Markovian stochastic Schrödinger equation.
Quantum cryptography over non-Markovian channels
NASA Astrophysics Data System (ADS)
Thapliyal, Kishore; Pathak, Anirban; Banerjee, Subhashish
2017-05-01
A three-party scheme for secure quantum communication, namely controlled quantum dialogue (CQD), is analyzed under the influence of non-Markovian channels. By comparing with the corresponding Markovian cases, it is seen that the average fidelity can be maintained for relatively longer periods of time. Interestingly, a number of facets of quantum cryptography, such as quantum secure direct communication, deterministic secure quantum communication and their controlled counterparts, quantum dialogue, quantum key distribution, quantum key agreement, can be reduced from the CQD scheme. Therefore, the CQD scheme is analyzed under the influence of damping, dephasing and depolarizing non-Markovian channels, and subsequently, the effect of these non-Markovian channels on the other schemes of secure quantum communication is deduced from the results obtained for CQD. The damped non-Markovian channel causes a periodic revival in the fidelity, while fidelity is observed to be sustained under the influence of the dephasing non-Markovian channel.
A framework for the direct evaluation of large deviations in non-Markovian processes
NASA Astrophysics Data System (ADS)
Cavallaro, Massimo; Harris, Rosemary J.
2016-11-01
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.
Measuring and using non-Markovianity
NASA Astrophysics Data System (ADS)
Pineda, Carlos; Gorin, Thomas; Davalos, David; Wisniacki, Diego A.; García-Mata, Ignacio
2016-02-01
We construct measures for the non-Markovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative measures, based on the largest revival of a channel capacity, avoiding some drawbacks of other non-Markovianity measures. We relate the proposed measures to the task of information screening. This shows that the non-Markovianity of a quantum process may be used as a resource. Under these considerations, we analyze two paradigmatic examples, a qubit in a quantum environment with classically mixed dynamics and the Jaynes-Cummings model.
Thermodynamic power of non-Markovianity
Bylicka, Bogna; Tukiainen, Mikko; Chruściński, Dariusz; Piilo, Jyrki; Maniscalco, Sabrina
2016-01-01
The natural framework to discuss thermodynamics at the quantum level is the theory of open quantum systems. Memory effects arising from strong system-environment correlations may lead to information back-flow, that is non-Markovian behaviour. The relation between non-Markovianity and quantum thermodynamics has been until now largely unexplored. Here we show by means of Landauer’s principle that memory effects control the amount of work extraction by erasure in presence of realistic environments. PMID:27323947
Energy backflow and non-Markovian dynamics
NASA Astrophysics Data System (ADS)
Guarnieri, G.; Uchiyama, C.; Vacchini, B.
2016-01-01
We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting statistics formalism, which we use to evaluate the first moment of its probability distribution. We focus in particular on the energy backflow from environment to system, to which we associate a suitable condition and quantifier, which enables us to draw a connection with a recently introduced notion of non-Markovianity based on information backflow. This quantifier is then studied in detail in the case of the spin-boson model, described within a second-order time-convolutionless approximation, observing that non-Markovianity allows for the observation of energy backflow. This analysis allows us to identify the parameters region in which energy backflow is higher.
Non-Markovian relaxation of a three-level system: quantum trajectory approach.
Jing, Jun; Yu, Ting
2010-12-10
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.
Colloquium: Non-Markovian dynamics in open quantum systems
NASA Astrophysics Data System (ADS)
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
Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model
NASA Astrophysics Data System (ADS)
Zhou, Zheng-Yang; Chen, Mi; Yu, Ting; You, J. Q.
2016-02-01
One longstanding difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derive a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schrödinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.
Generalization of Pairwise Models to non-Markovian Epidemics on Networks
NASA Astrophysics Data System (ADS)
Kiss, Istvan Z.; Röst, Gergely; Vizi, Zsolt
2015-08-01
In this Letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new R0 -like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integro-differential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between non-Markovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of non-Markovian dynamics.
Non-Markovianity in atom-surface dispersion forces
Intravaia, F.; Behunin, R. O.; Henkel, C.; ...
2016-10-18
Here, we discuss the failure of the Markov approximation in the description of atom-surface fluctuation-induced interactions, both in equilibrium (Casimir-Polder forces) and out of equilibrium (quantum friction). Using general theoretical arguments, we show that the Markov approximation can lead to erroneous predictions of such phenomena with regard to both strength and functional dependencies on system parameters. Particularly, we show that the long-time power-law tails of two-time dipole correlations and their corresponding low-frequency behavior, neglected in the Markovian limit, affect the prediction of the force. These findings highlight the importance of non-Markovian effects in dispersion interactions.
Non-Markovianity of Gaussian Channels
NASA Astrophysics Data System (ADS)
Torre, G.; Roga, W.; Illuminati, F.
2015-08-01
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.
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.
Generalized non-Markovian optical Bloch equations
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2007-02-01
By considering single chromophore systems whose radiative decay can be written in terms of a nonlocal Lindblad-type evolution, the authors extend the formalism of generalized optical Bloch equations [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] to non-Markovian dynamics. They demonstrate that photon statistical properties such as bunching and antibunching, as well as sub- and super-Poissonian photon statistics can be fitted in the context of non-Markovian dynamics. The nonlocal effects may arise due to the interaction with a complex structured environment. In this case, the photon statistics can be related with the parameters that define the microscopic system-environment interaction. Alternatively, the authors demonstrate that effective dynamics such as triplet blinking, where the system is coupled via incoherent transitions to an extra dark state, can also be worked out in terms of generalized non-Markovian optical Bloch equations. The corresponding memory contributions are mapped with those that arise from the microscopic approach.
Quantum metrology in non-Markovian environments.
Chin, Alex W; Huelga, Susana F; Plenio, Martin B
2012-12-07
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
Enabling quantum non-Markovian dynamics by injection of classical colored noise
NASA Astrophysics Data System (ADS)
Costa-Filho, J. I.; Lima, R. B. B.; Paiva, R. R.; Soares, P. M.; Morgado, W. A. M.; Franco, R. Lo; Soares-Pinto, D. O.
2017-05-01
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.
Non-Markovian effect on remote state preparation
Xu, Zhen-Yu; Liu, Chen; Luo, Shunlong; Zhu, Shiqun
2015-05-15
Memory effect of non-Markovian dynamics in open quantum systems is often believed to be beneficial for quantum information processing. In this work, we employ an experimentally controllable two-photon open system, with one photon experiencing a dephasing environment and the other being free from noise, to show that non-Markovian effect may also have a negative impact on quantum tasks such as remote state preparation: For a certain period of controlled time interval, stronger non-Markovian effect yields lower fidelity of remote state preparation, as opposed to the common wisdom that more information leads to better performance. As a comparison, a positive non-Markovian effect on the RSP fidelity with another typical non-Markovian noise is analyzed. Consequently, the observed dual character of non-Markovian effect will be of great importance in the field of open systems engineering.
Long-time memory in non-Markovian evolutions
Chruscinski, Dariusz; Pascazio, Saverio
2010-03-15
If the dynamics of an open quantum system is non-Markovian, its asymptotic state strongly depends on the initial conditions, even if the dynamics possesses an invariant state. This is the very essence of memory effects. In particular, the asymptotic state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the noninvariance of equilibrium becomes a clear sign of non-Markovianity.
Non-Markovianity hinders Quantum Darwinism
NASA Astrophysics Data System (ADS)
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.
Non-Markovianity hinders Quantum Darwinism.
Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina
2016-01-20
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.
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. PMID:26786857
Non-Markovian dynamics of quantum discord
Fanchini, F. F.; Caldeira, A. O.; Werlang, T.; Brasil, C. A.; Arruda, L. G. E.
2010-05-15
We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.
Non-Markovianity-assisted steady state entanglement.
Huelga, Susana F; Rivas, Ángel; Plenio, Martin B
2012-04-20
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.
Mean first-passage times of non-Markovian random walkers in confinement
NASA Astrophysics Data System (ADS)
Guérin, T.; Levernier, N.; Bénichou, O.; Voituriez, R.
2016-06-01
The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.
Entanglement and non-markovianity of quantum evolutions.
Rivas, Angel; Huelga, Susana F; Plenio, Martin B
2010-07-30
We address the problem of quantifying the non-markovian character of quantum time evolutions of general systems in contact with an environment. We introduce two different measures of non-markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts. When complete tomographic knowledge about the evolution is available, our measure provides a necessary and sufficient condition to quantify strictly the non-markovianity. In the opposite case, when no information whatsoever is available, we propose a sufficient condition for non-markovianity. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.
Solvable non-Markovian dynamic network
NASA Astrophysics Data System (ADS)
Georgiou, Nicos; Kiss, Istvan Z.; Scalas, Enrico
2015-10-01
Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.
General non-Markovian dynamics of open quantum systems.
Zhang, Wei-Min; Lo, Ping-Yuan; Xiong, Heng-Na; Tu, Matisse Wei-Yuan; Nori, Franco
2012-10-26
We present a general theory of non-Markovian dynamics for open systems of noninteracting fermions (bosons) linearly coupled to thermal environments of noninteracting fermions (bosons). We explore the non-Markovian dynamics by connecting the exact master equations with the nonequilibirum Green's functions. Environmental backactions are fully taken into account. The non-Markovian dynamics consists of nonexponential decays and dissipationless oscillations. Nonexponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian thermal environments show that non-Markovian dynamics can be largely understood from the environmental-modified spectra of open systems.
Optomechanical cooling in the non-Markovian regime
NASA Astrophysics Data System (ADS)
Zhang, Wen-Zhao; Cheng, Jiong; Li, Wen-Dong; Zhou, Ling
2016-06-01
We propose a scheme in which the cooling of a mechanical resonator is achieved by exposing the optomechanical system to a non-Markovian environment. Because of the backflow from the non-Markovian environment, the phonon number can go beyond the conventional cooling limit in a Markovian environment. Utilizing the spectrum density obtained in a recent experiment [S. Gröblacher et al., Nat. Commun. 6, 7606 (2015)], 10.1038/ncomms8606, we show that the cooling process is highly effective in a non-Markovian environment. Analysis of the cooling mechanism in a non-Markovian environment reveals that the non-Markovian memory effect is instrumental in the cooling process.
Delineating incoherent non-Markovian dynamics using quantum coherence
Chanda, Titas Bhattacharya, Samyadeb
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.
Classical non-Markovian Boltzmann equation
NASA Astrophysics Data System (ADS)
Alexanian, Moorad
2014-08-01
The modeling of particle transport involves anomalous diffusion, ⟨x2(t) ⟩ ∝ tα with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
Non-Markovian dynamics of a qubit
Maniscalco, Sabrina; Petruccione, Francesco
2006-01-15
In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the recently proposed post-Markovian master equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function and bring to light the limits of usability of master equations with memory for the system under consideration.
Classical non-Markovian Boltzmann equation
Alexanian, Moorad
2014-08-01
The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
Exploiting Non-Markovianity for Quantum Control
NASA Astrophysics Data System (ADS)
Reich, Daniel M.; Katz, Nadav; Koch, Christiane P.
2015-07-01
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.
Force-linearization closure for non-Markovian Langevin systems with time delay
NASA Astrophysics Data System (ADS)
Loos, Sarah A. M.; Klapp, Sabine H. L.
2017-07-01
This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of FP equations for the various n -time joint distribution functions. Here, we present an approach to close the hierarchy at the one-time level based on a linearization of the deterministic forces in all members of the hierarchy starting from the second one. This leads to a closed equation for the one-time probability density in the steady state. Considering two generic nonlinear systems, a colloidal particle in a sinusoidal or bistable potential supplemented by a linear delay force, we demonstrate that our approach yields a very accurate representation of the density as compared to quasiexact numerical results from direct solution of the Langevin equation. Moreover, the results are significantly improved against those from a small-delay approximation and a perturbation-theoretical approach. We also discuss the possibility of accessing transport-related quantities, such as escape times, based on an additional Kramers approximation. Our approach applies to a wide class of models with nonlinear deterministic forces.
Jump-diffusion unravelling of a non-Markovian generalized Lindblad master equation
Barchielli, A.; Pellegrini, C.
2010-11-15
The ''correlated-projection technique'' has been successfully applied to derive a large class of highly non-Markovian dynamics, the so called non-Markovian generalized Lindblad-type equations or Lindblad rate equations. In this article, general unravelings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unraveling can be interpreted in terms of measurements continuous in time but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.
Non-Markovian work fluctuation theorem in crossed electric and magnetic fields.
Jiménez-Aquino, J I
2015-08-01
The validity of the transient work fluctuation theorem for a charged Brownian harmonic oscillator embedded in a non-Markovian heat bath and under the action of crossed electric and magnetic fields is investigated. The aforementioned theorem is verified to be valid within the context of the generalized Langevin equation with an arbitrary memory kernel and arbitrary dragging in the potential minimum. The fluctuation-dissipation relation of the second kind is assumed to be valid and shows that the non-Markovian stochastic dynamics associated with the particle, in the absence of the external time-dependent electric field, reaches an equilibrium state, as is precisely demanded by such a relation. The Jarzynski equality in this problem is also analyzed.
Investigating non-Markovian dynamics of quantum open systems
NASA Astrophysics Data System (ADS)
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
Excitation energy transfer: Study with non-Markovian dynamics
Liang Xianting
2010-11-15
In this paper, we investigate the non-Markovian dynamics of a model to mimic the excitation energy transfer (EET) between chromophores in photosynthesis systems. The numerical path integral method is used. This method includes the non-Markovian effects of the environmental affects, and it does not need the perturbation approximation in solving the dynamics of systems of interest. It implies that the coherence helps the EET between chromophores through lasting the transfer time rather than enhancing the transfer rate of the EET. In particular, the non-Markovian environment greatly increases the efficiency of the EET in the photosynthesis systems.
Non-Markovianity: initial correlations and nonlinear optical measurements
Dijkstra, Arend G.; Tanimura, Yoshitaka
2012-01-01
By extending the response function approach developed in nonlinear optics, we analytically derive an expression for the non-Markovianity in the time evolution of a system in contact with a quantum mechanical bath, and find a close connection with the directly observable nonlinear optical response. The result indicates that memory in the bath-induced fluctuations rather than in the dissipation causes non-Markovianity. Initial correlations between states of the system and the bath are shown to be essential for a correct understanding of the non-Markovianity. These correlations are included in our treatment through a preparation function. PMID:22753819
Data-driven non-Markovian Reduced-Order Modeling
NASA Astrophysics Data System (ADS)
Kondrashov, D. A.
2016-12-01
This presentation will provide an overview of Multilayered Stochastic Modeling (MSM) [Kondrashov, Chekroun and Ghil, 2015] and its applications in hierarchy of models for oceanic and atmospheric turbulent flows. MSM is a data-driven reduced-order framework that aims to obtain a low-order nonlinear system of prognostic equations driven by stochastic forcing, and estimates both the dynamical operator and the properties of the driving noise from multivariate time series of observations or a high-end model's simulation. MSM leads to a system of stochastic differential equations (SDEs) involving hidden (auxiliary) variables of fast-small scales ranked by layers, which interact with the macroscopic (observed) variables of large-slow scales to model the dynamics of the latter. MSM dynamics of observed variables is governed by three types of interactions: (a) nonlinear deterministic Markovian part; (b) non-Markovian part conveying memory effects of interactions with hidden variables; and (c) spatio-temporal noise. New MSM applications focus on development of computationally efficient reduced-order models by using data-adaptive decomposition methods that convey memory effects by time-embedding techniques, such as Multichannel Singular Spectrum Analysis (M-SSA) [Ghil et al. 2002]. Recently developed Data-Adaptive Harmonic (DAH) decomposition method [Chekroun and Kondrashov, 2016] is another multivariate technique that adopts time-embedding information, but that is distinctly different from M-SSA by its frequency-based, rather than variance-based content, to decompose time-evolving signals. DAH decomposition allows in a data-adaptive way, for the extraction of mode pairs that come in exact phase quadrature, and are narrow-band time series in the frequency domain that can be very efficiently modeled as a system of coupled oscillators. New results by DAH modeling for geophysical flows will be presented.
Non-Markovian Quantum Friction of Bright Solitons in Superfluids
NASA Astrophysics Data System (ADS)
Efimkin, Dmitry K.; Hofmann, Johannes; Galitski, Victor
2016-06-01
We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from first principles. The equation contains a stochastic Langevin force (associated with quantum noise) and a nonlocal in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton (particle) interacts with excitations (radiation) originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.
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.
Characterizing non-Markovianity via quantum interferometric power
NASA Astrophysics Data System (ADS)
Dhar, Himadri Shekhar; Bera, Manabendra Nath; Adesso, Gerardo
2015-03-01
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamiołkowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.
Chen, Po-Wen; Ali, Md. Manirul
2014-01-01
Leggett-Garg inequalities (LGI) test the correlations of a single system measured at different times. Violation of LGI implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. We investigate the violation of the Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. We discuss the non-Markovian dynamics of the violation of LGI at zero temperature and also at finite temperature for different structured environments. An enhanced quantum coherence is shown through the violation of Leggett-Garg inequality in the strong non-Markovian regime of the environment. PMID:25145508
Non-Markovian full counting statistics in quantum dot molecules.
Xue, Hai-Bin; Jiao, Hu-Jun; Liang, Jiu-Qing; Liu, Wu-Ming
2015-03-10
Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.
Non-Markovian full counting statistics in quantum dot molecules
Xue, Hai-Bin; Jiao, Hu-Jun; Liang, Jiu-Qing; Liu, Wu-Ming
2015-01-01
Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules. PMID:25752245
Quantum regression theorem and non-Markovianity of quantum dynamics
NASA Astrophysics Data System (ADS)
Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano
2014-08-01
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.
Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning.
Cardenas, Alfredo E; Elber, Ron
2016-08-25
We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics. Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions. The construction of the two models makes it possible to examine their consistency and accuracy. The equilibrium and fluctuations of the phosphate groups along the normal to the membrane plane are estimated, and milestoning equations are constructed and solved. An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model. The equilibrium solution of both models is favorably compared to distributions obtained from straightforward molecular dynamics simulations. The picture for the kinetics is complex. Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process. In Markovian modeling, only a single relaxation time is assumed for a state. Mapping of particle dynamics to the dynamics of a field density offers a new way of coarse graining complex systems as membranes that may bridge between atomically detailed models and phenomenological descriptions of macroscopic membranes.
Non-Markovian errors and the cluster state machine gun
NASA Astrophysics Data System (ADS)
Rudolph, Terry; Lindner, Netanel
2010-03-01
The hyperfine interaction between an electron and a nuclear spin bath is one of the more significant non-Markovian decoherence mechanisms affecting spin qubits in quantum dots. For the purposes of quantum error correction typically Markovian noise models are assumed. We show here that a recent proposal for a quantum dot based photon source Phys. Rev. Lett. 103, 113602 (2009) is not deleteriously affected by the non-Markovian noise because the noise can actually be, in some sense, bounded by a Markovian noise model. This allows for standard quantum fault tolerance results to go trough and shows that the device could be useful for scalable quantum computation. The technique we introduce for simplifying the analysis of the non Markovian noise will be of generic use in other architectures affected by similar decoherence mechanisms.
Non-Markovian expansion in quantum Brownian motion
NASA Astrophysics Data System (ADS)
Fraga, Eduardo S.; Krein, Gastão; Palhares, Letícia F.
2014-01-01
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.
Non-Markovian Dynamics of Spin Squeezing Under Detuning Modulation
NASA Astrophysics Data System (ADS)
Xiao, Xing; Wu, Jia-Ju; Zhong, Wo-Jun; Li, Yan-Ling
The dynamics of spin squeezing of an ensemble of N separate spin-1/2 particles, each coupled to a zero-temperature non-Markovian reservoir have been investigated. We show that the initial spin squeezing could be prolonged for a long time by utilizing detuning modification. We further explore that the spin squeezing sudden death (SSSD) could be circumvented with the increasing of detuning. By comparison with the results in Markovian regime with detuning and those in non-Markovian regime without detuning, we conclude that the disappearance of SSSD and the robust preservation of spin squeezing should be attributed to the combination of detuning and non-Markovian effect. The present results may be of direct importance for quantum metrology in open systems.
Non-Markovian coherent feedback control of quantum dot systems
NASA Astrophysics Data System (ADS)
Xue, Shibei; Wu, Rebing; Hush, Michael R.; Tarn, Tzyh-Jong
2017-03-01
In this paper we present a non-Markovian coherent feedback scheme for decoherence suppression in single quantum dot systems. The feedback loop is closed via a quantum tunnelling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyse the Green’s function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. The effectiveness of decoherence suppression induced by non-Markovian coherent feedback is demonstrated by a single quantum dot example bathed with Lorentzian noises.
Quantum Monte Carlo method applied to non-Markovian barrier transmission
NASA Astrophysics Data System (ADS)
Hupin, Guillaume; Lacroix, Denis
2010-01-01
In nuclear fusion and fission, fluctuation and dissipation arise because of the coupling of collective degrees of freedom with internal excitations. Close to the barrier, quantum, statistical, and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte Carlo method is applied to systems with quadratic potentials. In all ranges of temperature and coupling, the stochastic method matches the exact evolution, showing that non-Markovian effects can be simulated accurately. A comparison with other theories, such as Nakajima-Zwanzig or time-convolutionless, shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated by different approaches including the Markovian limit. Large differences with an exact result are seen in the latter case or when only second order in the coupling strength is considered, as is generally assumed in nuclear transport models. In contrast, if fourth order in the coupling or quantum Monte Carlo method is used, a perfect agreement is obtained.
Measures of non-Markovianity: Divisibility versus backflow of information
Chruscinski, Dariusz; Kossakowski, Andrzej
2011-05-15
We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.
Quantum non-Markovianity induced by Anderson localization
Lorenzo, Salvatore; Lombardo, Federico; Ciccarello, Francesco; Palma, G. Massimo
2017-01-01
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath. PMID:28205542
Non-Markovian character in human mobility: Online and offline.
Zhao, Zhi-Dan; Cai, Shi-Min; Lu, Yang
2015-06-01
The dynamics of human mobility characterizes the trajectories that humans follow during their daily activities and is the foundation of processes from epidemic spreading to traffic prediction and information recommendation. In this paper, we investigate a massive data set of human activity, including both online behavior of browsing websites and offline one of visiting towers based mobile terminations. The non-Markovian character observed from both online and offline cases is suggested by the scaling law in the distribution of dwelling time at individual and collective levels, respectively. Furthermore, we argue that the lower entropy and higher predictability in human mobility for both online and offline cases may originate from this non-Markovian character. However, the distributions of individual entropy and predictability show the different degrees of non-Markovian character between online and offline cases. To account for non-Markovian character in human mobility, we apply a protype model with three basic ingredients, namely, preferential return, inertial effect, and exploration to reproduce the dynamic process of online and offline human mobilities. The simulations show that the model has an ability to obtain characters much closer to empirical observations.
Non-Markovian character in human mobility: Online and offline
NASA Astrophysics Data System (ADS)
Zhao, Zhi-Dan; Cai, Shi-Min; Lu, Yang
2015-06-01
The dynamics of human mobility characterizes the trajectories that humans follow during their daily activities and is the foundation of processes from epidemic spreading to traffic prediction and information recommendation. In this paper, we investigate a massive data set of human activity, including both online behavior of browsing websites and offline one of visiting towers based mobile terminations. The non-Markovian character observed from both online and offline cases is suggested by the scaling law in the distribution of dwelling time at individual and collective levels, respectively. Furthermore, we argue that the lower entropy and higher predictability in human mobility for both online and offline cases may originate from this non-Markovian character. However, the distributions of individual entropy and predictability show the different degrees of non-Markovian character between online and offline cases. To account for non-Markovian character in human mobility, we apply a protype model with three basic ingredients, namely, preferential return, inertial effect, and exploration to reproduce the dynamic process of online and offline human mobilities. The simulations show that the model has an ability to obtain characters much closer to empirical observations.
Non-Markovian time evolution of an accelerated qubit
NASA Astrophysics Data System (ADS)
Moustos, Dimitris; Anastopoulos, Charis
2017-01-01
We present a new method for evaluating the response of a moving qubit detector interacting with a scalar field in Minkowski spacetime. We treat the detector as an open quantum system, but we do not invoke the Markov approximation. The evolution equations for the qubit density matrix are valid at all times, for all qubit trajectories, and they incorporate non-Markovian effects. We analyze in detail the case of uniform acceleration, providing a detailed characterization of all regimes where non-Markovian effects are significant. We argue that the most stable characterization of acceleration temperature refers to the late time behavior of the detector because interaction with the field vacuum brings the qubit to a thermal state at the Unruh temperature. In contrast, the early-time transition rate, that is invoked in most discussions of acceleration temperature, does not exhibit a thermal behavior when non-Markovian effects are taken into account. Finally, we note that the non-Markovian evolution derived here also applies to the mathematically equivalent problem of a static qubit interacting with a thermal field bath.
Quantum non-Markovianity induced by Anderson localization
NASA Astrophysics Data System (ADS)
Lorenzo, Salvatore; Lombardo, Federico; Ciccarello, Francesco; Palma, G. Massimo
2017-02-01
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.
Geometric quantum discord and non-Markovianity of structured reservoirs
Hu, Ming-Liang Lian, Han-Li
2015-11-15
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated that the non-Markovianity induced by the backflow of information from the reservoirs to the system enhances the GQDs in most of the parameter regions. This highlights the potential of non-Markovianity as a resource for protecting the GQDs. -- Highlights: •Dependence of GQDs on a factor determined by spectrum of the structured reservoir. •Connection between the direction of information flow and variation of the GQDs. •Non-Markovianity with the backflow of information enhances GQDs in a wide region. •The GQDs are enhanced with the information loss in a very narrow region.
Quantum non-Markovianity induced by Anderson localization.
Lorenzo, Salvatore; Lombardo, Federico; Ciccarello, Francesco; Palma, G Massimo
2017-02-16
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.
A non-Markovian model of rill erosion
NASA Astrophysics Data System (ADS)
Winter, C.; Damron, M.
2009-12-01
Stochastic processes with reinforcement are inherently non-Markovian and therefore may model geophysical processes with memory, for instance patterns of rill erosion, more realistically than Markovian models. Reinforcement provides a bias to a system that is equivalent to infinite memory, making a system more likely to occupy a given state the more often the state is visited. Some well-studied examples in applied mathematics include variations on the urn of P'olya and reinforced random walks. Many natural phenomena exhibit similar behavior: for instance, an overall pattern of rills is relatively stable once it is established, although small details of the pattern may change frequently and catastrophes that permanently alter it may occasionally occur. To model the phenomenology of rill erosion, we propose a simple discrete time, infinite-memory random process defined on the nodes and edges of an oriented diagonal lattice. Lattice models have often been used to investigate the morphology of natural drainage networks, but our focus is as much on the dynamics of network formation as it is on morphology. The lattice in our model starts out smooth in the sense that it has no edges initially, but it sprouts edges everywhere the instant the process starts, much as rain can start soil erosion everywhere on a hillslope at once. Exactly one edge (rill segment) descends from each node, and it points either left or right. Sediment loads travel along networks of edges and are accumulated at nodes. At every node and at every time step, a simple two parameter reinforcing law randomly determines the direction of the node’s output and then is updated. The degree of reinforcement is set by comparing the node's current sediment load to the load history of the entire network above it and is governed by two system parameters representing respectively rainfall intensity and the soil’s resistance to change. The current pattern of connections among nodes represents the present state of
Programmable entanglement oscillations in a non-Markovian channel
Cialdi, Simone; Brivio, Davide; Tesio, Enrico; Paris, Matteo G. A.
2011-04-15
We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in an effective non-Markovian channel. We generate entangled photon pairs by spontaneous parametric down-conversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization-dependent phase shift on the spatial domain of the SPDC output. This creates an effective programmable non-Markovian environment where modulation of the environment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscillations of entanglement are achieved, where the entangled state obtained at the maximum of the revival after sudden death violates Bell's inequality by 17 standard deviations.
Linear Optics Simulation of Quantum Non-Markovian Dynamics
Chiuri, Andrea; Greganti, Chiara; Mazzola, Laura; Paternostro, Mauro; Mataloni, Paolo
2012-01-01
The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects. PMID:23236588
Linear Optics Simulation of Quantum Non-Markovian Dynamics
NASA Astrophysics Data System (ADS)
Chiuri, Andrea; Greganti, Chiara; Mazzola, Laura; Paternostro, Mauro; Mataloni, Paolo
2012-12-01
The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects.
Momentum coupling in non-Markovian quantum Brownian motion
NASA Astrophysics Data System (ADS)
Ferialdi, Luca; Smirne, Andrea
2017-07-01
We consider a model of non-Markovian quantum Brownian motion that consists of a harmonic oscillator bilinearly coupled to a thermal bath, both via its position and via its momentum operators. We derive the master equation for such a model, and we solve the equations of motion for a generic Gaussian system state. We then investigate the resulting evolution of the first and second moments for both an Ohmic and a super-Ohmic spectral density. In particular, we show that, irrespective of the specific form of the spectral density, the coupling with the momentum enhances the dissipation experienced by the system, accelerating its relaxation to the equilibrium as well as modifying the asymptotic state of the dynamics. Eventually, we characterize explicitly the non-Markovianity of the evolution using a general criterion which relies on the positivity of the master equation coefficients.
Non-Markovianity and memory of the initial state
NASA Astrophysics Data System (ADS)
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.
Comparisons of different witnesses of non-Markovianity
NASA Astrophysics Data System (ADS)
Zuo, Wei; Qian, Xiao-Qing; Liang, Xian-Ting
2017-01-01
In this paper, the evolutions of two kinds of witnesses of the non-Markovianity and their rates of changes with time are investigated and compared. Four definitions, the trace distance, fidelity, quantum relative entropy, and quantum Fisher information are used for the first kind of witnesses which are based on the completely positive maps (CPM). Three definitions, the quantum entanglement, quantum mutual information, and quantum discord are used for the second kind of witnesses, and they are based on the local completely positive maps (LCPM). An open two-level quantum system model and a numerically quantum dissipative dynamics method, hierarchy equation of motion (HEM) are used in the investigations. It is shown that the evolutions of the witnesses and their rates of the changes calculated with different definitions clearly show the characteristics of the non-Markovianity and they are in agreement with each other.
Non-Markovian State-Dependent Networks in Critical Loading
2013-01-23
orthant. We give an application to generalised Jackson networks with state-dependent rates. 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13...process is a continuous-path reflected process on the nonnegative orthant. We give an application to generalised Jackson networks with state-dependent...We give an application to generalised Jackson networks with state-dependent rates. Keywords: State-dependent networks, non-Markovian networks
Stochastic description of quantum Brownian dynamics
NASA Astrophysics Data System (ADS)
Yan, Yun-An; Shao, Jiushu
2016-08-01
such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.
Generalized trace-distance measure connecting quantum and classical non-Markovianity
NASA Astrophysics Data System (ADS)
Wißmann, Steffen; Breuer, Heinz-Peter; Vacchini, Bassano
2015-10-01
We establish a direct connection of quantum Markovianity of an open system to its classical counterpart by generalizing the criterion based on the information flow. Here the flow is characterized by the time evolution of Helstrom matrices, given by the weighted difference of statistical operators, under the action of the quantum dynamical map. It turns out that the introduced criterion is equivalent to P divisibility of a quantum process, namely, divisibility in terms of positive maps, which provides a direct connection to classical Markovian stochastic processes. Moreover, it is shown that mathematical representations similar to those found for the original trace-distance-based measure hold true for the associated generalized measure for quantum non-Markovianity. That is, we prove orthogonality of optimal states showing a maximal information backflow and establish a local and universal representation of the measure. We illustrate some properties of the generalized criterion by means of examples.
Maggiore, Michele; Riotto, Antonio
2010-03-10
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
Two-dimensional photon echoes reveal non-Markovian energy transfer in an excitonic dimer
NASA Astrophysics Data System (ADS)
Duan, Hong-Guang; Frey, Moritz; Thorwart, Michael; Nalbach, Peter
2016-11-01
We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.
Non-Markovian effects on quantum-communication protocols
Yeo, Ye; Oh, C. H.; An, Jun-Hong
2010-09-15
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.
Non-Markovian dynamics in ultracold Rydberg aggregates
NASA Astrophysics Data System (ADS)
Genkin, M.; Schönleber, D. W.; Wüster, S.; Eisfeld, A.
2016-07-01
We propose a setup of an open quantum system in which the environment can be tuned such that either Markovian or non-Markovian system dynamics can be achieved. The implementation uses ultracold Rydberg atoms, relying on their strong long-range interactions. Our suggestion extends the features available for quantum simulators of molecular systems employing Rydberg aggregates and presents a new test bench for fundamental studies of the classification of system-environment interactions and the resulting system dynamics in open quantum systems.
Non-Markovian quantum jump with generalized Lindblad master equation.
Huang, X L; Sun, H Y; Yi, X X
2008-10-01
The Monte Carlo wave function method or the quantum-trajectory-jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. We extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method is also discussed.
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.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Objectivity in the non-Markovian spin-boson model
NASA Astrophysics Data System (ADS)
Lampo, Aniello; Tuziemski, Jan; Lewenstein, Maciej; Korbicz, Jarosław K.
2017-07-01
Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present paper we study the emergence of such a state structure in one of the canonical models of the condensed-matter theory: the spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.
Affecting non-Markovian behaviour by changing bath structures
NASA Astrophysics Data System (ADS)
Venkataraman, V.; Plato, A. D. K.; Tufarelli, Tommaso; Kim, M. S.
2014-01-01
For many open quantum systems, a master equation approach employing the Markov approximation cannot reliably describe the dynamical behaviour. This is the case, for example, in a number of solid state or biological systems, and it has motivated a line of research aimed at quantifying the amount of non-Markovian behaviour (NMB) in a given model. Within this framework, we investigate the dynamics of a quantum harmonic oscillator linearly coupled to a bosonic bath. We focus on Gaussian states, which are suitably treated using a covariance matrix approach. Concentrating on an entanglement based NMB quantifier (NMBQ) proposed by Rivas et al (2010 Phys. Rev. Lett. 105 050403), we consider the role that near resonant and off-resonant modes play in affecting the NMBQ. By using a large but finite bath of oscillators for both Ohmic and super Ohmic spectral densities we find, by systematically increasing the coupling strength, initially the near resonant modes provide the most significant non-Markovian effects, while after a certain threshold of coupling strength the off-resonant modes play the dominant role. We also consider the NMBQ for two other models where we add a single strongly coupled oscillator to the model in extra bath mode and ‘buffer’ configurations, which affects the modes that determine NMB.
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
Bolivar, A.O.
2011-05-15
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.
Nonclassical correlations in non-Markovian continuous-variable systems
Vasile, Ruggero; Maniscalco, Sabrina; Giorda, Paolo; Olivares, Stefano; Paris, Matteo G. A.
2010-07-15
We consider two identical and noninteracting harmonic oscillators coupled to either two independent bosonic baths or to a common bosonic bath. Under the only assumption, weak coupling, we analyze in detail the non-Markovian short-time-scale evolution of intensity correlations, entanglement, and quantum discord for initial two-mode squeezed-thermal vacuum states. In the independent reservoirs case, we observe the detrimental effect of the environment for all these quantities and we establish a hierarchy for their robustness against the environmental noise. In the common reservoir case, for initial uncorrelated states, we find that only quantum discord can be created via interaction with the bath, while entanglement and subshot noise intensity correlations remain absent.
Entanglement oscillations in non-Markovian quantum channels
Maniscalco, Sabrina; Olivares, Stefano; Paris, Matteo G. A.
2007-06-15
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in detail the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density, entanglement persists for a longer time than in a Markovian channel. On the other hand, when the reservoir spectrum is out of resonance, short-time correlations lead to a faster decoherence and to the appearance of entanglement oscillations.
Observation of non-Markovian micromechanical Brownian motion
Gröblacher, S.; Trubarov, A.; Prigge, N.; Cole, G. D.; Aspelmeyer, M.; Eisert, J.
2015-01-01
All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification. PMID:26216619
Inequivalence of correlation-based measures of non-Markovianity
NASA Astrophysics Data System (ADS)
Neto, Alaor Cervati; Karpat, Göktuǧ; Fanchini, Felipe Fernandes
2016-09-01
We conclusively show that the entanglement- and the mutual-information-based measures of quantum non-Markovianity are inequivalent. To this aim, we first analytically solve the optimization problem in the definition of the entanglement-based measure for a two-level system. We demonstrate that the optimal initial bipartite state of the open system and the ancillary is always given by one of the Bell states for any one-qubit dynamics. On top of this result, we present an explicit example dynamics where memory effects emerge according to the mutual-information-based measure, even though the time evolution remains memoryless with respect to the entanglement-based measure. Finally, we explain this disagreement between the two measures in terms of the information dynamics of the open system, exploring the accessible and inaccessible parts of information.
Entropy production and non-Markovian dynamical maps.
Marcantoni, S; Alipour, S; Benatti, F; Floreanini, R; Rezakhani, A T
2017-09-29
In the weak-coupling limit approach to open quantum systems, the presence of the bath is eliminated and accounted for by a master equation that introduces dissipative contributions to the system reduced dynamics: within this framework, there are no bath entropy contributions to the entropy balance. We show that, as a consequence, the entropy production fails to be positive for a class of physically legitimate, that is completely positive and trace preserving, non-Markovian dynamical maps. Moreover, in absence of the semigroup property, if the reduced dynamics has a thermal asymptotic state, this need not be stationary. Then even the integrated entropy production becomes negative. These observations imply that, when the conditions leading to reduced dynamics of semigroup type are relaxed, a consistent formulation of the second law of thermodynamics requires that the environment contribution to the entropy balance be explicitly taken into account.
Non-Markovian Two-Time Correlation Dynamics and Nonergodicity
NASA Astrophysics Data System (ADS)
Bao, J.-D.
2017-08-01
The two-time correlation functions of the coordinate and velocity of a non-Markovian harmonic particle are derived analytically. They are decomposed into the components of differences between the initial variances and the equilibrium of the particle; in particular, the dependence of a random force on the initial preparation of the system is included. Using those expressions, we simultaneously investigate nonstationary, nonergodic, and nonequilibrium features of a forced system. It is demonstrated that the result of combining the oscillating relaxation and the initial preparation-dependent noise leads to breakdown of both ergodicity and equilibration of a forced system. The finite-size effect of a coupled-oscillator-chain heat bath is also discussed.
Fermionic-mode entanglement in non-Markovian environment
Cheng, Jiong; Han, Yan; An, Qing-zhi; Zhou, Ling
2015-03-15
We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman–Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.
NASA Astrophysics Data System (ADS)
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
NASA Astrophysics Data System (ADS)
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
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective.
Bylicka, B; Chruściński, D; Maniscalco, S
2014-07-21
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
Preservation Macroscopic Entanglement of Optomechanical Systems in non-Markovian Environment
Cheng, Jiong; Zhang, Wen-Zhao; Zhou, Ling; Zhang, Weiping
2016-01-01
We investigate dynamics of an optomechanical system under the non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage to generate and protect entanglement via non-Markovian environment. PMID:27032674
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
Bylicka, B.; Chruściński, D.; Maniscalco, S.
2014-01-01
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication. PMID:25043763
Dissipative particle dynamics incorporating non-Markovian effect
NASA Astrophysics Data System (ADS)
Kinefuchi, Ikuya; Yoshimoto, Yuta; Takagi, Shu
2015-11-01
The coarse-graining methodology of molecular simulations is of great importance to analyze large-scale, complex hydrodynamic phenomena. In the present study, we derive the equation of motion for non-Markovian dissipative particle dynamics (NMDPD) by introducing the history effects on the time evolution of the system. Our formulation is based on the generalized Langevin equation, which describes the motions of the centers of mass of clusters comprising microscopic particles. The mean, friction, and fluctuating forces in the NMDPD model are directly constructed from an underlying MD system without any scaling procedure. For the validation of our formulation, we construct NMDPD models from high-density Lennard-Jones systems, in which the typical time scales of the coarse-grained particle motions and the fluctuating forces are not fully separable. The NMDPD models reproduce the temperatures, diffusion coefficients, and viscosities of the corresponding MD systems more accurately than the conventional DPD models based on a Markovian approximation. Our results suggest that the NMDPD method is a promising alternative for simulating mesoscale flows where a Markovian approximation is not valid.
Entanglement dynamics in a non-Markovian environment: An exactly solvable model
NASA Astrophysics Data System (ADS)
Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.
2012-05-01
We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.
Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations
NASA Astrophysics Data System (ADS)
Pellegrini, Clément
2014-02-01
A new type of quantum random walks, called Open Quantum Random Walks, has been developed and studied in Attal et al. (Open quantum random walks, preprint) and (Central limit theorems for open quantum random walks, preprint). In this article we present a natural continuous time extension of these Open Quantum Random Walks. This continuous time version is obtained by taking a continuous time limit of the discrete time Open Quantum Random Walks. This approximation procedure is based on some adaptation of Repeated Quantum Interactions Theory (Attal and Pautrat in Annales Henri Poincaré Physique Théorique 7:59-104, 2006) coupled with the use of correlated projectors (Breuer in Phys Rev A 75:022103, 2007). The limit evolutions obtained this way give rise to a particular type of quantum master equations. These equations appeared originally in the non-Markovian generalization of the Lindblad theory (Breuer in Phys Rev A 75:022103, 2007). We also investigate the continuous time limits of the quantum trajectories associated with Open Quantum Random Walks. We show that the limit evolutions in this context are described by jump stochastic differential equations. Finally we present a physical example which can be described in terms of Open Quantum Random Walks and their associated continuous time limits.
Connecting two jumplike unravelings for non-Markovian open quantum systems
Luoma, Kimmo; Suominen, Kalle-Antti; Piilo, Jyrki
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.
Continuous-variable quantum key distribution in non-Markovian channels
Vasile, Ruggero; Olivares, Stefano; Paris, MatteoG. A.; Maniscalco, Sabrina
2011-04-15
We address continuous-variable quantum key distribution (QKD) in non-Markovian lossy channels and show how the non-Markovian features may be exploited to enhance security and/or to detect the presence and the position of an eavesdropper along the transmission line. In particular, we suggest a coherent-state QKD protocol which is secure against Gaussian individual attacks based on optimal 1{yields}2 asymmetric cloning machines for arbitrarily low values of the overall transmission line. The scheme relies on specific non-Markovian properties, and cannot be implemented in ordinary Markovian channels characterized by uniform losses. Our results give a clear indication of the potential impact of non-Markovian effects in QKD.
Entanglement and non-Markovianity of a multi-level atom decaying in a cavity
NASA Astrophysics Data System (ADS)
Zi-Long, Fan; Yu-Kun, Ren; Hao-Sheng, Zeng
2016-01-01
We present a paradigmatic method for exactly studying non-Markovian dynamics of a multi-level V-type atom interacting with a zero-temperature bosonic bath. Special attention is paid to the entanglement evolution and the dynamical non-Markovianity of a three-level V-type atom. We find that the entanglement negativity decays faster and non-Markovianity is smaller in the resonance regions than those in the non-resonance regions. More importantly, the quantum interference between the dynamical non-Markovianities induced by different transition channels is manifested, and the frequency domains for constructive and destructive interferences are found. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275064 and 11075050), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20124306110003), and the Construct Program of the National Key Discipline, China.
Gaussian interferometric power as a measure of continuous-variable non-Markovianity
NASA Astrophysics Data System (ADS)
Souza, Leonardo A. M.; Dhar, Himadri Shekhar; Bera, Manabendra Nath; Liuzzo-Scorpo, Pietro; Adesso, Gerardo
2015-11-01
We investigate the non-Markovianity of continuous-variable Gaussian quantum channels through the evolution of an operational metrological quantifier, namely, the Gaussian interferometric power, which captures the minimal precision that can be achieved using bipartite Gaussian probes in a black-box phase estimation setup, where the phase shift generator is a priori unknown. We observe that the monotonicity of the Gaussian interferometric power under the action of local Gaussian quantum channels on the ancillary arm of the bipartite probes is a natural indicator of Markovian dynamics; consequently, its breakdown for specific maps can be used to construct a witness and an effective quantifier of non-Markovianity. In our work, we consider two paradigmatic Gaussian models, the damping master equation and the quantum Brownian motion, and identify analytically and numerically the parameter regimes that give rise to non-Markovian dynamics. We then quantify the degree of non-Markovianity of the channels in terms of Gaussian interferometric power, showing, in particular, that even nonentangled probes can be useful to witness non-Markovianity. This establishes an interesting link between the dynamics of bipartite continuous-variable open systems and their potential for optical interferometry. The results are an important supplement to the recent research on characterization of non-Markovianity in continuous-variable systems.
NASA Astrophysics Data System (ADS)
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.
Optimized auxiliary representation of non-Markovian impurity problems by a Lindblad equation
NASA Astrophysics Data System (ADS)
Dorda, A.; Sorantin, M.; von der Linden, W.; Arrigoni, E.
2017-06-01
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
NASA Astrophysics Data System (ADS)
Jiang, Li; Zhang, Guo-Feng
2017-03-01
By using the effective non-Markovian measure (Breuer et al., Phys. Rev. Lett. 103, 210401 2009) we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local reservoir. We show that subsystem dynamics can be controlled by manipulating the coupling between TLAs, temperature and relaxation rate of the atoms. Moreover, the correlation between non-Markovianity of subsystem and entanglement between the subsystem and the structured bath is investigated, the results show that the emergence of non-Markovianity has a negative effect on the entanglement.
Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation
Sun, Zhe; Liu, Jing; Ma, Jian; Wang, Xiaoguang
2015-01-01
We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases. PMID:25676589
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
NASA Astrophysics Data System (ADS)
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.
Non-Markovianity, coherence, and system-environment correlations in a long-range collision model
NASA Astrophysics Data System (ADS)
Ćakmak, B.; Pezzutto, M.; Paternostro, M.; Müstecaplıoǧlu, Ö. E.
2017-08-01
We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-1 /2 particles. In order to include non-Markovian features in our model, we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest neighbor, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is nonmonotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behavior of quantum coherence in its state as the number of collisions grows. We complement our study with an investigation of system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.
Vega, Ines de; Alonso, Daniel
2006-02-15
In this paper we derive the evolution equation for the reduced propagator, an object that evolves vectors of the Hilbert space of a system S interacting with an environment B in a non-Markovian way. This evolution is conditioned to certain initial and final states of the environment. Once an average over these environmental states is made, reduced propagators permit the evaluation of multiple-time correlation functions of system observables. When this average is done stochastically the reduced propagator evolves according to a stochastic Schroedinger equation. In addition, it is possible to obtain the evolution equations of the multiple-time correlation functions which generalize the well-known quantum regression theorem to the non-Markovian case. Here, both methods, stochastic and evolution equations, are described by assuming a weak coupling between system and environment. Finally, we show that reduced propagators can be used to obtain a master equation with general initial conditions, and not necessarily an initial vacuum state for the environment. We illustrate the theory with several examples.
Lei, Chan U; Zhang Weimin
2011-11-15
In this paper, we provide a mechanism of decoherence suppression for open quantum systems in general and that for a ''Schroedinger cat-like'' state in particular, through strong couplings to non-Markovian reservoirs. Different from the usual strategies in the literature of suppressing decoherence by decoupling the system from the environment, here the decoherence suppression employs a strong back-reaction from non-Markovian reservoirs. The mechanism relies on the existence of the singularities (bound states) of the nonequilibrium retarded Green function, which completely determines the dissipation and decoherence dynamics of open systems. As an application, we examine the decoherence dynamics of a photonic crystal nanocavity that is coupled to a waveguide. The strong non-Markovian suppression of decoherence for the ''optical cat'' state is attained.
Equivalence of the measures of non-Markovianity for open two-level systems
Zeng Haosheng; Tang Ning; Zheng Yanping; Wang Guoyou
2011-09-15
Different measures have been presented to depict the deviation of quantum time evolution in open systems from Markovian processes. We demonstrate that the measure proposed by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga, and Plenio [Phys. Rev. Lett. 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent to each other when they are applied to open two-level systems coupled to environments via the Jaynes-Cummings or dephasing models. This equivalence implies that the three measures, in different ways, capture the intrinsic character of the non-Markovianity of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianity.
NASA Astrophysics Data System (ADS)
Mangaud, E.; Meier, C.; Desouter-Lecomte, M.
2017-09-01
The non-Markovianity of the electron transfer in an oligothiophene-fullerene heterojunction described by a spin-boson model is analyzed using the time dependent decoherence canonical rates and the volume of accessible states in the Bloch sphere. The dynamical map of the reduced electronic system is computed by the hierarchical equations of motion methodology (HEOM) providing an exact dynamics. Transitory witness of non-Markovianity is linked to the bath dynamics analyzed from the HEOM auxiliary matrices. The signature of the collective bath mode detected from HEOM in each electronic state is compared with predictions of the effective mode extracted from the spectral density. We show that including this main reaction coordinate in a one-dimensional vibronic system coupled to a residual bath satisfactorily describes the electron transfer by a simple Markovian Redfield equation. Non-Markovianity is computed for three inter fragment distances and compared with a priori criterion based on the system and bath characteristic timescales.
Exact Analytic Solution of the Non-Markovian Chemical Reaction Process Via Time-Subordination
NASA Astrophysics Data System (ADS)
Benson, D. A.
2015-12-01
Perfectly-mixed reactions are Markovian, because the advance of the state depends only on the current state. Poor mixing (or the partner process of upscaling over heterogeneous concentrations) renders the process non-Markovian because of memory of the chemical structure. In other words, a particle takes some time to reach a suitable reaction site. The time depends on structure, and the structure changes over time. For purely diffusive transport, a calculation of the random time to reach the edges of ``islands'' allows a solution of the non-Markovian reaction rates that evolve (decrease) over time. This randomization of the active (operational) reaction time leads to non-Markovian reactions and an integro-differential governing equation of chemical evolution. Implications for more complex (advection/diffusion) environments are discussed.
Robust fermionic-mode entanglement of a nanoelectronic system in non-Markovian environments
NASA Astrophysics Data System (ADS)
Cheng, Jiong; Zhang, Wen-Zhao; Han, Yan; Zhou, Ling
2015-02-01
A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely, the bound state and the modified Laplace transformation, are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environments have a finite band structure, we find that the system presents various kinds of relaxation processes. The final states can be thermal or thermal-like states, quantum memory states, and oscillating quantum memory states. Our study provides an analytical way to explore the non-Markovian entanglement dynamics of identical fermions in a realistic setting, i.e., finite-temperature reservoirs with a cutoff spectrum.
Refined weak-coupling limit: Coherence, entanglement, and non-Markovianity
NASA Astrophysics Data System (ADS)
Rivas, Ángel
2017-04-01
We study the properties of a refined weak-coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals, whereas the former not, despite the induced dynamics being fully incoherent. In addition, the evolution presents "quasieternal" non-Markovianity, becoming nondivisible at any time period where the system evolves qualitatively. Furthermore, the method allows for an exact derivation of a master equation that accounts for a reversible energy exchange between system and environment. Specifically, this is obtained in the form of a time-dependent Lamb shift term.
Quantum non-Markovian reservoirs of atomic condensates engineered via dipolar interactions
NASA Astrophysics Data System (ADS)
Yuan, Ji-Bing; Xing, Hai-Jun; Kuang, Le-Man; Yi, Su
2017-03-01
We investigate the quantum dephasing dynamics of an impurity qubit immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate whose collective excitations act as a reservoir for the qubit. We show that the properties of the environment are highly engineerable through the relative strength of the dipolar and contact interactions such that qubit's dephasing dynamics could be Markovian, weak non-Markovian, or even highly non-Markovian. It is also revealed that the appearance of the roton excitation is responsible for the highly non-Markovian dephasing dynamics. Since rotonlike dispersions also appear in condensates placed in cavities or with spin-orbit couplings, our results pave the way for searching for systems that are suitable environment engineering.
Equivalence between Non-Markovian and Markovian Dynamics in Epidemic Spreading Processes
NASA Astrophysics Data System (ADS)
Starnini, Michele; Gleeson, James P.; Boguñá, Marián
2017-03-01
A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail, where all the non-Markovian aspects are shown to be captured within a single parameter, the effective infection rate. Remarkably, this result is independent of the topology of the underlying network, as demonstrated by numerical simulations on two-dimensional lattices and various types of random networks. Furthermore, an analytic approximation for the effective infection rate is introduced, which enables the calculation of the critical point and of the critical exponents for the non-Markovian dynamics.
Statistical description and transport in stochastic magnetic fields
Vanden Eijnden, E.; Balescu, R.
1996-03-01
The statistical description of particle motion in a stochastic magnetic field is presented. Starting form the stochastic Liouville equation (or, hybrid kinetic equation) associated with the equations of motion of a test particle, the probability distribution function of the system is obtained for various magnetic fields and collisional processes. The influence of these two ingredients on the statistics of the particle dynamics is stressed. In all cases, transport properties of the system are discussed. {copyright} {ital 1996 American Institute of Physics.}
Minimal evolution time and quantum speed limit of non-Markovian open systems
Meng, Xiangyi; Wu, Chengjun; Guo, Hong
2015-01-01
We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized Hamiltonian and dissipator. For a non-Markovian quantum open system, the possible evolution time between two arbitrary states is not unique, among the set of which we find that the minimal one and its QSL can decrease more steeply by adjusting the coupling strength of the dissipator, which thus provides potential improvements of efficiency in many quantum physics and quantum information areas. PMID:26565062
Quantum trajectories under frequent measurements in a non-Markovian environment
NASA Astrophysics Data System (ADS)
Xu, Luting; Li, Xin-Qi
2016-09-01
In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth (Λ ), and find a perfect "scaling" property with the measurement frequency (τ-1) in terms of the scaling variable x =Λ τ . Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to x →∞ and x →0 , respectively. This x -dependent criterion improves the idea of using τ alone and quantitatively identifies the validity condition of the conventional QT theory.
Non-Markovian far-infrared spectra of HCl and DCl in liquid SF6
NASA Astrophysics Data System (ADS)
Hernández, A. Calvo; Velasco, S.; Mauricio, F.
1986-01-01
The far-infrared spectrum of dilute solutions of HCl and DCl in liquid SF6 have been calculated by applying of two non-Markovian spectral theories previously reported in a recent work [A. Calvo Hernández, S. Velasco, and F. Mauricio, Phys. Rev. A 31, 3419 (1985)]. The calculated spectra are compared with the experimental spectra. Even though the systems under study are relatively far from the Markovian limit, the agreement between theoretical and experimental spectra shows the wide range of validity of both non-Markovian spectral theories.
Non-Markovian dynamics of quantum systems. I. Formalism and transport coefficients.
Kanokov, Z; Palchikov, Yu V; Adamian, G G; Antonenko, N V; Scheid, W
2005-01-01
Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of general and linear couplings in the coordinate and momentum between the collective harmonic oscillator and heat bath. The long-time tails of correlation functions are investigated in the low- and high-temperature regimes of dissipation for different couplings. The Onsager's regression hypothesis is discussed for the non-Markovian dynamics. The Lindblad theory is justified on the basis of the microscopical model.
Optimal control of quantum non-Markovian dissipation: reduced Liouville-space theory.
Xu, Ruixue; Yan, YiJing; Ohtsuki, Yukiyoshi; Fujimura, Yuichi; Rabitz, Herschel
2004-04-08
An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results. (c) 2004 American Institute of Physics
Long-lived quantum coherence and non-Markovianity of photosynthetic complexes
NASA Astrophysics Data System (ADS)
Chen, Hong-Bin; Lien, Jiun-Yi; Hwang, Chi-Chuan; Chen, Yueh-Nan
2014-04-01
Long-lived quantum coherence in photosynthetic pigment-protein complexes has recently been reported at physiological temperature. It has been pointed out that the discrete vibrational modes may be responsible for the long-lived coherence. Here, we propose an analytical non-Markovian model to explain the origin of the long-lived coherence in pigment-protein complexes. We show that the memory effect of the discrete vibrational modes produces a long oscillating tail in the coherence. We further use the recently proposed measure to quantify the non-Markovianity of the system and find out the prolonged coherence is highly correlated to it.
Biele, R; Timm, C; D'Agosta, R
2014-10-01
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.
A Stochastic Description of Dictyostelium Chemotaxis
Amselem, Gabriel; Theves, Matthias; Bae, Albert; Bodenschatz, Eberhard; Beta, Carsten
2012-01-01
Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells. PMID:22662138
Fisher information due to a phase noisy laser under non-Markovian environment
Abdel-Khalek, S.
2014-12-15
More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.
Non-Markovian dynamics of an open quantum system with nonstationary coupling
Kalandarov, S. A.; Adamian, G. G.; Kanokov, Z.; Antonenko, N. V.; Scheid, W.
2011-04-15
The spectral, dissipative, and statistical properties of the damped quantum oscillator are studied in the case of non-Markovian and nonstationary system-heat bath coupling. The dissipation of collective energy is shown to be slowed down, and the decoherence rate and entropy grow with modulation frequency.
Enhancement of Quantum Correlations in Qubit-Qutrit Systems under the non-Markovian Environment
NASA Astrophysics Data System (ADS)
Basit, Abdul; Ali, Hamad; Badshah, Fazal; Ge, Guo-Qin
2017-07-01
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 /{{Γ }}) 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. Supported by the National Natural Science Foundation of China under Grant Nos. 11274132 and 11550110180
Fault-tolerant quantum computation for local non-Markovian noise
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{sub 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.
NASA Astrophysics Data System (ADS)
Hu, Juju; Ji, Yinghua; Ke, Qiang
2017-10-01
Utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and investigate the orbit tracking of quantum state for non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz-Drude regularization is numerically studied for a two-level system. The simulations show that the controlled quantum system will track the target orbit with a small oscillation due to the non-Markovian environmental memory effect, which indicates the orbit tracking of non-Markovian quantum system is incomplete.
NASA Astrophysics Data System (ADS)
Hu, Juju; Ji, Yinghua; Ke, Qiang
2017-08-01
Utilizing model reference adaptive control theory and Lyapunov stability theorem, we derive the adaptive law for the model reference adaptive system. Then we design the Lyapunov control law by double control functions and investigate the orbit tracking of quantum state for non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz-Drude regularization is numerically studied for a two-level system. The simulations show that the controlled quantum system will track the target orbit with a small oscillation due to the non-Markovian environmental memory effect, which indicates the orbit tracking of non-Markovian quantum system is incomplete.
Dynamics of non-Markovian open quantum systems
NASA Astrophysics Data System (ADS)
de Vega, Inés; Alonso, Daniel
2017-01-01
Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.
NASA Astrophysics Data System (ADS)
Luo, JunYan; Yan, Yiying; Huang, Yixiao; Yu, Li; He, Xiao-Ling; Jiao, HuJun
2017-01-01
We investigate the noise correlations of spin and charge currents through an electron spin resonance (ESR)-pumped quantum dot, which is tunnel coupled to three electrodes maintained at an equivalent chemical potential. A recursive scheme is employed with inclusion of the spin degrees of freedom to account for the spin-resolved counting statistics in the presence of non-Markovian effects due to coupling with a dissipative heat bath. For symmetric spin-up and spin-down tunneling rates, an ESR-induced spin flip mechanism generates a pure spin current without an accompanying net charge current. The stochastic tunneling of spin carriers, however, produces universal shot noises of both charge and spin currents, revealing the effective charge and spin units of quasiparticles in transport. In the case of very asymmetric tunneling rates for opposite spins, an anomalous relationship between noise autocorrelations and cross correlations is revealed, where super-Poissonian autocorrelation is observed in spite of a negative cross correlation. Remarkably, with strong dissipation strength, non-Markovian memory effects give rise to a positive cross correlation of the charge current in the absence of a super-Poissonian autocorrelation. These unique noise features may offer essential methods for exploiting internal spin dynamics and various quasiparticle tunneling processes in mesoscopic transport.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
NASA Technical Reports Server (NTRS)
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
NASA Technical Reports Server (NTRS)
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Data-driven non-Markovian closure models
NASA Astrophysics Data System (ADS)
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
Non-Markovian quantum feedback networks II: Controlled flows
NASA Astrophysics Data System (ADS)
Gough, John E.
2017-06-01
The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper, we build on the ideas presented by Bouten and van Handel [Quantum Stochastics and Information: Statistics, Filtering and Control (World Scientific, 2008)] and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes, Z, and the measured processes, Y, and to this end we make a distinction between what we call the input picture and the output picture. We should note that the input-output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent—we do this for the two main cases of quadrature measurement and photon-counting measurement. The theory is general enough to include a modulating filter which post-processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems. Finally, we give a brief argument as to why most of the rules for making instantaneous feedback connections [J. Gough and M. R. James, Commun. Math. Phys. 287, 1109 (2009)] ought to apply for controlled dynamical networks as well.
Non-Markovian Complexity in the Quantum-to-Classical Transition
Xiong, Heng-Na; Lo, Ping-Yuan; Zhang, Wei-Min; Feng, Da Hsuan; Nori, Franco
2015-01-01
The quantum-to-classical transition is due to environment-induced decoherence, and it depicts how classical dynamics emerges from quantum systems. Previously, the quantum-to-classical transition has mainly been described with memory-less (Markovian) quantum processes. Here we study the complexity of the quantum-to-classical transition through general non-Markovian memory processes. That is, the influence of various reservoirs results in a given initial quantum state evolving into one of the following four scenarios: thermal state, thermal-like state, quantum steady state, or oscillating quantum nonstationary state. In the latter two scenarios, the system maintains partial or full quantum coherence due to the strong non-Markovian memory effect, so that in these cases, the quantum-to-classical transition never occurs. This unexpected new feature provides a new avenue for the development of future quantum technologies because the remaining quantum oscillations in steady states are decoherence-free. PMID:26303002
Non-Markovianity measure based on the relative entropy of coherence in an extended space
NASA Astrophysics Data System (ADS)
He, Zhi; Zeng, Hao-Sheng; Li, Yan; Wang, Qiong; Yao, Chunmei
2017-08-01
An alternative non-Markovianity measure for open quantum processes is proposed, which takes advantage of the nonincreasing property of relative entropy of coherence under the incoherent completely positive and trace-preserving maps in the extended Hilbert space constituted by the open system and its ancillary. By applying the proposed measure to some typical noisy channels, we find that for phase damping and amplitude damping channels it is equivalent to the three previous measures of non-Markovianity, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, however, these measures do not coincide exactly, and the proposed measure in the witness of Markovianity is more general than the measures based on quantum trace distance and dynamical divisibility but overlaps partly with the measure based on quantum mutual information.
Prediction of future credit rating using a non-Markovian model
NASA Astrophysics Data System (ADS)
Peng, Gan Chew; Hin, Pooi Ah; Haur, Ng Kok
2017-04-01
The matrix of transition probabilities between rating classes is a popular approach for predicting the future credit rating. This paper instead attempts to predict the future credit rating using a non-Markovian model. The prediction is done via the probability of the future credit rating given the ratings in the present and previous quarters. The estimation of the conditional probability of future credit rating is carried out by means of simulation after fitting the data with a multivariate power-normal distribution. The results based on the quarterly credit ratings of ten companies over 15 years taken from the database of the Taiwan Economic Journal indicate the need of extending the Markovian model to the non-Markovian model.
Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps
Vasile, Ruggero; Maniscalco, Sabrina; Paris, Matteo G. A.; Breuer, Heinz-Peter; Piilo, Jyrki
2011-11-15
We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al.[Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.
Comparing different non-Markovianity measures in a driven qubit system
Haikka, P.; Cresser, J. D.; Maniscalco, S.
2011-01-15
We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation for this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures, and on the other hand, we investigate the effect of the driving force on the dissipative dynamics of the qubit. In particular we ask if the driving force introduces new channels for energy and/or information transfer between the system and the environment or if it amplifies existing ones. We show under which conditions the presence of the driving force slows down the inevitable loss of quantum properties of the qubit.
Transient unidirectional energy flow and diode-like phenomenon induced by non-Markovian environments
Jing, Jun; Segal, Dvira; Li, Baowen; Wu, Lian-Ao
2015-01-01
Relying on an exact time evolution scheme, we identify a novel transient energy transfer phenomenon in an exactly-solvable quantum microscopic model consisting of a three-level system coupled to two non-Markovian zero-temperature bosonic baths through two separable quantum channels. The dynamics of this model can be solved exactly using the quantum-state-diffusion equation formalism, demonstrating finite intervals of unidirectional energy flow across the system, typically, from the non-Markovian environment towards the more Markovian bath. Furthermore, when introducing a spatial asymmetry into the system, an analogue of the rectification effect is realized. In the long time limit, the dynamics arrives at a stationary state and the effects recede. Understanding temporal characteristics of directional energy flow will aid in designing microscopic energy transfer devices. PMID:26478230
Non-Markovian Complexity in the Quantum-to-Classical Transition.
Xiong, Heng-Na; Lo, Ping-Yuan; Zhang, Wei-Min; Feng, Da Hsuan; Nori, Franco
2015-08-25
The quantum-to-classical transition is due to environment-induced decoherence, and it depicts how classical dynamics emerges from quantum systems. Previously, the quantum-to-classical transition has mainly been described with memory-less (Markovian) quantum processes. Here we study the complexity of the quantum-to-classical transition through general non-Markovian memory processes. That is, the influence of various reservoirs results in a given initial quantum state evolving into one of the following four scenarios: thermal state, thermal-like state, quantum steady state, or oscillating quantum nonstationary state. In the latter two scenarios, the system maintains partial or full quantum coherence due to the strong non-Markovian memory effect, so that in these cases, the quantum-to-classical transition never occurs. This unexpected new feature provides a new avenue for the development of future quantum technologies because the remaining quantum oscillations in steady states are decoherence-free.
Dynamical invariants in a non-Markovian quantum-state-diffusion equation
NASA Astrophysics Data System (ADS)
Luo, Da-Wei; Pyshkin, P. V.; Lam, Chi-Hang; Yu, Ting; Lin, Hai-Qing; You, J. Q.; Wu, Lian-Ao
2015-12-01
We find dynamical invariants for open quantum systems described by the non-Markovian quantum-state-diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with a biorthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamical invariants to reverse engineering a Hamiltonian that is capable of driving the system to the target state, providing a different way to design control strategy for open quantum systems.
Jing, Jun; Segal, Dvira; Li, Baowen; Wu, Lian-Ao
2015-10-19
Relying on an exact time evolution scheme, we identify a novel transient energy transfer phenomenon in an exactly-solvable quantum microscopic model consisting of a three-level system coupled to two non-Markovian zero-temperature bosonic baths through two separable quantum channels. The dynamics of this model can be solved exactly using the quantum-state-diffusion equation formalism, demonstrating finite intervals of unidirectional energy flow across the system, typically, from the non-Markovian environment towards the more Markovian bath. Furthermore, when introducing a spatial asymmetry into the system, an analogue of the rectification effect is realized. In the long time limit, the dynamics arrives at a stationary state and the effects recede. Understanding temporal characteristics of directional energy flow will aid in designing microscopic energy transfer devices.
A measure of non-Markovianity for unital quantum dynamical maps
NASA Astrophysics Data System (ADS)
Haseli, S.; Salimi, S.; Khorashad, A. S.
2015-09-01
One of the most important topics in the study of the dynamics of open quantum systems is the information exchange between system and environment. Based on the features of back-flow information from an environment to a system, an approach is provided to detect non-Markovianity for unital dynamical maps. The method takes advantage of non-contraction property of the von Neumann entropy under completely positive and trace-preserving unital maps. Accordingly, for the dynamics of a single qubit as an open quantum system, the sign of the time derivative of the density matrix eigenvalues of the system determines the non-Markovianity of unital quantum dynamical maps. The main characteristics of the measure are to make the corresponding calculations and optimization procedure simpler.
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
NASA Astrophysics Data System (ADS)
Broadbent, Curtis J.; Jing, Jun; Yu, Ting; Eberly, Joseph H.
2012-08-01
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically.
Coupled exciton-photon Bose condensate: Non-Markovian character of the open system
NASA Astrophysics Data System (ADS)
Elistratov, A. A.; Lozovik, Yu. E.
2017-09-01
For an nonequilibrium system, in the framework of the Keldysh formalism we explore the kinetics of the polariton condensate in a quantum well embedded in an optical microcavity taking into account pumping and leakage of excitons and photons. We make ab initio derivation of the quantum kinetic equations for the condensates and for reservoirs. We show that the real open polariton system has the non-Markovian character at times comparable to the Rabi oscillation period.
Shot-noise at a Fermi-edge singularity: Non-Markovian dynamics
Ubbelohde, N.; Maire, N.; Haug, R. J.; Roszak, K.; Hohls, F.; Novotný, T.
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.
Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks.
Scholtes, Ingo; Wider, Nicolas; Pfitzner, René; Garas, Antonios; Tessone, Claudio J; Schweitzer, Frank
2014-09-24
Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.
Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics
Berrada, K.
2014-01-15
Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution. -- Highlights: •Geometric phase under noise phase laser. •Dynamics of the geometric phase under non-Markovian dynamics in the presence of classical noise. •Solution of master equation of the system in terms atomic inversion. •Nonlocal correlation between the system and its environment under non-Markovianity.
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.
Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field
Stefanescu, Eliade Scheid, Werner; Sandulescu, Aurel
2008-05-15
For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad's form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.
Test of fluctuation theorems in non-Markovian open quantum systems
NASA Astrophysics Data System (ADS)
Kawamoto, Tatsuro; Hatano, Naomichi
2011-09-01
We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.73.046129 73, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the “detailed balance” condition is well satisfied except in a strongly nonequilibrium transient situation, and hence our generalization of the definition of the “entropy production” is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.
Non-Markovian linear response theory for quantum open systems and its applications
NASA Astrophysics Data System (ADS)
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.
Non-Markovian dynamics in chiral quantum networks with spins and photons
NASA Astrophysics Data System (ADS)
Ramos, Tomás; Vermersch, Benoît; Hauke, Philipp; Pichler, Hannes; Zoller, Peter
2016-06-01
We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D X X spin chains representing spin waveguides. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channel as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization-group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.
Quantum measurements in spin-boson model under non-Markovian environment
NASA Astrophysics Data System (ADS)
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.
Non-Markovianity through flow of information between a system and an environment
NASA Astrophysics Data System (ADS)
Haseli, S.; Karpat, G.; Salimi, S.; Khorashad, A. S.; Fanchini, F. F.; ćakmak, B.; Aguilar, G. H.; Walborn, S. P.; Ribeiro, P. H. Souto
2014-11-01
Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian behavior of dynamical quantum processes following the decoherence approach, where we consider a quantum system that is initially correlated with its measurement apparatus, which in turn interacts with the environment. We introduce a way of looking at the information exchange between the system and environment using the quantum loss, which is shown to be closely related to the measure of non-Markovianity based on the quantum mutual information. We also extend the results of Fanchini et al. [Phys. Rev. Lett. 112, 210402 (2014), 10.1103/PhysRevLett.112.210402] in several directions, providing a more detailed investigation of the use of the accessible information for quantifying the backflow of information from the environment to the system. Moreover, we reveal a clear conceptual relation between the entanglement- and mutual-information-based measures of non-Markovianity in terms of the quantum loss and accessible information. We compare different ways of studying the information flow in two theoretical examples. We also present experimental results on the investigation of the quantum loss and accessible information for a two-level system undergoing a zero temperature amplitude damping process. We use an optical approach that allows full access to the state of the environment.
Equivalence of the measures of non-Markovianity for open two-level systems
NASA Astrophysics Data System (ADS)
Zeng, Hao-Sheng; Tang, Ning; Zheng, Yan-Ping; Wang, Guo-You
2011-09-01
Different measures have been presented to depict the deviation of quantum time evolution in open systems from Markovian processes. We demonstrate that the measure proposed by Breuer, Laine, and Piilo [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.210401 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga, and Plenio [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.050403 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent to each other when they are applied to open two-level systems coupled to environments via the Jaynes-Cummings or dephasing models. This equivalence implies that the three measures, in different ways, capture the intrinsic character of the non-Markovianity of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianity.
Using non-Markovian measures to evaluate quantum master equations for photosynthesis
Chen, Hong-Bin; Lambert, Neill; Cheng, Yuan-Chung; Chen, Yueh-Nan; Nori, Franco
2015-01-01
When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment. PMID:26238479
Non-Markovian dynamics in the extended cluster spin-1/2 XX chain
NASA Astrophysics Data System (ADS)
Mahmoudi, M.; Mahdavifar, S.; Zadeh, T. Mohammad Ali; Soltani, M. R.
2017-01-01
We study the dynamics of entanglement, mutual information, and quantum discord in the extended cluster spin-1/2 XX chain, equivalent to a one-dimensional spin-1/2 XX model with three-spin interaction (TSI). Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the environment. The two-point Heisenberg and the TSI are responsible for coupling between the system and the environment. Although the revival phenomenon of quantum correlations as an indication of non-Markovian dynamics is observed for TSI stronger than the Heisenberg interaction, the study of the trace distance has proven that the dynamical phase transition from the Markovian to the non-Markovian regime happens at a critical value where the TSI is equal to half of the Heisenberg interaction. By focusing on the nearest neighbor pair spins of the environment, we have also shown that the dynamics of quantum correlation in the environment is sensitive to Markovian and non-Markovian regions.
NASA Astrophysics Data System (ADS)
Jungblut, Swetlana; Dellago, Christoph
2015-02-01
Using the crystallization transition in a Lennard-Jones fluid as example, we show that mean first-passage time based methods may underestimate the reaction rates. We trace the reason of this deficiency back to the non-Markovian character of the dynamics caused by the projection to a poorly chosen reaction coordinate. The non-Markovianity of the dynamics becomes apparent in the behavior of the recurrence times.
NASA Astrophysics Data System (ADS)
Bhattacharya, Samyadeb; Misra, Avijit; Mukhopadhyay, Chiranjib; Pati, Arun Kumar
2017-01-01
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
NASA Astrophysics Data System (ADS)
Ferialdi, L.
2017-02-01
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.
Error Distributions on Large Entangled States with Non-Markovian Dynamics
NASA Astrophysics Data System (ADS)
McCutcheon, Dara P. S.; Lindner, Netanel H.; Rudolph, Terry
2014-12-01
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.
Non-Markovian autoresonant dynamics of tunneling from discrete to continuum modes
Barak, Assaf; Segev, Mordechai
2011-09-15
We study the autoresonant dynamics of a discrete level coupled to a continuum, and show that passing adiabatically through a linear resonance, above a well-defined threshold, yields a transition to nonlinear phase locking and linear non-Markovian decay to the continuum. This process results in broadening of the population of the continuum modes beyond its natural linewidth. This concept can be employed to alter spontaneous emission, where driving an atom into phase locking with continuum modes will yield the emission of short pulses.
Role of environmental correlations in the non-Markovian dynamics of a spin system
Lorenzo, Salvatore; Plastina, Francesco; Paternostro, Mauro
2011-09-15
We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.
NASA Astrophysics Data System (ADS)
Ding, Zhi-yong; He, Juan; Ye, Liu
2017-02-01
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.
Efficient superdense coding in the presence of non-Markovian noise
NASA Astrophysics Data System (ADS)
Liu, Bi-Heng; Hu, Xiao-Min; Huang, Yun-Feng; Li, Chuan-Feng; Guo, Guang-Can; Karlsson, Antti; Laine, Elsi-Mari; Maniscalco, Sabrina; Macchiavello, Chiara; Piilo, Jyrki
2016-04-01
Many quantum information tasks rely on entanglement, which is used as a resource, for example, to enable efficient and secure communication. Typically, noise, accompanied by loss of entanglement, reduces the efficiency of quantum protocols. We develop and demonstrate experimentally a superdense coding scheme with noise, where the decrease of entanglement in Alice's encoding state does not reduce the efficiency of the information transmission. Having an almost fully dephased classical two-photon polarization state at the time of encoding with concurrence of 0.163+/-0.007 , we reach values of mutual information close to 1.52+/- 0.02 (1.89+/- 0.05) with 3-state (4-state) encoding. This high efficiency relies both on non-Markovian features, that Bob exploits just before his Bell state measurement, and on very high visibility (99.6{%}+/-0.1{%}) of the Hong-Ou-Mandel interference within the experimental set-up. Our proof-of-principle results with measurements on mutual information pave the way for exploiting non-Markovianity to improve the efficiency and security of quantum information processing tasks.
Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
NASA Astrophysics Data System (ADS)
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.
Quantum Zeno-type effect and non-Markovianity in a three-level system
Karlsson, Antti; Francica, Francesco; Piilo, Jyrki; Plastina, Francesco
2016-01-01
We study the coexistence of the quantum Zeno-type effect and non-Markovianity for a system decaying in a structured bosonic environment and subject to a control field. The interaction with the environment induces decay from the excited to the ground level, which, in turn, is coherently coupled to another meta-stable state. The control of the strength of the coherent coupling between the stable levels allows the engineering of both the dissipation and of the memory effects, without modifying neither the system-reservoir interaction, nor environmental properties. We use this framework in two different parameter regimes corresponding to fast (bad cavity limit) and slow dissipation (good cavity limit) in the original and un-controlled qubit system. Our results show a non-monotonic behavior of memory effects when increasing the effectiveness of the Zeno-like freezing. Moreover, we identify a new source of memory effects which allows the persistence of non-Markovianity for long times while the excited state has already been depleted. PMID:27996016
Self-Diffusion and Non-Markovian Dynamics in Strongly Coupled Ultracold Neutral Plasmas
NASA Astrophysics Data System (ADS)
Strickler, Trevor; Langin, Thomas; McQuillen, Patrick; Killian, Thomas
2015-05-01
Collisional processes in weakly coupled plasmas are well-described by the Landau-Spitzer formalism. Classical plasma theory breaks down, however, in strongly coupled systems because of the non-perturbative nature of particle interactions, and improving our understanding of this regime is an important fundamental challenge. We present experimental measurements of the self-diffusion constant and observation of non-Markovian equilibration for strongly coupled ions in an ultracold neutral plasma (UCNP) created by photoionizing strontium atoms in a magneto-optical trap. Our diagnostic uses optical pumping to create ``spin-tagged'' subpopulations of ions having skewed velocity distributions that then relax back to equilibrium. A Green-Kubo relation is used to extract the self-diffusion constant from the equilibration curves. With improved time resolution (down to 30 ns), we have explored the early time dynamics of these skewed ion distributions within 100 ns after the optical pumping, where molecular dynamics simulations predict non-Markovian deviations from the exponential velocity damping expected for weakly coupled systems. At longer times, we observe oscillations of the average velocity during the relaxation, which indicate coupling of single-particle motion to collective modes. This work was supported by the United States National Science Foundation and the Department of Energy (PHY-0714603), and the Air Force Office of Scientific Research (FA9550-12-1-0267).
Non-Markovian continuous-time quantum walks on lattices with dynamical noise
NASA Astrophysics Data System (ADS)
Benedetti, Claudia; Buscemi, Fabrizio; Bordone, Paolo; Paris, Matteo G. A.
2016-04-01
We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e., strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.
Quantum Zeno-type effect and non-Markovianity in a three-level system
NASA Astrophysics Data System (ADS)
Karlsson, Antti; Francica, Francesco; Piilo, Jyrki; Plastina, Francesco
2016-12-01
We study the coexistence of the quantum Zeno-type effect and non-Markovianity for a system decaying in a structured bosonic environment and subject to a control field. The interaction with the environment induces decay from the excited to the ground level, which, in turn, is coherently coupled to another meta-stable state. The control of the strength of the coherent coupling between the stable levels allows the engineering of both the dissipation and of the memory effects, without modifying neither the system-reservoir interaction, nor environmental properties. We use this framework in two different parameter regimes corresponding to fast (bad cavity limit) and slow dissipation (good cavity limit) in the original and un-controlled qubit system. Our results show a non-monotonic behavior of memory effects when increasing the effectiveness of the Zeno-like freezing. Moreover, we identify a new source of memory effects which allows the persistence of non-Markovianity for long times while the excited state has already been depleted.
Non-Markovian dynamics of quantum coherence of two-level system driven by classical field
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Situ, Haozhen
2017-09-01
In this paper, we study the quantum coherence dynamics of two-level atom system embedded in non-Markovian reservoir in the presence of classical driving field. We analyze the influence of memory effects, classical driving, and detuning on the quantum coherence. It is found that the quantum coherence has different behaviors in resonant case and non-resonant case. In the resonant case, in stark contrast with previous results, the strength of classical driving plays a negative effect on quantum coherence, while detuning parameter has the opposite effect. However, in non-resonant case through a long time, classical driving and detuning parameter have a different influence on quantum coherence compared with resonant case. Due to the memory effect of environment, in comparison with Markovian regime, quantum coherence presents vibrational variations in non-Markovian regime. In the resonant case, all quantum coherence converges to a fixed maximum value; in the non-resonant case, quantum coherence evolves to different stable values. For zero-coherence initial states, quantum coherence can be generated with evolution time. Our discussions and results should be helpful in manipulating and preserving the quantum coherence in dissipative environment with classical driving field.
Non-Markovian near-infrared Q branch of HCl diluted in liquid Ar
NASA Astrophysics Data System (ADS)
Padilla, Antonio; Pérez, Justo
2013-08-01
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.
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.
Efficient real-time path integrals for non-Markovian spin-boson models
NASA Astrophysics Data System (ADS)
Strathearn, A.; Lovett, B. W.; Kirton, P.
2017-09-01
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.
Markovian and Non-Markovian Protein Sequence Evolution: Aggregated Markov Process Models
Kosiol, Carolin; Goldman, Nick
2011-01-01
Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models. PMID:21718704
Zhao Xinyu; Jing Jun; Corn, Brittany; Yu Ting
2011-09-15
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.
NASA Astrophysics Data System (ADS)
Ebadi, H.; Saeedian, M.; Ausloos, M.; Jafari, G. R.
2016-11-01
The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.
Deterministic and Stochastic Descriptions of Gene Expression Dynamics
NASA Astrophysics Data System (ADS)
Marathe, Rahul; Bierbaum, Veronika; Gomez, David; Klumpp, Stefan
2012-09-01
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.
Bellomo, Bruno; De Pasquale, Antonella; Gualdi, Giulia; Marzolino, Ugo
2010-12-15
We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography-based approach with a proper data sampling, our proposal allows to relate the time-dependent coefficients governing the dissipative evolution of a quantum system to experimentally accessible quantities. The proposed scheme not only provides a way to retrieve the full information about potentially unknown dissipative coefficients, but also, most valuably, can be employed as a reliable consistency test for the approximations involved in the theoretical derivation of a given non-Markovian convolutionless master equation.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-05
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
Non-Markovian dynamics of fully coupled fermionic and bosonic oscillators
NASA Astrophysics Data System (ADS)
Sargsyan, V. V.; Lacroix, D.; Adamian, G. G.; Antonenko, N. V.
2017-03-01
The non-Markovian Langevin approach is applied to study the dynamics of fermionic (bosonic) oscillator linearly coupled to a fermionic (bosonic) environment. The analytical expressions for occupation numbers in two different types of couplings (rotating-wave approximation and fully coupled) are compared and discussed. The weak-coupling and high- and low-temperature limits are considered as well. The conditions under which the environment imposes its thermal equilibrium on the collective subsystem are discussed. The sameness of the results, obtained with both the Langevin approach and the discretized environment method are shown. Short- and long-time nonequilibrium dynamics of fermionic and bosonic open quantum systems are analyzed both analytically and numerically.
Non-Markovian Brownian motion in a magnetic field and time-dependent force fields
NASA Astrophysics Data System (ADS)
Hidalgo-Gonzalez, J. C.; Jiménez-Aquino, J. I.; Romero-Bastida, M.
2016-11-01
This work focuses on the derivation of the velocity and phase-space generalized Fokker-Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time-dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation-dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.
Correlation and response functions with non-Markovian dissipation: A reduced Liouville-space theory
NASA Astrophysics Data System (ADS)
Mo, Yan; Xu, Rui-Xue; Cui, Ping; Yan, YiJing
2005-02-01
Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.
NASA Astrophysics Data System (ADS)
Shi, Pengqin; Hu, Menghan; Ying, Yaofeng; Jin, Jinshuang
2016-09-01
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.
Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics
NASA Astrophysics Data System (ADS)
Berrada, K.
2014-01-01
Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit-environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.
NASA Astrophysics Data System (ADS)
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.
Electronic energy transfer in model photosynthetic systems: Markovian vs. non-Markovian dynamics.
Singh, Navinder; Brumer, Paul
2011-01-01
A simple numerical algorithm for solving the non-Markovian master equation in the second Born approximation is developed and used to propagate the traditional dimer system that models electronic energy transfer in photosynthetic systems. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to access the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second-order approximation is useful. For example, the use of Redfield theory for lambda > 10 cm(-1) in Fenna-Mathews-Olson (FMO) type systems is shown to be fundamentally inaccurate.
Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
NASA Astrophysics Data System (ADS)
Orieux, Adeline; D'Arrigo, Antonio; Ferranti, Giacomo; Franco, Rosario Lo; Benenti, Giuliano; Paladino, Elisabetta; Falci, Giuseppe; Sciarrino, Fabio; Mataloni, Paolo
2015-02-01
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely local operation, without acquiring any information on the environment; then, we use a closed-loop scheme in which the environment is measured, the outcome controling the local operations on the system. The restored entanglement is a manifestation of ``hidden'' quantum correlations resumed by the local control. Relying on local control, both schemes improve the efficiency of entanglement sharing in distributed quantum networks.
Non-Markovian Model for Transport and Reactions of Particles in Spiny Dendrites
NASA Astrophysics Data System (ADS)
Fedotov, Sergei; Méndez, Vicenç
2008-11-01
Motivated by the experiments [Santamaria , Neuron 52, 635 (2006)NERNET0896-627310.1016/j.neuron.2006.10.025] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent dendrite is described by a non-Markovian random process and, as a result, the overall movement of particles can be subdiffusive. A system of integrodifferential equations is derived for the particles densities in dendrites and spines. This system involves the spine-dendrite interaction term which describes the memory effects and nonlocality in space. We consider the impact of power-law waiting time distributions on the transport of biochemical signals and mechanism of the accumulation of plasticity-inducing signals inside spines.
NASA Astrophysics Data System (ADS)
Nourmandipour, A.; Tavassoly, M. K.; Rafiee, M.
2016-02-01
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
NASA Astrophysics Data System (ADS)
Berrada, K.
2016-11-01
In this paper, we study the Fisher information for a quantum system consisting of two identical qubits, each of them locally interacting with a bosonic reservoir in the same environment for non-Markovian open, dissipative quantum system. Based on the influx of the information, we propose an information-theoretical approach for characterizing the time-dependent memory effect of environment and diffusion function under the effect of the physical parameters. More precisely, an interesting monotonic relation between the time derivative of quantum Fisher information (QFI) and diffusion function behavior is observed during the time evolution. The phenomenon is that the QFI, namely the precision of estimation, changes dramatically with the environment structure. The dependence of the physical parameters shows that the increasing in the temperature will damage the amount of the QFI with respect of the ratio between the reservoir cutoff frequency and the system oscillation frequency.
Correlation and response functions with non-Markovian dissipation: a reduced Liouville-space theory.
Mo, Yan; Xu, Rui-Xue; Cui, Ping; Yan, YiJing
2005-02-22
Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime.
Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
Orieux, Adeline; D'Arrigo, Antonio; Ferranti, Giacomo; Franco, Rosario Lo; Benenti, Giuliano; Paladino, Elisabetta; Falci, Giuseppe; Sciarrino, Fabio; Mataloni, Paolo
2015-01-01
In many applications entanglement must be distributed through noisy communication channels that unavoidably degrade it. Entanglement cannot be generated by local operations and classical communication (LOCC), implying that once it has been distributed it is not possible to recreate it by LOCC. Recovery of entanglement by purely local control is however not forbidden in the presence of non-Markovian dynamics, and here we demonstrate in two all-optical experiments that such entanglement restoration can even be achieved on-demand. First, we implement an open-loop control scheme based on a purely local operation, without acquiring any information on the environment; then, we use a closed-loop scheme in which the environment is measured, the outcome controling the local operations on the system. The restored entanglement is a manifestation of “hidden” quantum correlations resumed by the local control. Relying on local control, both schemes improve the efficiency of entanglement sharing in distributed quantum networks. PMID:25712406
Digital quantum simulation of many-body non-Markovian dynamics
NASA Astrophysics Data System (ADS)
Sweke, R.; Sanz, M.; Sinayskiy, I.; Petruccione, F.; Solano, E.
2016-08-01
We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: first, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and second, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.
Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach
NASA Astrophysics Data System (ADS)
Ritschel, Gerhard; Strunz, Walter T.; Eisfeld, Alexander
2017-08-01
To find a practical scheme to numerically solve the non-Markovian Quantum State Diffusion equation (NMQSD), one often uses a functional expansion of the functional derivative that appears in the general NMQSD equation. This expansion leads to a hierarchy of coupled operators. It turned out that if one takes only the zeroth order term into account, one has a very efficient method that agrees remarkably well with the exact results for many cases of interest. We denote this approach as zeroth order functional expansion (ZOFE). In the present work, we investigate two extensions of ZOFE. Firstly, we investigate how the hierarchy converges when taking higher orders into account (which, however, leads to a fast increase in numerical size). Secondly, we demonstrate that by using a terminator that approximates the higher order contributions, one can obtain significant improvement, at hardly any additional computational cost. We carry out our investigations for the case of absorption spectra of molecular aggregates.
Analysis of non-Markovian coupling of a lattice-trapped atom to free space
NASA Astrophysics Data System (ADS)
Stewart, Michael; Krinner, Ludwig; Pazmiño, Arturo; Schneble, Dominik
2017-01-01
Behavior analogous to that of spontaneous emission in photonic band-gap materials has been predicted for an atom-optical system consisting of an atom confined in a well of a state-dependent optical lattice that is coupled to free space through an internal-state transition [de Vega et al., Phys. Rev. Lett. 101, 260404 (2008), 10.1103/PhysRevLett.101.260404]. Using the Weisskopf-Wigner approach and considering a one-dimensional geometry, we analyze the properties of this system in detail, including the evolution of the lattice-trapped population, the momentum distribution of emitted matter waves, and the detailed structure of an evanescent matter-wave state below the continuum boundary. We compare and contrast our findings for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions.
NASA Astrophysics Data System (ADS)
Chen, Yu; Zou, Jian; Yang, Zi-Yi; Li, Longwu; Li, Hai; Shao, Bin
2016-08-01
The dynamics of N-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N-qubit GHZ state and show that when the ratio of the PNL rate and the system-environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system-environment coupling strength and the atom number N, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system-environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit-qubit interaction under random telegraph noises (RTNs).
A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro
2015-05-15
In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
NASA Astrophysics Data System (ADS)
Zeng, H. S.; Tang, N.; Zheng, Y. P.; Xu, T. T.
2012-10-01
By use of the recently presented two measures, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and its reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relation between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.
Fractional noise destroys or induces a stochastic bifurcation
Yang, Qigui; Zeng, Caibin; Wang, Cong
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
Fractional noise destroys or induces a stochastic bifurcation
Yang, Qigui; Zeng, Caibin; Wang, Cong
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
Stochastic Schroedinger equations with general complex Gaussian noises
Bassi, Angelo
2003-06-01
Within the framework of non-Markovian stochastic Schroedinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.
NASA Astrophysics Data System (ADS)
Salimi, S.; Haseli, S.; Khorashad, A. S.; Adabi, F.
2016-09-01
The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.
Yao, Yao
2015-09-15
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 dynamics in plasmon-induced spontaneous emission interference
NASA Astrophysics Data System (ADS)
Thanopulos, I.; Yannopapas, V.; Paspalakis, E.
2017-02-01
We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Green's tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradual total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong-coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the vacuum modified by the metallic nanosphere is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by nonoverlapping plasmonic resonances.
The Design of Collectives of Agents to Control Non-Markovian Systems
NASA Technical Reports Server (NTRS)
Lawson, John W.; Wolpert, David H.
2004-01-01
The Collective Intelligence (COIN) framework concerns the design of collectives of reinforcement-learning agents such that their interaction causes a provided "world" utility function concerning the entire collective to be maximized. Previously, we applied that framework to scenarios involving Markovian dynamics where no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. This approach sets the individual utility function of each agent to be both aligned with the world utility, and at the same time, easy for the associated agents to optimize. Here we extend that approach to systems involving non-Markovian dynamics. In computer simulations, we compare our techniques with each other and with conventional "team games". We show whereas in team games performance often degrades badly with time, it steadily improves when our techniques are used. We also investigate situations where the system's dimensionality is effectively reduced. We show that this leads to difficulties in the agents ability to learn. The implication is that learning is a property only of high-enough dimensional systems.
The Design of Collectives of Agents to Control Non-Markovian Systems
NASA Technical Reports Server (NTRS)
Lawson, John W.; Wolpert, David H.
2004-01-01
The Collective Intelligence (COIN) framework concerns the design of collectives of reinforcement-learning agents such that their interaction causes a provided "world" utility function concerning the entire collective to be maximized. Previously, we applied that framework to scenarios involving Markovian dynamics where no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. This approach sets the individual utility function of each agent to be both aligned with the world utility, and at the same time, easy for the associated agents to optimize. Here we extend that approach to systems involving non-Markovian dynamics. In computer simulations, we compare our techniques with each other and with conventional "team games". We show whereas in team games performance often degrades badly with time, it steadily improves when our techniques are used. We also investigate situations where the system's dimensionality is effectively reduced. We show that this leads to difficulties in the agents ability to learn. The implication is that learning is a property only of high-enough dimensional systems.
Berezhkovskii, Alexander M; Weiss, George H
2008-01-28
There are many current applications of the continuous-time random walk (CTRW), particularly in describing kinetic and transport processes in different chemical and biophysical phenomena. We derive exact solutions for the Laplace transforms of the propagators for non-Markovian asymmetric one-dimensional CTRW's in an infinite space and in the presence of an absorbing boundary. The former is used to produce exact results for the Laplace transforms of the first two moments of the displacement of the random walker, the asymptotic behavior of the moments as t-->infinity, and the effective diffusion constant. We show that in the infinite space, the propagator satisfies a relation that can be interpreted as a generalized fluctuation theorem since it reduces to the conventional fluctuation theorem at large times. Based on the Laplace transform of the propagator in the presence of an absorbing boundary, we derive the Laplace transform of the survival probability of the random walker, which is then used to find the mean lifetime for terminated trajectories of the random walk.
The Design of Collectives of Agents to Control Non-Markovian Systems
NASA Technical Reports Server (NTRS)
Lawson, John W.; Wolpert, David H.; Clancy, Daniel (Technical Monitor)
2002-01-01
The 'Collective Intelligence' (COIN) framework concerns the design of collectives of reinforcement-learning agents such that their interaction causes a provided 'world' utility function concerning the entire collective to be maximized. Previously, we applied that framework to scenarios involving Markovian dynamics where no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. This approach sets the individual utility function of each agent to be both aligned with the world utility, and at the same time, easy for the associated agents to optimize. Here we extend that approach to systems involving non-Markovian dynamics. In computer simulations, we compare our techniques with each other and with conventional-'team games'. We show whereas in team games performance often degrades badly with time, it steadily improves when our techniques are used. We also investigate situations where the system's dimensionality is effectively reduced. We show that this leads to difficulties in the agents' ability to learn. The implication is that 'learning' is a property only of high-enough dimensional systems.
Extracting work from a single reservoir in the non-Markovian underdamped regime.
Paredes-Altuve, Oscar; Medina, Ernesto; Colmenares, Pedro J
2016-12-01
We derive optimal-work finite time protocols for a colloidal particle in a harmonic well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal-work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behavior of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quasistatic processes. When measurements are performed, protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below that predicted by Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.
Extending the applicability of Redfield theories into highly non-Markovian regimes
NASA Astrophysics Data System (ADS)
Montoya-Castillo, Andrés; Berkelbach, Timothy C.; Reichman, David R.
2015-11-01
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
Extending the applicability of Redfield theories into highly non-Markovian regimes
Montoya-Castillo, Andrés; Reichman, David R.; Berkelbach, Timothy C.
2015-11-21
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna–Matthews–Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
Extending the applicability of Redfield theories into highly non-Markovian regimes.
Montoya-Castillo, Andrés; Berkelbach, Timothy C; Reichman, David R
2015-11-21
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
NASA Astrophysics Data System (ADS)
Jiménez-Aquino, J. I.; Romero-Bastida, M.
2016-09-01
In this paper we derive the non-Markovian barotropic-type and Hall-type fluctuation relations for noninteracting charged Brownian particles embedded in a memory heat bath and under the action of crossed electric and magnetic fields. We first obtain a more general non-Markovian fluctuation relation formulated within the context of a generalized Langevin equation with arbitrary friction memory kernel and under the action of a constant magnetic field and an arbitrary time-dependent electric field. It is shown that this fluctuation relation is related to the total amount of an effective work done on the charged particle as it is driven out of equilibrium by the applied time-dependent electric field. Both non-Markovian barotropic- and Hall-type fluctuation relations are then derived when the electric field is assumed to be also a constant vector pointing along just one axis. In the Markovian limit, we show explicitly that they reduce to the same results reported in the literature.
NASA Astrophysics Data System (ADS)
Wang, Chao-Quan; Zou, Jian; Shao, Bin
2017-06-01
We propose a quantum collision model in which the environment is abstractively divided into two hierarchies including "environment-bus" that has direct interactions with the system and "environment-stations" that has not. Based on the model, we investigate the effects of initial system-environment correlations, initial states of environment, and various interactions on the dynamics of open quantum systems associated genuinely with such a hierarchical environment. We illustrate that the initial quantum correlation between the system and environment leads to a transition from Markovian to non-Markovian dynamics, while for initial classical correlation the transition can only be confirmed to happen when the couplings rather than the correlations in environment are present. In addition, we investigate the degree of non-Markovianity varying with environment initial states and reveal that the interaction strength between two environmental hierarchies plays an important role in it. In particular, we show that in such a hierarchically structured environment the degree of non-Markovianity is not equivalent to memory effects of the environment-stations as a reservoir due to the presence of the environment-bus.
Non-Markovian coarse-grained modeling of polymeric fluids based on the Mori-Zwanzig formalism
NASA Astrophysics Data System (ADS)
Li, Zhen; Bian, Xin; Li, Xiantao; Karniadakis, George
The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables based on the Mori-Zwanzig formalism. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons on both static and dynamic properties between the CG models with Markovian and non-Markovian approximations will be presented. Supported by the DOE Center on Mathematics for Mesoscopic Modeling of Materials (CM4) and an INCITE grant.
Jiménez-Aquino, J I; Romero-Bastida, M
2016-09-01
In this paper we derive the non-Markovian barotropic-type and Hall-type fluctuation relations for noninteracting charged Brownian particles embedded in a memory heat bath and under the action of crossed electric and magnetic fields. We first obtain a more general non-Markovian fluctuation relation formulated within the context of a generalized Langevin equation with arbitrary friction memory kernel and under the action of a constant magnetic field and an arbitrary time-dependent electric field. It is shown that this fluctuation relation is related to the total amount of an effective work done on the charged particle as it is driven out of equilibrium by the applied time-dependent electric field. Both non-Markovian barotropic- and Hall-type fluctuation relations are then derived when the electric field is assumed to be also a constant vector pointing along just one axis. In the Markovian limit, we show explicitly that they reduce to the same results reported in the literature.
Stochastic thermodynamics of a tagged particle within a harmonic chain.
Lacoste, David; Lomholt, Michael A
2015-02-01
We study the stochastic thermodynamics of an overdamped harmonic chain, which can be viewed equivalently as a one-dimensional Rouse chain or as an approximate model of single file diffusion. We discuss mainly two levels of description of this system: the Markovian level for which the trajectories of all the particles of the chain are known and the non-Markovian level in which only the motion of a tagged particle is available. For each case, we analyze the energy dissipation and its dependence on initial conditions. Surprisingly, we find that the average coarse-grained entropy production rate can become transiently negative when an oscillating force is applied to the tagged particle. This occurs due to memory effects as shown in a framework based on path integrals or on a generalized Langevin equation.
Mathematical Descriptions of Biochemical Networks: Stability, Stochasticity, Evolution
Rosenfeld, Simon
2011-01-01
In this paper, we review some fundamental aspects, as well as some new developments, in the emerging field of network biology. The focus of attention is placed on mathematical approaches to conceptual modeling of biomolecular networks with special emphasis on dynamic stability, stochasticity and evolution. PMID:21419158
NASA Astrophysics Data System (ADS)
Kato, Akihito; Tanimura, Yoshitaka
2016-12-01
We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)—which have a purely quantum mechanical origin—the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat currents and the work performed by the heat engine, and we find that their phases depend on the system-bath coupling strength. Through consideration of the bath heat current, we show that the efficiency of the heat engine decreases as the strength of the system-bath coupling increases, due to the CASBI contribution. In the case of a large system-bath coupling, the efficiency decreases further if the bath temperature is increased, even if the ratio of the bath temperatures is fixed, due to the discretized nature of energy eigenstates. This is also considered to be a unique feature of quantum heat engines.
Kato, Akihito; Tanimura, Yoshitaka
2016-12-14
We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)-which have a purely quantum mechanical origin-the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat currents and the work performed by the heat engine, and we find that their phases depend on the system-bath coupling strength. Through consideration of the bath heat current, we show that the efficiency of the heat engine decreases as the strength of the system-bath coupling increases, due to the CASBI contribution. In the case of a large system-bath coupling, the efficiency decreases further if the bath temperature is increased, even if the ratio of the bath temperatures is fixed, due to the discretized nature of energy eigenstates. This is also considered to be a unique feature of quantum heat engines.
Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism
NASA Astrophysics Data System (ADS)
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.
Li, Zhen; Lee, Hee Sun; Darve, Eric; Karniadakis, George Em
2017-01-07
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Schmidt, R.; Carusela, M. F.; Pekola, J. P.; Suomela, S.; Ankerhold, J.
2015-06-01
Work, moments of work, and heat flux are studied for the generic case of a strongly driven two-level system immersed in a bosonic heat bath in domains of parameter space where perturbative treatments fail. This includes in particular the interplay between non-Markovian dynamics and moderate to strong external driving. Exact data are compared with predictions from weak-coupling approaches. Further, the role of system-bath correlations in the initial thermal state and their impact on the heat flux are addressed. The relevance of these results for current experimental activities on solid-state devices is discussed.
NASA Astrophysics Data System (ADS)
Xiong, Heng-Na; Li, Yi; Le, Zichun; Huang, Yixiao
2017-05-01
We evaluate exactly the non-Markovian effect on the decoherence dynamics of a qubit coupling with a waveguide in photonic crystals. In our study, we extend the previous investigation that the waveguide is structured as a semi-infinite cavity array to the case that it is set as an infinite cavity array. For the infinite cavity array, we utilize the quantity of fidelity to characterize the ability of the system to preserve its initial quantum information. We make a discussion for different initial states of the qubit. Similar to the case of semi-infinite cavity array, we find that the quantum information of the qubit in the long-time scale could also be partially preserved when the qubit-waveguide coupling strength goes beyond a critical value. This is a strong non-Markovian memory effect induced by the strong qubit-waveguide coupling strength. Interestingly, the critical coupling strength for infinite cavity array happens to be zero, which means that in this real physical system, the quantum-to-classical transition behavior of the qubit never occurs. Therefore, by reasonably choosing the structure of the environment, the quantum information of the quantum systems could be more easily preserved. Moreover, we find that the higher probability of the qubit initially in its ground state, the more easily for it to preserve its initial information in the long-time scale, which proves that the quantum open system always tends to stay in its ground state.
NASA Astrophysics Data System (ADS)
Fedotov, Sergei; Iomin, Alexander; Ryashko, Lev
2011-12-01
Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth
NASA Astrophysics Data System (ADS)
Iemini, Fernando; da Silva Souza, Leonardo; Debarba, Tiago; Cesário, André T.; Maciel, Thiago O.; Vianna, Reinaldo O.
2017-05-01
We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.
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.
NASA Astrophysics Data System (ADS)
Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham; Whaley, K. Birgitta
2014-10-01
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.
Jesenko, Simon; Znidaric, Marko
2013-05-07
We analyze efficiency of excitation energy transfer in photosynthetic complexes in transient and stationary setting. In the transient setting, the absorption process is modeled as an individual event resulting in a subsequent relaxation dynamics. In the stationary setting the absorption is a continuous stationary process, leading to the nonequilibrium steady state. We show that, as far as the efficiency is concerned, both settings can be considered to be the same, as they result in almost identical efficiency. We also show that non-Markovianity has no effect on the resulting efficiency, i.e., corresponding Markovian dynamics results in identical efficiency. Even more, if one maps dynamics to appropriate classical rate equations, the same efficiency as in quantum case is obtained.
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
The One-on-One Stochastic Duel. Parts I and II
1979-04-15
BRIGHAM, E. ORAN . The Fast Fourier Transform, Prentice Hall, Inc., New Jersey, 1974. COK, D.R. "The Analysis of Non-Markovian Stochastic Processes by...1977. 6. THONPSCNj, D. See, Tl in Research Papers,. PP. 573-576. -38- S t APPMIXfl SOME USEM •ULTS 1N TM THM OY OF CHMCERMISTIC FUCTIONS 0. Introduction
NASA Astrophysics Data System (ADS)
Buldyreva, Jeanna
2013-06-01
Reliable modeling of radiative transfer in planetary atmospheres requires accounting for the collisional line mixing effects in the regions of closely spaced vibrotational lines as well as in the spectral wings. Because of too high CPU cost of calculations from ab initio potential energy surfaces (if available), the relaxation matrix describing the influence of collisions is usually built by dynamical scaling laws, such as Energy-Corrected Sudden law. Theoretical approaches currently used for calculation of absorption near the band center are based on the impact approximation (Markovian collisions without memory effects) and wings are modeled via introducing some empirical parameters [1,2]. Operating with the traditional non-symmetric metric in the Liouville space, these approaches need corrections of the ECS-modeled relaxation matrix elements ("relaxation times" and "renormalization procedure") in order to ensure the fundamental relations of detailed balance and sum rules.We present an extension to the infrared absorption case of the previously developed [3] for rototranslational Raman scattering spectra of linear molecules non-Markovian approach of ECS-type. Owing to the specific choice of symmetrized metric in the Liouville space, the relaxation matrix is corrected for initial bath-molecule correlations and satisfies non-Markovian sum rules and detailed balance. A few standard ECS parameters determined by fitting to experimental linewidths of the isotropic Q-branch enable i) retrieval of these isolated-line parameters for other spectroscopies (IR absorption and anisotropic Raman scattering); ii) reproducing of experimental intensities of these spectra. Besides including vibrational angular momenta in the IR bending shapes, Coriolis effects are also accounted for. The efficiency of the method is demonstrated on OCS-He and CO_2-CO_2 spectra up to 300 and 60 atm, respectively. F. Niro, C. Boulet, and J.-M. Hartmann, J. Quant. Spectrosc. Radiat. Transf. 88, 483
Stochastic semi-classical description of fusion at near-barrier energies
Ayik, Sakir; Yilmaz, Bulent
2010-03-15
Fusion reactions of heavy ions are investigated by employing a simple stochastic semi-classical model, which includes coupling between the relative motion and low frequency collective surface modes of colliding ions similarly to the quantal coupled-channels description. The quantal effect enters into the calculation through the initial zero-point fluctuations of the surface vibrations. A good agreement with results of coupled-channels calculations as well as experimental data is obtained for fusion cross sections of Ni isotopes. The internal excitations in nonfusing events as well as the fusion time are investigated.
A stochastic-field description of finite-size spiking neural networks
Longtin, André
2017-01-01
Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447
A stochastic-field description of finite-size spiking neural networks.
Dumont, Grégory; Payeur, Alexandre; Longtin, André
2017-08-01
Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity-the density of active neurons per unit time-is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.
Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
NASA Astrophysics Data System (ADS)
Schütz, Gunter M.; Trimper, Steffen
2004-10-01
We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p . At a critical value pc(1)=1/2 where memory effects vanish there is a transition from a weakly localized regime [where the walker (elephant) returns to its starting point] to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant k=(2p-1)/t . The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.
NASA Astrophysics Data System (ADS)
Liu, Da-Jiang; Chen, Hung-Ting; Lin, Victor S.-Y.; Evans, J. W.
2010-04-01
We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to exhibit non-Markovian scaling behavior. This feature is attributed to the long-tail in the "return-time distribution" for the protruding end of the partially extruded polymer to return to the pore, such return being necessary for further reaction and growth. The detailed form of the scaled length distribution is elucidated by application of continuous-time random walk theory.
NASA Astrophysics Data System (ADS)
Strasberg, Philipp; Schaller, Gernot; Lambert, Neill; Brandes, Tobias
2016-07-01
We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.
Liu, Da-Jiang; Chen, Hung-Ting; Lin, Victor S-Y; Evans, J W
2010-04-21
We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to exhibit non-Markovian scaling behavior. This feature is attributed to the long-tail in the "return-time distribution" for the protruding end of the partially extruded polymer to return to the pore, such return being necessary for further reaction and growth. The detailed form of the scaled length distribution is elucidated by application of continuous-time random walk theory.
NASA Astrophysics Data System (ADS)
Forsling, Robin; Sanders, Lloyd P.; Ambjörnsson, Tobias; Lizana, Ludvig
2014-09-01
The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates koff (kon). The tracer particle is restricted to diffuse with rate kD on the lattice and the density of crowders is constant (on average). The unbinding rate koff is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (koff ≫ kD) to the non-Markovian case (koff ≪ kD) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DNA. We quantify the first-passage time distribution, f (t) (t is time), numerically using the Gillespie algorithm, and estimate f (t) analytically. In terms of koff (keeping kD fixed), we study the transition between the two known regimes: (i) when koff ≫ kD the particles may effectively pass each other and we recover the single particle result f (t) ˜ t-3/2, with a reduced diffusion constant; (ii) when koff ≪ kD unbinding is rare and we obtain the single-file result f (t) ˜ t-7/4. The intermediate region displays rich dynamics where both the characteristic f (t) - peak and the long-time power-law slope are sensitive to koff.
NASA Astrophysics Data System (ADS)
Lensky, Vadim; Birse, Michael C.; Walet, Niels R.
2016-09-01
We construct a coordinate-space potential based on pionless effective field theory (EFT) with a Gaussian regulator. Charge-symmetry breaking is included through the Coulomb potential and through two- and three-body contact interactions. Starting with the effective field theory potential, we apply the stochastic variational method to determine the ground states of nuclei with mass number A ≤4 . At next-to-next-to-leading order, two out of three independent three-body parameters can be fitted to the three-body binding energies. To fix the remaining one, we look for a simultaneous description of the binding energy of 4He and the charge radii of 3He and 4He. We show that at the order considered we can find an acceptable solution, within the uncertainty of the expansion. We find that the EFT expansion shows good agreement with empirical data within the estimated uncertainty, even for a system as dense as 4He.
Theory of frequency and phase synchronization in a rocked bistable stochastic system.
Casado-Pascual, Jesús; Gómez-Ordóñez, José; Morillo, Manuel; Lehmann, Jörg; Goychuk, Igor; Hänggi, Peter
2005-01-01
We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of stochastic resonance. We present an approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics, one finds upon contraction onto two states a non-Markovian renewal dynamics. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. In this case, for an appropriate choice of the parameter values, the system exhibits a noise-induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior ones.
NASA Astrophysics Data System (ADS)
da Silva, Roberto; Vainstein, Mendeli H.; Lamb, Luis C.; Prado, Sandra D.
2013-03-01
We propose a novel probabilistic model that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential (ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a team future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirão) if the starting potential is the same for all teams. Other leagues such as the Italian (Calcio) and the Spanish (La Liga) tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model with simple initial conditions. However, we show that by setting the initial abilities based on data from previous tournaments, our model is able to capture the stylized statistical features of double round robin system (DRRS) tournaments in general. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: here several teams have been crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserve the Gaussian traces during the tournament. On the other hand, in the Italian and Spanish cases, only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the Brazilian tournament “Brasileirão” cannot be reproduced. This shows that the evolutionary aspects are not superfluous and play an important role which must be considered in
NASA Astrophysics Data System (ADS)
Mandani, Somayeh; Sarbishaei, Mohsen; Javidan, Kurosh
2017-10-01
We have investigated the dynamics of a four-level N-type atom in cavity QED with consideration to the Kerr effect. The non-Markovianity of the system has been studied using the Breuer-Laine-Piilo (BLP) measure ( N B L P ). Moreover the effects of system parameters like temperature and atom-field coupling have also been discussed. The evolution equation of the system has been derived using the time convolution-less(TCL) master equation. Some interesting behaviour of the system and their reasons are discussed.
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Sarmah, D.; Nicolini, P.
2008-12-01
Extending the statistical approach proposed in a parallel paper [1], purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a suitable local phase-space probability density function (pdf). In particular, we pose the problem of the construction of Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here adopted is based on the so-called IKT approach (inverse kinetic theory), developed by Tessarotto et al. (2004-2008) which permits an exact phase-space description of incompressible fluids based on the adoption of a local pdf. We intend to show that for prescribed models of stochasticity the present approach permits to determine uniquely the time evolution of the stochastic fluid fields. The stochastic-averaged local pdf is shown to obey a kinetic equation which, although generally non-Markovian, locally in velocity-space can be approximated by means of a suitable Fokker-planck kinetic equation. As a side result, the same pdf is proven to have generally a non-Gaussian behavior.
NASA Astrophysics Data System (ADS)
Helbing, Dirk; Schönhof, Martin; Kern, Daniel
2002-06-01
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc, they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified methods of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems and for information service providers. One of the promising fields of application is traffic optimization.
Wetland Ecohydrology: stochastic description of water level fluctuations across the soil surface
NASA Astrophysics Data System (ADS)
Tamea, S.; Muneepeerakul, R.; Laio, F.; Ridolfi, L.; Rodriguez-Iturbe, I.
2009-12-01
Wetlands provide a suite of social and ecological critical functions such as being habitats of disease-carrying vectors, providing buffer zones against hurricanes, controlling sediment transport, filtering nutrients and contaminants, and a repository of great biological diversity. More recently, wetlands have also been recognized as crucial for carbon storage in the context of global climate change. Despite such importance, quantitative approaches to many aspects of wetlands are far from adequate. Therefore, improving our quantitative understanding of wetlands is necessary to our ability to maintain, manage, and restore these invaluable environments. In wetlands, hydrologic factors and ecosystem processes interplay and generate unique characteristics and a delicate balance between biotic and abiotic elements. The main hydrologic driver of wetland ecosystems is the position of the water level that, being above or below ground, determines the submergence or exposure of soil. When the water level is above the soil surface, soil saturation and lack of oxygen causes hypoxia, anaerobic functioning of microorganisms and anoxic stress in plants, that might lead to the death of non-adapted organisms. When the water level lies below the soil surface, the ecosystem becomes groundwater-dependent, and pedological and physiological aspects play their role in the soil water balance. We propose here a quantitative description of wetland ecohydrology, through a stochastic process-based water balance, driven by a marked compound Poisson noise representing rainfall events. The model includes processes such as rainfall infiltration, evapotranspiration, capillary rise, and the contribution of external water bodies, which are quantified in a simple yet realistic way. The semi-analytical steady-state probability distributions of water level spanning across the soil surface are validated with data from the Everglades (Florida, USA). The model and its results allow for a quantitative
NASA Astrophysics Data System (ADS)
Cerrillo, Javier; Buser, Maximilian; Brandes, Tobias
2016-12-01
Nonequilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady-state nonequilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to establish general relationships between transport coefficients in the transient regime which take the form of fluctuation-dissipation theorems in the steady state. This result becomes most conspicuous in the transient dynamics of open quantum systems under strong-coupling to non-Markovian environments in nonequilibrium settings. In order to explore this regime, a new simulation method based in a hierarchy of equations of motion has been developed. We instantiate our proposal with the study of energetic conductance between two baths connected via a few level system.
NASA Astrophysics Data System (ADS)
Smith, Eric
2011-04-01
The meaning of thermodynamic descriptions is found in large-deviations scaling (Ellis 1985 Entropy, Large Deviations, and Statistical Mechanics (New York: Springer); Touchette 2009 Phys. Rep. 478 1-69) of the probabilities for fluctuations of averaged quantities. The central function expressing large-deviations scaling is the entropy, which is the basis both for fluctuation theorems and for characterizing the thermodynamic interactions of systems. Freidlin-Wentzell theory (Freidlin and Wentzell 1998 Random Perturbations in Dynamical Systems 2nd edn (New York: Springer)) provides a quite general formulation of large-deviations scaling for non-equilibrium stochastic processes, through a remarkable representation in terms of a Hamiltonian dynamical system. A number of related methods now exist to construct the Freidlin-Wentzell Hamiltonian for many kinds of stochastic processes; one method due to Doi (1976 J. Phys. A: Math. Gen. 9 1465-78 1976 J. Phys. A: Math. Gen. 9 1479) and Peliti (1985 J. Physique 46 1469; 1986 J. Phys. A: Math. Gen. 19 L365, appropriate to integer counting statistics, is widely used in reaction-diffusion theory. Using these tools together with a path-entropy method due to Jaynes (1980 Annu. Rev. Phys. Chem. 31 579-601), this review shows how to construct entropy functions that both express large-deviations scaling of fluctuations, and describe system-environment interactions, for discrete stochastic processes either at or away from equilibrium. A collection of variational methods familiar within quantum field theory, but less commonly applied to the Doi-Peliti construction, is used to define a 'stochastic effective action', which is the large-deviations rate function for arbitrary non-equilibrium paths. We show how common principles of entropy maximization, applied to different ensembles of states or of histories, lead to different entropy functions and different sets of thermodynamic state variables. Yet the relations among all these levels of
Rossi, Matteo A. C.; Paris, Matteo G. A.
2016-01-14
We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where the two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.
Chakrabarti, Rajarshi; Sebastian, K L
2009-12-14
We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.
NASA Astrophysics Data System (ADS)
Giona, Massimiliano
2017-05-01
A variational Lagrangian formulation for stochastic processes and for the evolution equations of the associated probability density functions is developed. Particular attention is dedicated to Poisson-Kac processes possessing finite propagation velocity. The variational formulation in terms of Lagrangian and Hamiltonian densities permits to address different forms of "reversibility" characterizing these processes with respect to processes driven by nowhere differentiable Wiener fluctuations, and associated with the concepts of dynamic and statistical reversibility. The latter property, i.e. the statistical reversibility, implies that the extended Markov operator associated with Poisson-Kac and Generalized Poisson-Kac processes forms a group, continuously parametrized with respect to time.
NASA Astrophysics Data System (ADS)
Howell, S. M.; Furbish, D. J.; Morris, J. T.
2009-12-01
Sea-level rise and sedimentation interact to control productivity on coastal salt marshes since the mean sea level influences flood frequency. Irregularly flooded marshes are inundated during spring and storm tides and during extended periods of north-easterly winds. The weak and irregular inundation in marshes may effect rates of decomposition, organic matter accumulation, and the vertical distribution of marsh vegetation. Whereas astronomical tides are predictable, wind driven tides depend on the strength and direction of the wind. Because these systems are stochastic, a non-hydrodynamic approach is used to describe the tides and determine the distribution of water depths. Here we present a description of salt-marsh inundation from mixed astronomical-wind driven tides that removes the astronomical forcing from water level records to determine the role of wind, storms, and forecasting of stochastic platform wetting. Using a 3 year record of water level and wind from sites in Carteret County, North Carolina, we calculate the mean high water (MHW) level and the ratio of inundation for a given elevation and corresponding macrophyte. The frequency of inundation or marsh platform wetting will vary from the frequency of MHW level, yet it is this stochastic wetting process that determines productivity and plant distribution since infrequent flooding may cause stress or hypersaline conditions. An ARIMA model is used to describe this higher order structure of the inundation signal. Wind can be described as an AR1 and a transfer function model is used to determine the dynamic response of the effect of noise and sustained winds on water levels. Harmonic analysis is also performed for comparison of predicted water levels using various tidal constituents to determine the phases and amplitudes and to explore model simplification.
Hierarchy of Stochastic Pure States for Open Quantum System Dynamics
NASA Astrophysics Data System (ADS)
Suess, D.; Eisfeld, A.; Strunz, W. T.
2014-10-01
We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact reduced density operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate that HOPS provides an efficient theoretical tool and apply it to the spin-boson model, the calculation of absorption spectra of molecular aggregates, and energy transfer in a photosynthetic pigment-protein complex.
NASA Astrophysics Data System (ADS)
Vico, Giulia; Porporato, Amilcare
2013-03-01
Supplemental irrigation represents one of the main strategies to mitigate the effects of climatic variability on agroecosystems, stabilizing yields and profits. Because of the significant investments and water requirements associated with irrigation, strategic choices are needed to preserve productivity and profitability while ensuring a sustainable water management, a nontrivial task given rainfall unpredictability. Decision-making under uncertainty requires the knowledge of the probability density function (pdf) of the outcome variable (yield and economic return) for the different management alternatives to be considered (here, irrigation strategies). A stochastic framework is proposed, linking probabilistically the occurrence of rainfall events and irrigation applications to crop development during the growing season. Based on these linkages, the pdf of yields and the corresponding irrigation requirements are obtained analytically as a function of climate, soil, and crop parameters, for different irrigation strategies and both unlimited and limited water availability. Approximate expressions are also presented to facilitate their application. Our results employ relatively few parameters and are thus broadly applicable to different crops and sites, under current- and future-climate scenarios, offering a quantitative tool to quantify the impact of irrigation strategies and water allocation on yields. As a tool for decision-making under uncertainty (e.g., via expected utility theory), our framework will be useful for the assessment of the feasibility of different irrigation strategies and water allocations, toward a sustainable management of water resources for human and environmental needs.
2012-01-01
Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a
Two-layer symbolic representation for stochastic models with phase-type distributed events
NASA Astrophysics Data System (ADS)
Longo, Francesco; Scarpa, Marco
2015-07-01
Among the techniques that have been proposed for the analysis of non-Markovian models, the state space expansion approach showed great flexibility in terms of modelling capacities.The principal drawback is the explosion of the state space. This paper proposes a two-layer symbolic method for efficiently storing the expanded reachability graph of a non-Markovian model in the case in which continuous phase-type distributions are associated with the firing times of system events, and different memory policies are considered. At the lower layer, the reachability graph is symbolically represented in the form of a set of Kronecker matrices, while, at the higher layer, all the information needed to correctly manage event memory is stored in a multi-terminal multi-valued decision diagram. Such an information is collected by applying a symbolic algorithm, which is based on a couple of theorems. The efficiency of the proposed approach, in terms of memory occupation and execution time, is shown by applying it to a set of non-Markovian stochastic Petri nets and comparing it with a classical explicit expansion algorithm. Moreover, a comparison with a classical symbolic approach is performed whenever possible.
Linear noise approximation for oscillations in a stochastic inhibitory network with delay
NASA Astrophysics Data System (ADS)
Dumont, Grégory; Northoff, Georg; Longtin, André
2014-07-01
Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm.
Non-markovian boltzmann equation
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-08-01
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.
Transport in sheared stochastic magnetic fields
Vanden Eijnden, E.; Balescu, R.
1997-02-01
The transport of test particles in a stochastic magnetic field with a sheared component is studied. Two stages in the particle dynamics are distinguished depending on whether the collisional effects perpendicular to the main field are negligible or not. Whenever the perpendicular collisions are unimportant, the particles show a subdiffusive behavior which is slower in the presence of shear. The particle dynamics is then inhomogeneous and non-Markovian and no diffusion coefficient may be properly defined. When the perpendicular collision frequency is small, this subdiffusive stage may be very long. In the truly asymptotic stage, however, the perpendicular collisions must be accounted for and the particle motion eventually becomes diffusive. Here again, however, the shear is shown to reduce the anomalous diffusion coefficient of the system. {copyright} {ital 1997 American Institute of Physics.}
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
On stochastic evolution equations for chaos and turbulence
NASA Astrophysics Data System (ADS)
Mori, Hazime
2005-06-01
The chaotic orbits of dynamical systems have positive Liapunov exponents, and become stochastic and random on long timescales due to the orbital instability, leading to various remarkable phenomena, such as the loss of memory with respect to the initial states, the dissipation of the kinetic energy into random fluctuations, turbulent transport phenomena (e.g., turbulent viscosity, turbulent thermal diffusivity). In order to obtain a statistical-mechanical approach to these phenomena, we have formulated the randomization of chaotic orbits by deriving a non-Markovian stochastic evolution equation in terms of a nonlinear fluctuating force and a memory function. In the following, we outline its derivation and its application to the Boussinesq equations of turbulent Bénard convection. Then we find that turbulence produces an interference between the velocity flux and the heat flux which is similar to the interference between the electric current and the heat flux in the thermoelectric phenomena of metals.
Stochastic Modeling of Decadal Variability in Ocean Gyres
NASA Astrophysics Data System (ADS)
Kondrashov, Dmitri; Berloff, Pavel
2015-04-01
Decadal large-scale low-frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data-driven approach that addresses this challenge. We propose non-Markovian low-order methodology with stochastic closure and data-adaptive mode decomposition. The multilayer stochastic linear model is obtained from the coarse-grained eddy-resolving ocean model solution, and it reproduces with high accuracy the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data.
Stochastic modeling of decadal variability in ocean gyres
NASA Astrophysics Data System (ADS)
Kondrashov, D.; Berloff, P.
2015-03-01
Decadal large-scale low-frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data driven approach that addresses this challenge. Proposed is non-Markovian low-order methodology with stochastic closure and use of mode decomposition by multichannel Singular Spectrum Analysis. The multilayer stochastic linear model is obtained from the coarse-grained eddy-resolving ocean model solution, and with high accuracy it reproduces the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data.
Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
NASA Astrophysics Data System (ADS)
Goychuk, Igor; Goychuk, Andriy
2015-04-01
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.
Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing
NASA Technical Reports Server (NTRS)
Jones, Robert L.; Goode, Plesent W. (Technical Monitor)
2000-01-01
The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.
Gerdes, Frank; Finette, Steven
2012-10-01
A modeling and simulation study is performed in a littoral ocean waveguide subject to uncertainty in four quantities: source depth, tidal forcing, initial thermocline structure, and sediment sound speed. In this partially known shelf-break environment, tidal forcing over a density-stratified water column produces internal tides and solitary wave packets. The resulting uncertainty in the space-time oceanographic field is mapped into the sound speed distribution which, in turn, introduces uncertainty into the acoustic wave field. The latter is treated as a stochastic field whose intensity is described by a polynomial chaos expansion. The expansion coefficients are estimated through constrained multivariate linear regression, and an analysis of the chaos coefficients provides insight into the relative contribution of the uncertain acoustic and oceanographic quantities. Histograms of acoustic intensity are estimated and compared to a reference solution obtained through Latin Hypercube sampling. A sensitivity analysis is performed to illustrate the relative importance of the four contributions of incomplete information about the environment. The simulation methodology represents an end-to-end analysis approach including both oceanographic and acoustic field uncertainty where the latter is quantified using stochastic basis expansions in the form of a polynomial chaos representation.
Stochastic Loewner evolution relates anomalous diffusion and anisotropic percolation.
Credidio, Heitor F; Moreira, André A; Herrmann, Hans J; Andrade, José S
2016-04-01
We disclose the origin of anisotropic percolation perimeters in terms of the stochastic Loewner evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multilayered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being superdiffusive and subdiffusive, respectively. The connection between anomalous diffusion and fractal anisotropy is further tested by using long-range power-law correlated time series (fractional Brownian motion) as the driving functions in the evolution process. The fact that the resulting traces are distinctively anisotropic corroborates our hypothesis. Under the conceptual framework of SLE, our study therefore reveals different perspectives for mathematical and physical interpretations of non-Markovian processes in terms of anisotropic paths at criticality and vice versa.
Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows.
Minier, Jean-Pierre; Profeta, Christophe
2015-11-01
This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Z(p)=(x(p),U(p)) and is represented by its PDF p(t; y(p),V(p)) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Z(p)=(x(p),U(p),U(s)), and, consequently, handles an extended PDF p(t; y(p),V(p),V(s)) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to
NASA Astrophysics Data System (ADS)
Costa, A. C. S.; Beims, M. W.; Angelo, R. M.
2016-11-01
Generalized quantum discord (Dq) , Einstein-Podolsky-Rosen steering (S) , entanglement (E) , and Bell nonlocality (N), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that N ⊳ S ⊳ E ⊳Dq, meaning that nonlocality implies steering, which in turn implies entanglement, which then implies q-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels.
Wiegel, A A; Wilson, K R; Hinsberg, W D; Houle, F A
2015-02-14
The heterogeneous oxidation of organic aerosol by hydroxyl radicals (OH) can proceed through two general pathways: functionalization, in which oxygen functional groups are added to the carbon skeleton, and fragmentation, in which carbon-carbon bonds are broken, producing higher volatility, lower molecular weight products. An ongoing challenge is to develop a quantitative molecular description of these pathways that connects the oxidative evolution of the average aerosol properties (e.g. size and hygroscopicity) to the transformation of free radical intermediates. In order to investigate the underlying molecular mechanism of aerosol oxidation, a relatively compact kinetics model is developed for the heterogeneous oxidation of squalane particles by OH using free radical intermediates that convert reactive hydrogen sites into oxygen functional groups. Stochastic simulation techniques are used to compare calculated system properties over ten oxidation lifetimes with the same properties measured in experiment. The time-dependent average squalane aerosol mass, volume, density, carbon number distribution of scission products, and the average elemental composition are predicted using known rate coefficients. For functionalization, the calculations reveal that the distribution of alcohol and carbonyl groups is controlled primarily by the initial OH abstraction rate and to lesser extent by the branching ratio between secondary peroxy radical product channels. For fragmentation, the calculations reveal that the formation of activated alkoxy radicals with neighboring functional groups controls the molecular decomposition, particularly at high O/C ratios. This kinetic scheme provides a framework for understanding the oxidation chemistry of a model organic aerosol and informs parameterizations of more complex systems.
Wang, Xiao; Weinberg, Seth H; Hao, Yan; Sobie, Eric A; Smith, Gregory D
2015-03-01
Population density approaches to modeling local control of Ca(2+)-induced Ca(2+) release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca(2+) signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca(2+) release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca(2+) concentration ([Ca(2+)]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca(2+) homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca(2+)] promotes elevated network sarcoplasmic reticulum (SR) [Ca(2+)] via SR Ca(2+)-ATPase-mediated Ca(2+) uptake. However, elevated myoplasmic [Ca(2+)] may also activate RyRs and promote stochastic SR Ca(2+) release, which can in turn decrease SR [Ca(2+)]. Increasing myoplasmic [Ca(2+)] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca(2+)] depending on whether myoplasmic [Ca(2+)] is low or high. In the later case, spontaneous release decreases SR [Ca(2+)] in a manner that maintains robust Ca(2+) sparks.
Dynamics of non-Markovian exclusion processes
NASA Astrophysics Data System (ADS)
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.
High Resolution non-Markovianity in NMR
Bernardes, Nadja K.; Peterson, John P. S.; Sarthour, Roberto S.; Souza, Alexandre M.; Monken, C. H.; Roditi, Itzhak; Oliveira, Ivan S.; Santos, Marcelo F.
2016-01-01
Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts. PMID:27669652
Trajectory based non-markovian dissipative tunneling.
Koch, Werner; Grossmann, Frank; Tannor, David J
2010-12-03
The influence of a dissipative environment on scattering of a particle by a barrier is investigated by using the recently introduced bohmian mechanics with complex action [J. Chem. Phys. 125, 231103 (2006)]. An extension of this complex trajectory based formalism to include the interaction of the tunneling particle with an environment of harmonic oscillators with a continuous spectral density and at a certain finite temperature allows us to calculate transmission probabilities beyond the weak system bath coupling regime. The results display an increasing tunneling probability for energies below the barrier and a decreased transmission above the barrier due to the coupling. Furthermore, we demonstrate that solutions of a markovian master equation fail to do so in general.
High Resolution non-Markovianity in NMR
NASA Astrophysics Data System (ADS)
Bernardes, Nadja K.; Peterson, John P. S.; Sarthour, Roberto S.; Souza, Alexandre M.; Monken, C. H.; Roditi, Itzhak; Oliveira, Ivan S.; Santos, Marcelo F.
2016-09-01
Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.
Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory
NASA Astrophysics Data System (ADS)
Lisý, Vladimír; Tóthová, Jana
2017-03-01
The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.
Brett, Tobias; Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Non-stochastic matrix Schrödinger equation for open systems
NASA Astrophysics Data System (ADS)
Joubert-Doriol, Loïc; Ryabinkin, Ilya G.; Izmaylov, Artur F.
2014-12-01
We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as hat{ρ }= {m} {m}^dagger. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.
Brett, Tobias Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Delay-induced stochastic oscillations in gene regulation
Bratsun, Dmitri; Volfson, Dmitri; Tsimring, Lev S.; Hasty, Jeff
2005-01-01
The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale. PMID:16199522
Stabilizing simulations of complex stochastic representations for quantum dynamical systems
NASA Astrophysics Data System (ADS)
Perret, C.; Petersen, W. P.
2011-03-01
Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs). In a series of papers, Corney and Drummond (2004 Phys. Rev. Lett. 93 260401), Deuar and Drummond (2001 Comput. Phys. Commun. 142 442-5), Drummond and Gardnier (1980 J. Phys. A: Math. Gen. 13 2353-68), Gardiner and Zoller (2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Series in Synergetics) 3rd edn (Berlin: Springer)) and Gilchrist et al (1997 Phys. Rev. A 55 3014-32) and their collaborators have derived SDEs from coherent states representations for density matrices. Computationally, these SDEs are attractive because they seem simple to simulate. They can be quite unstable, however. In this paper, we consider some of the instabilities and propose a few remedies. Particularly, because the variances of the simulated paths typically grow exponentially, the processes become de-localized in relatively short times. Hence, the issues of boundary conditions and stable integration methods become important. We use the Bose-Einstein Hamiltonian as an example. Our results reveal that it is possible to significantly extend integration times and show the periodic structure of certain functionals.
Population density equations for stochastic processes with memory kernels
NASA Astrophysics Data System (ADS)
Lai, Yi Ming; de Kamps, Marc
2017-06-01
We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
Liu, Fuliang; Li, Yaping Sun, Xiaoming
2014-01-28
When considering stochastic oscillations of heterogeneous catalyst systems, most researches have focused on the surface of a metal or its oxide catalysts, but there have been few studies on porous catalysts. In this work, the effects of internal noise on oscillations of N{sub 2}O decomposition over Cu-ZSM-5 zeolites are investigated, using the chemical Langevin equation and a mesoscopic stochastic model. Considering that Cu-ZSM-5 particles are finely divided particles, the number of Cu ions (N{sub s}) is proportional to the particle size at a certain Cu/Al, and the internal noise is inversely proportional to N{sub s}. Stochastic oscillations can be observed outside the deterministic oscillatory region. Furthermore, the performance of the oscillation characterized by the signal-to-noise ratio has a maximum within the optimal size range of 4–8 nm. This suggests that a nanometer-sized zeolite may be best for oscillations.
Evolution with Stochastic Fitness and Stochastic Migration
Rice, Sean H.; Papadopoulos, Anthony
2009-01-01
Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory
Evolution with stochastic fitness and stochastic migration.
Rice, Sean H; Papadopoulos, Anthony
2009-10-09
Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory.
Stochastic quantum Zeno-based detection of noise correlations
NASA Astrophysics Data System (ADS)
Müller, Matthias M.; Gherardini, Stefano; Caruso, Filippo
2016-12-01
A system under constant observation is practically freezed to the measurement subspace. If the system driving is a random classical field, the survival probability of the system in the subspace becomes a random variable described by the Stochastic Quantum Zeno Dynamics (SQZD) formalism. Here, we study the time and ensemble average of this random survival probability and demonstrate how time correlations in the noisy environment determine whether the two averages do coincide or not. These environment time correlations can potentially generate non-Markovian dynamics of the quantum system depending on the structure and energy scale of the system Hamiltonian. We thus propose a way to detect time correlations of the environment by coupling a quantum probe system to it and observing the survival probability of the quantum probe in a measurement subspace. This will further contribute to the development of new schemes for quantum sensing technologies, where nanodevices may be exploited to image external structures or biological molecules via the surface field they generate.
Stochastic quantum Zeno-based detection of noise correlations
Müller, Matthias M.; Gherardini, Stefano; Caruso, Filippo
2016-01-01
A system under constant observation is practically freezed to the measurement subspace. If the system driving is a random classical field, the survival probability of the system in the subspace becomes a random variable described by the Stochastic Quantum Zeno Dynamics (SQZD) formalism. Here, we study the time and ensemble average of this random survival probability and demonstrate how time correlations in the noisy environment determine whether the two averages do coincide or not. These environment time correlations can potentially generate non-Markovian dynamics of the quantum system depending on the structure and energy scale of the system Hamiltonian. We thus propose a way to detect time correlations of the environment by coupling a quantum probe system to it and observing the survival probability of the quantum probe in a measurement subspace. This will further contribute to the development of new schemes for quantum sensing technologies, where nanodevices may be exploited to image external structures or biological molecules via the surface field they generate. PMID:27941889
Solan, Eilon; Vieille, Nicolas
2015-01-01
In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution. PMID:26556883
Limits in the characteristic-function description of non-Lindblad-type open quantum systems
Maniscalco, Sabrina
2005-08-15
In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized master equation containing a memory kernel which may lead to nonphysical time evolutions characterized by negative values of the density matrix diagonal elements [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)]. The main result of the paper is to demonstrate that there exist situations in which the symmetrically ordered characteristic function is perfectly well-defined while the corresponding density matrix loses positivity. Therefore, nonphysical situations may not show up in the characteristic function. As a consequence, the characteristic function cannot be considered an alternative complete description of the non-Lindblad dynamics.
Martínez-López, B; Ivorra, B; Ramos, A M; Sánchez-Vizcaíno, J M
2011-01-27
A new stochastic and spatial model was developed to evaluate the potential spread of classical swine fever virus (CSFV) within- and between-farms, and considering the specific farm-to-farm contact network. Within-farm transmission was simulated using a modified SI model. Between-farm transmission was assumed to occur by direct contacts (i.e. animal movement) and indirect contacts (i.e. local spread, vehicle and person contacts) and considering the spatial location of farms. Control measures dictated by the European legislation (i.e. depopulation of infected farms, movement restriction, zoning, surveillance, contact tracing) were also implemented into the model. Model experimentation was performed using real data from Segovia, one of the provinces with highest density of pigs in Spain, and results were presented using the mean, 95% probability intervals [95% PI] and risk maps. The estimated mean [95% PI] number of infected, quarantined and depopulated farms were 3 [1,17], 23 [0,76] and 115 [0,318], respectively. The duration of the epidemic was 63 [26,177] days and the most important way of transmission was associated with local spread (61.4% of the infections). Results were consistent with the spread of previous CSFV introductions into the study region. The model and results presented here may be useful for the decision making process and for the improvement of the prevention and control programmes for CSFV.
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.
NASA Astrophysics Data System (ADS)
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2009-05-01
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.
Elliott, Terry
2011-01-01
Stochastic models of synaptic plasticity propose that single synapses perform a directed random walk of fixed step sizes in synaptic strength, thereby embracing the view that the mechanisms of synaptic plasticity constitute a stochastic dynamical system. However, fluctuations in synaptic strength present a formidable challenge to such an approach. We have previously proposed that single synapses must interpose an integration and filtering mechanism between the induction of synaptic plasticity and the expression of synaptic plasticity in order to control fluctuations. We analyze a class of three such mechanisms in the presence of possibly non-Markovian plasticity induction processes, deriving expressions for the mean expression time in these models. One of these filtering mechanisms constitutes a discrete low-pass filter that could be implemented on a small collection of molecules at single synapses, such as CaMKII, and we analyze this discrete filter in some detail. After considering Markov induction processes, we examine our own stochastic model of spike-timing-dependent plasticity, for which the probability density functions of the induction of plasticity steps have previously been derived. We determine the dependence of the mean time to express a plasticity step on pre- and postsynaptic firing rates in this model, and we also consider, numerically, the long-term stability against fluctuations of patterns of neuronal connectivity that typically emerge during neuronal development.
BLASKIEWICZ,M.BRENNAN,J.M.CAMERON,P.WEI,J.
2003-05-12
Emittance growth due to Intra-Beam Scattering significantly reduces the heavy ion luminosity lifetime in RHIC. Stochastic cooling of the stored beam could improve things considerably by counteracting IBS and preventing particles from escaping the rf bucket [1]. High frequency bunched-beam stochastic cooling is especially challenging but observations of Schottky signals in the 4-8 GHz band indicate that conditions are favorable in RHIC [2]. We report here on measurements of the longitudinal beam transfer function carried out with a pickup kicker pair on loan from FNAL TEVATRON. Results imply that for ions a coasting beam description is applicable and we outline some general features of a viable momentum cooling system for RHIC.
NASA Astrophysics Data System (ADS)
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Fokker-Planck approach to stochastic delay differential equations
NASA Astrophysics Data System (ADS)
Guillouzic, Steve
2001-10-01
Models written in terms of stochastic delay differential equations (SDDE's) have recently appeared in a number of fields, such as physiology, optics, and climatology. Unfortunately, the development of a Fokker-Planck approach for these equations is being hampered by their non-Markovian nature. In this thesis, an exact Fokker- Planck equation (FPE) is formulated for univariate SDDE's involving Gaussian white noise. Although this FPE is not self-sufficient, it is found to be helpful in at least two different contexts: with a short delay approximation and under an appropriate separation of time scales. In the short delay approximation, a Taylor expansion is applied to an SDDE with nondelayed diffusion and yields a nondelayed stochastic differential equation. The aforementioned FPE then allows the derivation of an alternate and complementary approximation of the original SDDE. This method is illustrated with linear and logistic SDDE's. Under the separation of time scales assumption, the FPE of a bistable system is reduced to a form that is uniquely determined by the steady-state probability density when the diffusion term of the SDDE is nondelayed. In the context of an overdamped particle with delayed coupling to a symmetrical and stochastically driven potential, the resulting FPE is used with standard techniques to express the transition rate between wells in terms of the noise amplitude and of the steady-state probability density. The same is also accomplished for the mean first passage time from one point to another. This whole approach is then applied to the case of a quartic potential, for which all realisations eventually stabilise on an oscillatory trajectory with an ever increasing amplitude. Although this latter phenomenon prevents the existence of a steady-state limit, a pseudo- steady-state probability density can be defined and used instead of the non-existent steady-state one when the transition rate to these unbounded oscillatory trajectories is
Rosinberg, M L; Munakata, T; Tarjus, G
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
Stochastic excitation of stellar oscillations
NASA Astrophysics Data System (ADS)
Samadi, Reza
2001-05-01
Since more than about thirty years, solar oscillations are thought to be excited stochastically by the turbulent motions in the solar convective zone. It is currently believed that oscillations of stars lower than 2 solar masses - which possess an upper convective zone - are excited stochastically by turbulent convection in their outer layers. Providing that accurate measurements of the oscillation amplitudes and damping rates are available it is possible to evaluate the power injected into the modes and thus - by comparison with the observations - to constrain current theories. A recent theoretical work (Samadi & Goupil, 2001; Samadi et al., 2001) supplements and reinforces the theory of stochastic excitation of star vibrations. This process was generalized to a global description of the turbulent state of their convective zone. The comparison between observation and theory, thus generalized, will allow to better know the turbulent spectrum of stars, and this in particular thanks to the COROT mission.
NASA Astrophysics Data System (ADS)
Ross, D. K.; Moreau, William
1995-08-01
We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics ( sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h µυ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(ω), must be proportional to 1/ω 2. The proportionality constant is determined by the Planck condition that the energy density consist ofħω/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh(ω) =√16πc 2Lp/ω2. As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R iojo(Oτ-δτ/2)R kolo(O,τ+δτ/2)) of the measureable geodesic deviation tensor field,R iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order inaδτ/c provided that the temperature and acceleration satisfy the relationkT=ħa/2πc.
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
Non-Markovian State-Dependent Networks in Critical Loading
2015-02-04
information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. Colorado State University - Ft ...integers. We use D([0,∞), IR ) to represent the Skorohod space of right continuous IR -valued functions with left hand limits which is endowed with the...Precisely, the model is defined as follows. Let λni and μ n i , where i ∈ IK , be Borel functions mapping IRK+ to IR +, with λ n i (x) = 0 if i ∈ J
Stabilizing strongly correlated photon fluids with non-Markovian reservoirs
NASA Astrophysics Data System (ADS)
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.
Relations between entanglement and purity in non-Markovian dynamics
NASA Astrophysics Data System (ADS)
González-Gutiérrez, Carlos A.; Román-Ancheyta, Ricardo; Espitia, Diego; Lo Franco, Rosario
2016-09-01
Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence-purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
Płoszajczak, M.; Srokowski, T.
1997-05-01
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
Pirozzi, Enrica
2017-09-01
High variability in the neuronal response to stimulations and the adaptation phenomenon cannot be explained by the standard stochastic leaky integrate-and-fire model. The main reason is that the uncorrelated inputs involved in the model are not realistic. There exists some form of dependency between the inputs, and it can be interpreted as memory effects. In order to include these physiological features in the standard model, we reconsider it with time-dependent coefficients and correlated inputs. Due to its hard mathematical tractability, we perform simulations of it for a wide investigation of its output. A Gauss-Markov process is constructed for approximating its non-Markovian dynamics. The first passage time probability density of such a process can be numerically evaluated, and it can be used to fit the histograms of simulated firing times. Some estimates of the moments of firing times are also provided. The effect of the correlation time of the inputs on firing densities and on firing rates is shown. An exponential probability density of the first firing time is estimated for low values of input current and high values of correlation time. For comparison, a simulation-based investigation is also carried out for a fractional stochastic model that allows to preserve the memory of the time evolution of the neuronal membrane potential. In this case, the memory parameter that affects the firing activity is the fractional derivative order. In both models an adaptation level of spike frequency is attained, even if along different modalities. Comparisons and discussion of the obtained results are provided.
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, Murugappan
We study the translocation of a flexible polymer in a confined geometry subjected to a time-periodic external drive to explore stochastic resonance. We describe the equilibrium translocation process in terms of a Fokker-Planck description and use a discrete two-state model to describe the effect of the external driving force on the translocation dynamics. We observe that no stochastic resonance is possible if the associated free-energy barrier is purely entropic in nature. The polymer chain experiences a stochastic resonance effect only in presence of an energy threshold in terms of polymer-pore interaction. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic dynamics of cholera epidemics
NASA Astrophysics Data System (ADS)
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Stochastic dynamics of cholera epidemics.
Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea
2010-05-01
We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.
Analysis of stochastically forced quasi-periodic attractors
Ryashko, Lev
2015-11-30
A problem of the analysis of stochastically forced quasi-periodic auto-oscillations of nonlinear dynamic systems is considered. A stationary distribution of random trajectories in the neighborhood of the corresponding deterministic attractor (torus) is studied. A parametric description of quadratic approximation of the quasipotential based on the stochastic sensitivity functions (SSF) technique is given. Using this technique, we analyse a dispersion of stochastic flows near the torus. For the case of two-torus in three-dimensional space, the stochastic sensitivity function is constructed.
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Stochastic Physicochemical Dynamics
NASA Astrophysics Data System (ADS)
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Method to describe stochastic dynamics using an optimal coordinate.
Krivov, Sergei V
2013-12-01
A general method to describe the stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems: the determination of an optimal coordinate for the description of stochastic dynamics; the reconstruction of time from an ensemble of stochastic trajectories; and the decomposition of stationary stochastic dynamics into eigenmodes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated by a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multivalued function. An optimal coordinate for a random walk on a line corresponds to the conventional eigenvector of the one-dimensional Dirac equation. The equation for the optimal coordinate in a slowly varying potential reduces to the Hamilton-Jacobi equation for the action function.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
Stochastic symmetries of Wick type stochastic ordinary differential equations
NASA Astrophysics Data System (ADS)
Ünal, Gazanfer
2015-04-01
We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space (S)-1N. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in (S)-1N are obtained. A stochastic version of canonical variables is also introduced.
Stochastic thermodynamics of information processing
NASA Astrophysics Data System (ADS)
Cardoso Barato, Andre
2015-03-01
We consider two recent advancements on theoretical aspects of thermodynamics of information processing. First we show that the theory of stochastic thermodynamics can be generalized to include information reservoirs. These reservoirs can be seen as a sequence of bits which has its Shannon entropy changed due to the interaction with the system. Second we discuss bipartite systems, which provide a convenient description of Maxwell's demon. Analyzing a special class of bipartite systems we show that they can be used to study cellular information processing, allowing for the definition of an entropic rate that quantifies how much a cell learns about a fluctuating external environment and that is bounded by the thermodynamic entropy production.
Interacting Stochastic Processes: From Viciousness to Caging to Force Chains
NASA Astrophysics Data System (ADS)
Xu, Shiliyang
This thesis documents a quest to develop and study several novel interacting stochastic processes. As for the first example, we generalize a system of vicious random walkers in which the only interaction between any two random walkers is that when they intersect, both walkers are annihilated. We define a system of N vicious accelerating walkers with each walker undergoing random acceleration and compute the survival probability distribution for this system. We also define and study a system of N vicious Levy flights in which any two Levy flights crossing one another annihilate each other. The average mean-squared displacement of a Levy flight is not proportional to time, but scales with what is known as the Levy index divided by two. In both cases, vicious accelerating walkers and vicious Levy flights, we are motivated by ultimately generalizing our understanding of Gaussian random matrices via non-Markovian and non-Gaussian extensions respectively. Moreover, inspired by recent experiments on periodically sheared colloids at low densities, we define and investigate several new contact processes, or interacting stochastic processes, with conserved particle number and three-or-more-body interactions. We do so to characterize the periodically sheared colloidal system at higher densities. We find two new dynamical phase transitions between an active phase, where some fraction of the colloids are always being displaced from their position at the beginning and end of each shear cycle, and an inactive phase in which all colloids return to their initial positions at the end of each shear cycle. One of the transitions is discontinuous, while the second, which is due to a caging, or crowding, effect at high densities, appears to be continuous and in a new universality from what is known as conserved directed percolation. The latter transition may have implications for the onset of glassiness in dense, particulate systems. In addition, this thesis also includes analysis of
Turbulence, Spontaneous Stochasticity and Climate
NASA Astrophysics Data System (ADS)
Eyink, Gregory
Turbulence is well-recognized as important in the physics of climate. Turbulent mixing plays a crucial role in the global ocean circulation. Turbulence also provides a natural source of variability, which bedevils our ability to predict climate. I shall review here a recently discovered turbulence phenomenon, called ``spontaneous stochasticity'', which makes classical dynamical systems as intrinsically random as quantum mechanics. Turbulent dissipation and mixing of scalars (passive or active) is now understood to require Lagrangian spontaneous stochasticity, which can be expressed by an exact ``fluctuation-dissipation relation'' for scalar turbulence (joint work with Theo Drivas). Path-integral methods such as developed for quantum mechanics become necessary to the description. There can also be Eulerian spontaneous stochasticity of the flow fields themselves, which is intimately related to the work of Kraichnan and Leith on unpredictability of turbulent flows. This leads to problems similar to those encountered in quantum field theory. To quantify uncertainty in forecasts (or hindcasts), we can borrow from quantum field-theory the concept of ``effective actions'', which characterize climate averages by a variational principle and variances by functional derivatives. I discuss some work with Tom Haine (JHU) and Santha Akella (NASA-Goddard) to make this a practical predictive tool. More ambitious application of the effective action is possible using Rayleigh-Ritz schemes.
Lenormand, Thomas; Roze, Denis; Rousset, François
2009-03-01
The debate over the role of stochasticity is central in evolutionary biology, often summarised by whether or not evolution is predictable or repeatable. Here we distinguish three types of stochasticity: stochasticity of mutation and variation, of individual life histories and of environmental change. We then explain when stochasticity matters in evolution, distinguishing four broad situations: stochasticity contributes to maladaptation or limits adaptation; it drives evolution on flat fitness landscapes (evolutionary freedom); it might promote jumps from one fitness peak to another (evolutionary revolutions); and it might shape the selection pressures themselves. We show that stochasticity, by directly steering evolution, has become an essential ingredient of evolutionary theory beyond the classical Wright-Fisher or neutralist-selectionist debates.
Stochastic longshore current dynamics
NASA Astrophysics Data System (ADS)
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
The Quadrature Master Equations
NASA Astrophysics Data System (ADS)
Hassan, N. J.; Pourdarvish, A.; Sadeghi, J.; Olaomi, J. O.
2017-04-01
In this paper, we derive the non-Markovian stochastic equation of motion (SEM) and master equations (MEs) for the open quantum system by using the non-Markovian stochastic Schrödinger equations (SSEs) for the quadrature unraveling in linear and nonlinear cases. The SSEs for quadrature unraveling arise as a special case of a quantum system. Also we derive the Markovian SEM and ME by using linear and nonlinear Itô SSEs for the measurement probabilities. In linear non-Markovian case, we calculate the convolutionless linear quadrature non-Markovian SEM and ME. We take advantage from example and show that corresponding theory.
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Research in Stochastic Processes
1988-10-10
26 L. Gorostiza ................................................. 25 G. Hardy...Technical Report No. 219, Dec. 1987. Sequential Anat., 7. 1988, 111-126 25 DONALD DAWSON and LUIS G. GOROSTIZA The work of Professors Dawson and Gorostiza ... Gorostiza , Generalized solutions of a class of nuclear space valued stochastic evolution equations. University of North Carolina Center for Stochastic
Stochastic Convection Parameterizations
NASA Technical Reports Server (NTRS)
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Perspective: Stochastic algorithms for chemical kinetics
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-01-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. PMID:23656106
The appreciation of stochastic motion in particle accelerators
Symon, Keith; Sessler, Andrew
2003-08-03
A description is given of the analytic and numerical work, performed from July 1955 through August 1956, so as to develop, and then study, the process of making intense proton beams, suitable for colliding beams. It is shown how this investigation led, in a most natural way, to the realization that stochasticity can arise in a simple Hamiltonian system. Furthermore, the criterion for the onset of stochasticity was understood, and carefully studied, in two different situations. The first situation was the proposed (and subsequently used) ''stacking process'' for developing an intense beam, where stochasticity occurs as additional particles are added to the intense circulating beam. The second situation occurs when one seeks to develop ''stochastic accelerators'' in which particles are accelerated (continuously) by a collection of radio frequency systems. It was in the last connection that the well-known criterion for stochasticity, resonance overlap, was obtained.
Stochastic mapping of the Michaelis-Menten mechanism.
Dóka, Éva; Lente, Gábor
2012-02-07
The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.
Plasma Equilibria With Stochastic Magnetic Fields
NASA Astrophysics Data System (ADS)
Krommes, J. A.; Reiman, A. H.
2009-05-01
Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.
Stochastic Pseudo-Boolean Optimization
2011-07-31
analysis of two-stage stochastic minimum s-t cut problems; (iv) exact solution algorithm for a class of stochastic bilevel knapsack problems; (v) exact...57 5 Bilevel Knapsack Problems with Stochastic Right-Hand Sides 58 6 Two-Stage Stochastic Assignment Problems 59 6.1 Introduction...programming formulations and related computational complexity issues. • Section 5 considers a specific stochastic extension of the bilevel knapsack
Spring, William Joseph
2009-04-13
We consider quantum analogues of n-parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].
Research in Stochastic Processes.
1985-09-01
appear. G. Kallianpur, Finitely additive approach to nonlinear filtering, Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to...Nov. 85, in Proc. Bernoulli Soc. Conf. on Stochastic Processes, T. Hida , ed., Springer, to appear. i. Preparation T. Hsing, Extreme value theory for...1507 Carroll, R.J., Spiegelman, C.H., Lan, K.K.G., Bailey , K.T. and Abbott, R.D., Errors in-variables for binary regression models, Aug.82. 1508
Eliminating inertia in a stochastic model of a micro-swimmer with constant speed
NASA Astrophysics Data System (ADS)
Milster, S.; Nötel, J.; Sokolov, I. M.; Schimansky-Geier, L.
2017-06-01
We are concerned with the dynamical description of the motion of a stochastic micro-swimmer with constant speed and fluctuating orientation in the long time limit by adiabatic elimination of the orientational variable. Starting with the corresponding full set of Langevin equations, we eliminate the memory in the stochastic orientation and obtain a stochastic equation for the position alone in the overdamped limit. An equivalent procedure based on the Fokker-Planck equation is presented as well.
Agent based reasoning for the non-linear stochastic models of long-range memory
NASA Astrophysics Data System (ADS)
Kononovicius, A.; Gontis, V.
2012-02-01
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.
Stochastic Simulation Tool for Aerospace Structural Analysis
NASA Technical Reports Server (NTRS)
Knight, Norman F.; Moore, David F.
2006-01-01
Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.
Stochastic properties of the plant circadian clock.
Guerriero, Maria Luisa; Pokhilko, Alexandra; Fernández, Aurora Piñas; Halliday, Karen J; Millar, Andrew J; Hillston, Jane
2012-04-07
Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model. First, the introduction of stochasticity in the model allowed us to estimate the unknown size of the system. Moreover, stochasticity improved the description of the available experimental data in several light conditions: noise-induced fluctuations yield a faster entrainment of the plant clock under certain photoperiods and are able to explain the experimentally observed dampening of the oscillations in plants under constant light conditions. The model predicts that the desynchronization between noisy oscillations in single cells contributes to the observed damped oscillations at the level of the cell population. Analysis of the phase, period and amplitude distributions under various light conditions demonstrated robust entrainment of the plant clock to light/dark cycles which closely matched the available experimental data.
Heterogeneous ice nucleation: bridging stochastic and singular freezing behavior
NASA Astrophysics Data System (ADS)
Niedermeier, D.; Shaw, R. A.; Hartmann, S.; Wex, H.; Clauss, T.; Voigtländer, J.; Stratmann, F.
2011-01-01
Heterogeneous ice nucleation, a primary pathway for ice formation in the atmosphere, has been described alternately as being stochastic, in direct analogy with homogeneous nucleation, or singular, with ice nuclei initiating freezing at deterministic temperatures. We present an idealized model that bridges these stochastic and singular descriptions of heterogeneous ice nucleation. This "soccer ball" model treats statistically similar particles as being covered with surface sites (patches of finite area) characterized by different nucleation barriers, but with each surface site following the stochastic nature of ice embryo formation. The model provides a phenomenological explanation for seemingly contradictory experimental results obtained in our research groups. We suggest that ice nucleation is fundamentally a stochastic process but that for realistic atmospheric particle populations this process can be masked by the heterogeneity of surface properties. Full evaluation of the model will require experiments with well characterized ice nucleating particles and the ability to vary both temperature and waiting time for freezing.
Losick, Richard; Desplan, Claude
2008-01-01
Summary Fundamental to living cells is the capacity to differentiate into subtypes with specialized attributes. Understanding the way cells acquire their fates is a major challenge in developmental biology. How cells adopt a particular fate is usually thought of as being deterministic, and in the large majority of cases it is. That is, cells acquire their fate by virtue of their lineage or their proximity to an inductive signal from another cell. In some cases, however, and in organisms ranging from bacteria to humans, cells choose one or another pathway of differentiation stochastically without apparent regard to environment or history. Stochasticity has important mechanistic requirements as we discuss. We will also speculate on why stochasticity is advantageous, and even critical in some circumstances, to the individual, the colony, or the species. PMID:18388284
Stochastic cooling at Fermilab
Marriner, J.
1986-08-01
The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Stochastic demographic forecasting.
Lee, R D
1992-11-01
"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary.... Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented."
Stochastic modeling of rainfall
Guttorp, P.
1996-12-31
We review several approaches in the literature for stochastic modeling of rainfall, and discuss some of their advantages and disadvantages. While stochastic precipitation models have been around at least since the 1850`s, the last two decades have seen an increased development of models based (more or less) on the physical processes involved in precipitation. There are interesting questions of scale and measurement that pertain to these modeling efforts. Recent modeling efforts aim at including meteorological variables, and may be useful for regional down-scaling of general circulation models.
Markov stochasticity coordinates
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
NASA Astrophysics Data System (ADS)
Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong
The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.
A simple stochastic weather generator for ecological modeling
A.G. Birt; M.R. Valdez-Vivas; R.M. Feldman; C.W. Lafon; D. Cairns; R.N. Coulson; M. Tchakerian; W. Xi; Jim Guldin
2010-01-01
Stochastic weather generators are useful tools for exploring the relationship between organisms and their environment. This paper describes a simple weather generator that can be used in ecological modeling projects. We provide a detailed description of methodology, and links to full C++ source code (http://weathergen.sourceforge.net) required to implement or modify...
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
Analysis of bilinear stochastic systems
NASA Technical Reports Server (NTRS)
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications.
Potapov, Alex; Rajakaruna, Harshana
2013-11-21
We consider the problem of estimating the time needed for species colonization. The analysis is based upon the known population dynamic models by Dennis with minor modification to the Allee effect description, which allows us to obtain an analytical expression for the colonization time. For the stochastic counterpart of the models in diffusion approximation, we (1) propose the description of immigration stochasticity, (2) provide the estimates of time required for the population to overcome strong demographic Allee effect, and (3) consider the numerical results for mean colonization time and its uncertainty. Strong Allee effect strictly disallows populations at small immigration rates to colonize new habitats, unless the stochasticity in immigration, environment, or demography is present, or incorporated into the model. Immigration stochasticity, complementing with environmental and demographic stochasticity, enables the populations to overcome the Allee threshold even at low values of propagule pressure.
Research in Stochastic Processes.
1982-10-31
locally convex spaces is studied. We obtain a general form of convergent p-cylindrical martingales in barrelled spaces. Using the locally convex space...topology of certain Orlicz and Lorentz spaces. References 1. Z. Suchanecki and A. Weron, Decomposability of p-cylindrical martingales, Center for Stochastic
Stochastic Local Distinguishability
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Somshubhro; Roy, Anirban; Walgate, Jonathan
2007-03-01
We pose the question, ``when is globally available information is also locally available?'', formally as the problem of local state discrimination, and show that the deep qualitative link between local distinguishability and entanglement lies at the level of stochastic rather than deterministic local protocols. We restrict our attention to sets of mutually orthogonal pure quantum states. We define a set of states |ψi> as beingstochastically locally distinguishable if and only if there is a LOCC protocol whereby the parties can conclusively identify a member of the set with some nonzero probability. If a set is stochastically locally distinguishable, then the complete global information is potentially locally available. If not, the physical information encoded by the system can never be completely locally exposed. Our results are proved true for all orthogonal quantum states regardless of their dimensionality or multipartiality. First, we prove that entanglement is a necessary property of any system whose total global information can never be locally accessed. Second, entangled states that form part of an orthogonal basis can never be locally singled out. Completely entangled bases are, always stochastically locally indistinguishable. Third, we prove that any set of three orthogonal states, is stochastically locally distinguishable.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Research in Stochastic Processes
1988-08-31
25 L. de Haan ................................................... 26 L. Gorostiza ...DAISON and LUIS C. COROSTIZA The work of Professors Dawson and Gorostiza is concerned with obtaining a Langevin equation for the fluctuation limit of a...its uniqueness established. Reference 1. D.A. Dawson and L.G. Gorostiza , Generalized solutions of a class of nuclear space valued stochastic
Stochastic decentralized systems
NASA Astrophysics Data System (ADS)
Barfoot, Timothy David
Fundamental aspects of decentralized systems are considered from a control perspective. The stochastic framework afforded by Markov systems is presented as a formal setting in which to study decentralized systems. A stochastic algebra is introduced which allows Markov systems to be considered in matrix format but also strikes an important connection to the classic linear system originally studied by Kalman [1960]. The process of decentralization is shown to impose constraints on observability and controllability of a system. However, it is argued that communicating decentralized controllers can implement any control law possible with a centralized controller. Communication is shown to serve a dual role, both enabling sensor data to be shared and actions to be coordinated. The viabilities of these two types of communication are tested on a real network of mobile robots where they are found to be successful at a variety of tasks. Action coordination is reframed as a decentralized decision making process whereupon stochastic cellular automata (SCA) are introduced as a model. Through studies of SCA it is found that coordination in a group of arbitrarily and sparsely connected agents is possible using simple rules. The resulting stochastic mechanism may be immediately used as a practical decentralized decision making tool (it is tested on a group of mobile robots) but, it furthermore provides insight into the general features of self-organizing systems.
Controlled Stochastic Dynamical Systems
2007-04-18
the existence of value functions of two-player zero-sum stochastic differential games Indiana Univ. Math. Journal, 38 (1989), pp 293-314. [6] George ...control problems, Adv. Appl. Prob., 15, (1983) pp 225-254. [10] Karatzas, I. Ocone, D., Wang, H. and Zervos , M., Finite fuel singular control with
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Stochastic computing with biomolecular automata.
Adar, Rivka; Benenson, Yaakov; Linshiz, Gregory; Rosner, Amit; Tishby, Naftali; Shapiro, Ehud
2004-07-06
Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure.
ON NONSTATIONARY STOCHASTIC MODELS FOR EARTHQUAKES.
Safak, Erdal; Boore, David M.
1986-01-01
A seismological stochastic model for earthquake ground-motion description is presented. Seismological models are based on the physical properties of the source and the medium and have significant advantages over the widely used empirical models. The model discussed here provides a convenient form for estimating structural response by using random vibration theory. A commonly used random process for ground acceleration, filtered white-noise multiplied by an envelope function, introduces some errors in response calculations for structures whose periods are longer than the faulting duration. An alternate random process, filtered shot-noise process, eliminates these errors.
Stochastic Time-Dependent Current-Density Functional Theory
NASA Astrophysics Data System (ADS)
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Stochastic analysis of a miRNA-protein toggle switch.
Giampieri, E; Remondini, D; de Oliveira, L; Castellani, G; Lió, P
2011-10-01
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous time Markov chain (CTMC). In this paper we consider the stochastic properties of a toggle switch, involving a protein compound (E2Fs and Myc) and a miRNA cluster (miR-17-92), known to control the eukaryotic cell cycle and possibly involved in oncogenesis, recently proposed in the literature within a deterministic framework. Due to the inherent stochasticity of biochemical processes and the small number of molecules involved, the stochastic approach should be more correct in describing the real system: we study the agreement between the two approaches by exploring the system parameter space. We address the problem by proposing a simplified version of the model that allows analytical treatment, and by performing numerical simulations for the full model. We observed optimal agreement between the stochastic and the deterministic description of the circuit in a large range of parameters, but some substantial differences arise in at least two cases: (1) when the deterministic system is in the proximity of a transition from a monostable to a bistable configuration, and (2) when bistability (in the deterministic system) is "masked" in the stochastic system by the distribution tails. The approach provides interesting estimates of the optimal number of molecules involved in the toggle switch. Our discussion of the points of strengths, potentiality and weakness of the chemical master equation in systems biology and the differences with respect to deterministic modeling are leveraged in order to provide useful advice for both the bioinformatician and the theoretical scientist.
Conservative Diffusions: a Constructive Approach to Nelson's Stochastic Mechanics.
NASA Astrophysics Data System (ADS)
Carlen, Eric Anders
In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions; this thesis is a study of that description. We emphasize that we are concerned here with the possibility of describing, as opposed to explaining, quantum phenomena in terms of diffusions. In this direction, the following questions arise: "Do the diffusions of stochastic mechanics--which are formally given by stochastic differential equations with extremely singular coefficients--really exist?" Given that they exist, one can ask, "Do these diffusions have physically reasonable sample path behavior, and can we use information about sample paths to study the behavior of physical systems?" These are the questions we treat in this thesis. In Chapter I we review stochastic mechanics and diffusion theory, using the Guerra-Morato variational principle to establish the connection with the Schroedinger equation. This chapter is largely expository; however, there are some novel features and proofs. In Chapter II we settle the first of the questions raised above. Using PDE methods, we construct the diffusions of stochastic mechanics. Our result is sufficiently general to be of independent mathematical interest. In Chapter III we treat potential scattering in stochastic mechanics and discuss direct probabilistic methods of studying quantum scattering problems. Our results provide a solid "Yes" in answer to the second question raised above.
Stochastic field modeling of cavitating flows in OpenFOAM
NASA Astrophysics Data System (ADS)
Ranft, Michael; Class, Andreas G.
2013-11-01
In analysis is presented for a fluidic diode with low/high pressure drop in forward/reverse flow direction. Accurate description of cavitation is needed due to the dominant effect of vapor bubbles on sound speed. The stochastic field method developed in represents the statistics of growing cavitation bubbles by a set of stochastic fields of vapor fraction which evolve according to the Rayleigh-Plesset equation and local instantaneous LES flow conditions. Cavitation may originate from nucleation sites in the core of turbulent vortices. In this work a RANS model is used instead of LES. Local turbulent pressure fluctuations are recovered based on kinetic energy k of turbulence and its Dissipation ɛ. In the Rayleigh-Plesset equation these fluctuations are represented by a Wiener process which is superimposed on the mean pressure. Usually a set of stochastic fields is introduced for each stochastic variable. Here two independent Wiener processes, both acting on the vapor-fraction stochastic fields, drive the evolution of vapor bubble growth, so that a single set of stochastic fields can be maintained. The proposed methodology is implemented in OpenFOAM and applied to verification cases including the fluidic diode. Funded by ANPS.
Stochastic hyperfine interactions modeling library
NASA Astrophysics Data System (ADS)
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
Extraction of stochastic dynamics from time series.
Petelczyc, M; Żebrowski, J J; Gac, J M
2012-07-01
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin equation. The deterministic f and stochastic g components of the stochastic equation are directly extracted from the measurement data with the assumption that the noise has finite moments and has a zero mean and a unit variance. No other information about the noise distribution is needed. This is contrary to the usual Langevin description, in which the additional assumption that the noise is Gaussian (δ-correlated) distributed as necessary. We test the method using one dimensional deterministic systems (the tent and logistic maps) with Gaussian and with Gumbel noise. In addition, results for human heart rate variability are presented as an example of the application of our method to real data. The differences between cardiological cases can be observed in the properties of the deterministic part f and of the reconstructed noise distribution.
A stochastic approach to model validation
NASA Astrophysics Data System (ADS)
Luis, Steven J.; McLaughlin, Dennis
This paper describes a stochastic approach for assessing the validity of environmental models. In order to illustrate basic concepts we focus on the problem of modeling moisture movement through an unsaturated porous medium. We assume that the modeling objective is to predict the mean distribution of moisture content over time and space. The mean moisture content describes the large-scale flow behavior of most interest in many practical applications. The model validation process attempts to determine whether the model's predictions are acceptably close to the mean. This can be accomplished by comparing small-scale measurements of moisture content to the model's predictions. Differences between these two quantities can be attributed to three distinct 'error sources': (1) measurement error, (2) spatial heterogeneity, and (3) model error. If we adopt appropriate stochastic descriptions for the first two sources of error we can view model validation as a hypothesis testing problem where the null hypothesis states that model error is negligible. We illustrate this concept by comparing the predictions of a simple two-dimensional deterministic model to measurements collected during a field experiment carried out near Las Cruces, New Mexico. Preliminary results from this field test indicate that a stochastic approach to validation can identify model deficiencies and provide objective standards for model performance.
Extraction of stochastic dynamics from time series
NASA Astrophysics Data System (ADS)
Petelczyc, M.; Żebrowski, J. J.; Gac, J. M.
2012-07-01
We present a method for the reconstruction of the dynamics of processes with discrete time. The time series from such a system is described by a stochastic recurrence equation, the continuous form of which is known as the Langevin equation. The deterministic f and stochastic g components of the stochastic equation are directly extracted from the measurement data with the assumption that the noise has finite moments and has a zero mean and a unit variance. No other information about the noise distribution is needed. This is contrary to the usual Langevin description, in which the additional assumption that the noise is Gaussian (δ-correlated) distributed as necessary. We test the method using one dimensional deterministic systems (the tent and logistic maps) with Gaussian and with Gumbel noise. In addition, results for human heart rate variability are presented as an example of the application of our method to real data. The differences between cardiological cases can be observed in the properties of the deterministic part f and of the reconstructed noise distribution.
Stochastic Flow Modeling for Resin Transfer Moulding
NASA Astrophysics Data System (ADS)
Desplentere, Frederik; Verpoest, Ignaas; Lomov, Stepan
2009-07-01
Liquid moulding processes suffer from inherently present scatter in the textile reinforcement properties. This variability can lead to unwanted filling patterns within the mould resulting in bad parts. If thermoplastic resins are used with the in-situ polymerisation technique, an additional difficulty appears. The time window to inject the material is small if industrial processing parameters are used (<5 minutes). To model the stochastic nature of RTM, Darcy's description of the mould filling process has been used with the permeability distribution of the preform given as a random field. The random field of the permeability is constructed as a correlated field with an exponential correlation function. Optical microscopy and X-ray micro-CT have been used to study the stochastic parameters of the geometry for 2D and 3D woven textile preforms. The parameters describing the random permeability field (average, standard deviation and correlation length) are identified based on the stochastic parameters of the geometry for the preforms, analytical estimations and CFD modelling of the permeability. In order to implement the random field for the permeability and the variability for the resin viscosity, an add-on to the mould filling simulation software PAM-RTM™ has been developed. This analysis has been validated on case studies.
Chromatography as Lévy stochastic process.
Dondi, Francesco; Cavazzini, Alberto; Pasti, Luisa
2006-09-08
The Stochastic Theory of Chromatography has been revised in light of some of the most relevant Lévy's findings in Theory of Probability, including the so-called Lévy's distance, the characteristic function and the theory of infinitesimally divisible distributions. These concepts represent the key to exploit and understand, at a molecular basis, phenomena typical of chromatographic separations under linear conditions, such as peak tailing and splitting. In particular, Lévy's distance has been used to quantify the degree of convergence of real peaks towards an ideal Gaussian shape; the characteristic function properties, introduced by Lévy to deal with the problem of the addition of independent random variables, have been employed to solve a wide variety of chromatographic models (including adsorption on heterogeneous surfaces) and to interpret mobile phase dispersion from a probabilistic point of view. Finally, Lévy's studies concerning infinitesimally divisible distributions have allowed to introduce in the stochastic description of chromatography, effects associated to dispersion in mobile phase. It has been demonstrated that, according to Lévy's canonical representation of stochastic processes, the basis of chromatography is a mobile phase Poisson Process. Represented as a Lévy's process, the microscopic-probabilistic model of chromatography permits the establishment of a connection between single-molecule properties and their statistical fluctuations and shapes of real chromatographic peaks allowing, at the same time, for the constitution of a link between different branches of physical sciences.
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
Stochastic ice stream dynamics
Bertagni, Matteo Bernard; Ridolfi, Luca
2016-01-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution. PMID:27457960
Stochastic ice stream dynamics.
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-09
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic ice stream dynamics
NASA Astrophysics Data System (ADS)
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic contribution to the growth factor in the LCDM model
Ribeiro, A. L.B.; Andrade, A. P.A.; Letelier, P. S.
2009-01-01
We study the effect of noise on the evolution of the growth factor of density perturbations in the context of the LCDM model. Stochasticity is introduced as a Wiener process amplified by an intensity parameter alpha. By comparing the evolution of deterministic and stochastic cases for different values of alpha we estimate the intensity level necessary to make noise relevant for cosmological tests based on large-scale structure data. Our results indicate that the presence of random forces underlying the fluid description can lead to significant deviations from the nonstochastic solution at late times for alpha>0.001.
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Stochastic Thermodynamics of Learning
NASA Astrophysics Data System (ADS)
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Dorogovtsev, Andrei A
2010-06-29
For sets in a Hilbert space the concept of quadratic entropy is introduced. It is shown that this entropy is finite for the range of a stochastic flow of Brownian particles on R. This implies, in particular, the fact that the total time of the free travel in the Arratia flow of all particles that started from a bounded interval is finite. Bibliography: 10 titles.
Methodology for Stochastic Modeling.
1985-01-01
AD-AISS 851 METHODOLOGY FOR STOCHASTIC MODELING(U) ARMY MATERIEL 11 SYSTEMS ANALYSIS ACTIYITY ABERDEEN PROVING GROUND MD H E COHEN JAN 95 RNSAA-TR-41...FORM T REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT’$ CATALOG NUMBER 4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED Methodology for...autoregression models, moving average models, ARMA, adaptive modeling, covariance methods , singular value decom- position, order determination rational
NASA Astrophysics Data System (ADS)
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Simulations of stochastic biological phenomena.
Hayot, Fernand
2011-09-20
This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture that introduces stochastic modeling of biological systems. The first lecture uses biological examples to present the concept of cell-to-cell variability and makes the connection between the variability of single-cell measurements and concepts from statistical mechanics and probability theory. This section makes the point that for low copy number of a species, the usual differential equation formalism is no longer applicable and needs to be replaced by a probabilistic approach based on the so-called Master Equation. As an example, a simple model of gene transcription is discussed in detail, the different contributions to the relevant Master Equation are highlighted, and the equation itself is derived. The second lecture describes how, for more complex and biologically interesting applications, direct solution of the Master Equation becomes difficult. Gillespie's algorithm, which is used in most cases of biological interest, is then introduced as a practical alternative. The lecture delves into the crux of Gillespie's algorithm, which entails the drawing of two random numbers at each time step. It establishes the corresponding formalism, details the connection between chemical rate constants and Gillespie rates, and culminates in a description and explanation of a core MATLAB program for the transcriptional model considered in the first lecture. This core program, written for a single cell, is expanded by the students in the homework assignment to consider both transcription and translation.
Stochastic Quantization of Instantons
NASA Astrophysics Data System (ADS)
Grandati, Y.; Bérard, A.; Grangé, P.
1996-03-01
The method of Parisi and Wu to quantize classical fields is applied to instanton solutionsϕIof euclidian non-linear theory in one dimension. The solutionϕεof the corresponding Langevin equation is built through a singular perturbative expansion inε=ℏ1/2in the frame of the center of mass of the instanton, where the differenceϕε-ϕIcarries only fluctuations of the instanton form. The relevance of the method is shown for the stochasticK dVequation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, we obtain explicit expressions for the first two orders inεof the perturbed instanton and of its Green function. Specializing to the Sine-Gordon andϕ4models, the first anharmonic correction is obtained analytically. The calculation is carried to second order for theϕ4model, showing good convergence.
Analytic descriptions of stochastic bistable systems under force ramp
Friddle, Raymond W.
2016-05-13
Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. We show an accurate approximation to this problem by considering the system in the control parameter regime. Moreover, the results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.
STOCHASTIC DESCRIPTION OF SUBGRID POLLUTANT VARIABILITY IN CMAQ
This paper describes a tool for investigating and describing fine scale spatial variability in model concentration fields with the goal of improving the use of air quality models for driving exposure modeling to assess human risk to hazardous air pollutants or air toxics. Region...
STOCHASTIC DESCRIPTION OF SUBGRID POLLUTANT VARIABILITY IN CMAQ
This paper describes a tool for investigating and describing fine scale spatial variability in model concentration fields with the goal of improving the use of air quality models for driving exposure modeling to assess human risk to hazardous air pollutants or air toxics. Region...
Analytic descriptions of stochastic bistable systems under force ramp
Friddle, Raymond W.
2016-05-13
Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. We show an accurate approximation to this problem by considering the system in the control parameter regime. Moreover, the results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.
Brownian motion description of heat conduction by phonons.
Naqvi, K Razi; Waldenstrøm, S
2005-08-05
A non-Markovian partial differential equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Although a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front that results from the application of Cattaneo's equation. Even a simplified, analytically tractable version of the equation yields results close to those found by solving, through more elaborate means, the equation of phonon radiative transfer.
Probabilistic description of traffic flow
NASA Astrophysics Data System (ADS)
Mahnke, R.; Kaupužs, J.; Lubashevsky, I.
2005-03-01
A stochastic description of traffic flow, called probabilistic traffic flow theory, is developed. The general master equation is applied to relatively simple models to describe the formation and dissolution of traffic congestions. Our approach is mainly based on spatially homogeneous systems like periodically closed circular rings without on- and off-ramps. We consider a stochastic one-step process of growth or shrinkage of a car cluster (jam). As generalization we discuss the coexistence of several car clusters of different sizes. The basic problem is to find a physically motivated ansatz for the transition rates of the attachment and detachment of individual cars to a car cluster consistent with the empirical observations in real traffic. The emphasis is put on the analogy with first-order phase transitions and nucleation phenomena in physical systems like supersaturated vapour. The results are summarized in the flux-density relation, the so-called fundamental diagram of traffic flow, and compared with empirical data. Different regimes of traffic flow are discussed: free flow, congested mode as stop-and-go regime, and heavy viscous traffic. The traffic breakdown is studied based on the master equation as well as the Fokker-Planck approximation to calculate mean first passage times or escape rates. Generalizations are developed to allow for on-ramp effects. The calculated flux-density relation and characteristic breakdown times coincide with empirical data measured on highways. Finally, a brief summary of the stochastic cellular automata approach is given.
Hybrid approaches for multiple-species stochastic reaction–diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-15
Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.
Rendón-Macías, Mario Enrique; Villasís-Keever, Miguel Ángel; Miranda-Novales, María Guadalupe
2016-01-01
Descriptive statistics is the branch of statistics that gives recommendations on how to summarize clearly and simply research data in tables, figures, charts, or graphs. Before performing a descriptive analysis it is paramount to summarize its goal or goals, and to identify the measurement scales of the different variables recorded in the study. Tables or charts aim to provide timely information on the results of an investigation. The graphs show trends and can be histograms, pie charts, "box and whiskers" plots, line graphs, or scatter plots. Images serve as examples to reinforce concepts or facts. The choice of a chart, graph, or image must be based on the study objectives. Usually it is not recommended to use more than seven in an article, also depending on its length.
A retrodictive stochastic simulation algorithm
Vaughan, T.G. Drummond, P.D.; Drummond, A.J.
2010-05-20
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
ERIC Educational Resources Information Center
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Stochastic ontogenetic growth model
NASA Astrophysics Data System (ADS)
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Stochastic processes in cosmology
NASA Astrophysics Data System (ADS)
Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.
1987-08-01
The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.
Stochastic Coupled Cluster Theory
NASA Astrophysics Data System (ADS)
Thom, Alex J. W.
2010-12-01
We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.
Stochastic thermodynamics of resetting
NASA Astrophysics Data System (ADS)
Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo
2016-03-01
Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
NASA Astrophysics Data System (ADS)
Hairer, Martin
2006-03-01
We consider a class of parabolic stochastic PDEs driven by white noise in time, and we are interested in showing ergodicity for some cases where the noise is degenerate, i.e., acts only on part of the equation. In some cases where the standard Strong Feller / Irreducibility argument fails, one can nevertheless implement a coupling construction that ensures uniqueness of the invariant measure. We focus on the example of the complex Ginzburg-Landau equation driven by real space-time white noise.
Dana E. Veron
2012-04-09
This project had two primary goals: (1) development of stochastic radiative transfer as a parameterization that could be employed in an AGCM environment, and (2) exploration of the stochastic approach as a means for representing shortwave radiative transfer through mixed-phase layer clouds. To achieve these goals, climatology of cloud properties was developed at the ARM CART sites, an analysis of the performance of the stochastic approach was performed, a simple stochastic cloud-radiation parameterization for an AGCM was developed and tested, a statistical description of Arctic mixed phase clouds was developed and the appropriateness of stochastic approach for representing radiative transfer through mixed-phase clouds was assessed. Significant progress has been made in all of these areas and is detailed in the final report.
Veron, Dana E
2009-03-12
This project had two primary goals: 1) development of stochastic radiative transfer as a parameterization that could be employed in an AGCM environment, and 2) exploration of the stochastic approach as a means for representing shortwave radiative transfer through mixed-phase layer clouds. To achieve these goals, an analysis of the performance of the stochastic approach was performed, a simple stochastic cloud-radiation parameterization for an AGCM was developed and tested, a statistical description of Arctic mixed phase clouds was developed and the appropriateness of stochastic approach for representing radiative transfer through mixed-phase clouds was assessed. Significant progress has been made in all of these areas and is detailed below.
Horowitz, Jordan M.
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Horowitz, Jordan M
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Stochastic power flow modeling
Not Available
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less
Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan
2015-05-19
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.
Stochastic simulation of transport phenomena
Wedgewood, L.E.; Geurts, K.R.
1995-10-01
In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.
Stochastic and delayed stochastic models of gene expression and regulation.
Ribeiro, Andre S
2010-01-01
Gene expression and gene regulatory networks dynamics are stochastic. The noise in the temporal amounts of proteins and RNA molecules in cells arises from the stochasticity of transcription initiation and elongation (e.g., due to RNA polymerase pausing), translation, and post-transcriptional regulation mechanisms, such as reversible phosphorylation and splicing. This is further enhanced by the fact that most RNA molecules and proteins exist in cells in very small amounts. Recently, the time needed for transcription and translation to be completed once initiated were shown to affect the stochasticity in gene networks. This observation stressed the need of either introducing explicit delays in models of transcription and translation or to model processes such as elongation at the single nucleotide level. Here we review stochastic and delayed stochastic models of gene expression and gene regulatory networks. We first present stochastic non-delayed and delayed models of transcription, followed by models at the single nucleotide level. Next, we present models of gene regulatory networks, describe the dynamics of specific stochastic gene networks and available simulators to implement these models. Copyright 2009 Elsevier Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Olivares-Rivas, Wilmer; Colmenares, Pedro J.
2016-09-01
The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.
NASA Astrophysics Data System (ADS)
Ryashko, Lev
2015-11-01
A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.
Ryashko, Lev
2015-11-30
A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.
Stochastic Mean-Field Dynamics For Nuclear Collisions
Ayik, Sakir
2008-11-11
We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.
Fast approximate stochastic tractography.
Iglesias, Juan Eugenio; Thompson, Paul M; Liu, Cheng-Yi; Tu, Zhuowen
2012-01-01
Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore
NASA Astrophysics Data System (ADS)
Van Willigenburg, L. Gerard; De Koning, Willem L.
2013-02-01
Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others. Another, that is more general and concise, uses Kronecker products instead. This article relates the statistics of both descriptions and shows their advantages and disadvantages. As to the first description, an important result that comes out is the minimum number of matrices multiplied by scalar, independent, stochastic processes needed to represent a certain matrix valued white stochastic process, together with an associated minimal representation. As to the second description, an important result concerns the generation of all Kronecker products that represent relevant statistics. Both results facilitate the specification of statistics of systems with white stochastic parameters. The second part of this article further exploits these results to perform an U-D factorisation of an algorithm to compute optimal dynamic output feedback controllers (optimal compensators) for linear discrete-time systems with white stochastic parameters and quadratic sum criteria. U-D factorisation of this type of algorithm is new. By solving several numerical examples, the U-D factored algorithm is compared with a conventional algorithm.
Stochastization in gravitating systems
NASA Astrophysics Data System (ADS)
Ovod, D. V.; Ossipkov, L. P.
2013-10-01
We discuss the effective stochastization time τ_e for gravitating systems in terms of the Krylov and Gurzadyan-Savvidi paradigm. The truncated Holtsmark distribution for a random force proposed by Rastorguev and Sementsov implies {τ_e/τ_c ∝ N0.20}, where τ_c is the crossing time. We find in the case of the Petrovskaya distribution for a random force {τ_e/τ_c ∝ Nk}, where {k=0.27}-0.31, depending on the oblateness and rotation of the system, and {τ_e/τ_c ∝ N1/3/(ln N)1/2} when N≫ 1. The latter result agrees with those of Genkin (1969) and Gurzadyan & Kocharyan (2009) (k=1/3). Dedicated to Igor L'vovich Genkin (1931-2011)
Bunched beam stochastic cooling
Wei, Jie.
1992-01-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Bunched beam stochastic cooling
Wei, Jie
1992-09-01
The scaling laws for bunched-beam stochastic cooling has been derived in terms of the optimum cooling rate and the mixing condition. In the case that particles occupy the entire sinusoidal rf bucket, the optimum cooling rate of the bunched beam is shown to be similar to that predicted from the coasting-beam theory using a beam of the same average density and mixing factor. However, in the case that particles occupy only the center of the bucket, the optimum rate decrease in proportion to the ratio of the bunch area to the bucket area. The cooling efficiency can be significantly improved if the synchrotron side-band spectrum is effectively broadened, e.g. by the transverse tune spread or by using a double rf system.
Hybrid stochastic simplifications for multiscale gene networks
Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu
2009-01-01
Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach. PMID:19735554
Assessment of stochastic and deterministic models of 6304 quasar lightcurves from SDSS Stripe 82
NASA Astrophysics Data System (ADS)
Andrae, R.; Kim, D.-W.; Bailer-Jones, C. A. L.
2013-06-01
The optical lightcurves of many quasars show variations of tenths of a magnitude or more on timescales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of over 20 deterministic and stochastic models on 6304 quasi-steller object (QSO) lightcurves in SDSS Stripe 82. We include the damped random walk (or Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model, which recent studies have focused on. Further models we consider are single and double sinusoids, multiple OU processes, higher order continuous autoregressive processes, and composite models. We find that only 29 out of 6304 QSO lightcurves are described significantly better by a deterministic model than a stochastic one. The OU process is an adequate description of the vast majority of cases (6023). Indeed, the OU process is the best single model for 3462 lightcurves, with the composite OU process/sinusoid model being the best in 1706 cases. The latter model is the dominant one for brighter/bluer QSOs. Furthermore, a non-negligible fraction of QSO lightcurves show evidence that not only the mean is stochastic but the variance is stochastic, too. Our results confirm earlier work that QSO lightcurves can be described with a stochastic model, but place this on a firmer footing, and further show that the OU process is preferred over several other stochastic and deterministic models. Of course, there may well exist yet better (deterministic or stochastic) models, which have not been considered here.
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
Stochastic reinforcement benefits skill acquisition.
Dayan, Eran; Averbeck, Bruno B; Richmond, Barry J; Cohen, Leonardo G
2014-02-14
Learning complex skills is driven by reinforcement, which facilitates both online within-session gains and retention of the acquired skills. Yet, in ecologically relevant situations, skills are often acquired when mapping between actions and rewarding outcomes is unknown to the learning agent, resulting in reinforcement schedules of a stochastic nature. Here we trained subjects on a visuomotor learning task, comparing reinforcement schedules with higher, lower, or no stochasticity. Training under higher levels of stochastic reinforcement benefited skill acquisition, enhancing both online gains and long-term retention. These findings indicate that the enhancing effects of reinforcement on skill acquisition depend on reinforcement schedules.
Stochastic dynamics with a mesoscopic bath
NASA Astrophysics Data System (ADS)
Plyukhin, Alexander V.; Schofield, Jeremy
2001-10-01
We consider the effects of bath size on the nature of the dynamics and transport properties for two simple models in which the bath is composed of a collinear chain of harmonic oscillators. The first model consists of an untwisted rotating chain (elastic rotor) for which we obtain a non-Markovian equation analogous to the generalized Langevin equation for the rotational degrees of freedom. We demonstrate that the corresponding memory function oscillates with a frequency close to that of the lowest mode of the chain. The second model considered consists of a tagged oscillator in a finite harmonic chain. For this model, we find an additional harmonic force in the generalized Langevin equation for the terminal atom that does not appear in the equation of motion for the semi-infinite chain. It is demonstrated that the force constant for the additional harmonic force scales as 1/N, where N is the number of oscillators in the chain. Using an exact representation for the velocity correlation function, the transport properties of the model are discussed.
Stochastic thermodynamics of chemical reaction networks.
Schmiedl, Tim; Seifert, Udo
2007-01-28
For chemical reaction networks in a dilute solution described by a master equation, the authors define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work, and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations such as a generalized Jarzynski relation and a generalized Clausius inequality are discussed. The authors illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.
The stochastic search dynamics of interneuron migration.
Britto, Joanne M; Johnston, Leigh A; Tan, Seong-Seng
2009-08-05
Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment.
Recent Developments in Linear Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.
2006-01-01
A detailed analysis of stochastic electrodynamics (SED) as a foundation for quantum mechanics has shown that the reasons for its failure in the case of nonlinear forces are not to be ascribed to the founding principles of the theory but to the approximation methods introduced, particularly the use of the Fokker-Planck approximation and perturbation theory. To recover the intrinsic possibilities of SED a new, non perturbative approach has been developed, namely linear stochastic electrodynamics (LSED). We here present the basic principles on which LSED is constructed. The demand that the solutions of the SED problem comply with as few as three principles, each one of which is shown to have a clear physical meaning, leads in a natural way to the quantum mechanical description in its Heisenberg form. We briefly re-examine some of the most often discussed conceptual problems of quantum mechanics from the point of view offered by the new theory and show that it offers well defined and clear physical anwers to them, within a realist and causal perspective. To conclude we add brief comments on a couple of predictions of the theory, the test of which could eventually lead to its validation or refutation.
The Stochastic Search Dynamics of Interneuron Migration
Britto, Joanne M.; Johnston, Leigh A.; Tan, Seong-Seng
2009-01-01
Abstract Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment. PMID:19651028
Stochastic fluctuations of the synaptic function.
Ventriglia, Francesco; Di Maio, Vito
2002-01-01
The peak amplitudes of the quantal Excitatory Post Synaptic Currents in single hippocampal synapses show a large variability. Here, we present the results of a mathematical, computational investigation on the main sources of this variability. A detailed description of the synaptic cleft, rigorously based on empirically-derived parameters, was used. By using a Brownian motion model of neurotransmitter molecule diffusion, quantal EPSCs were computed by a simple kinetic schema of AMPA receptor dynamics. Our results show that the lack of saturation of AMPA receptors obtained in these conditions, combined with stochastic variations in basic presynaptic elements, such as the vesicle volume, the vesicle docking position, and the vesicle neurotransmitter concentration can explain almost the entire range of EPSC variability experimentally observed.
Stochastic unraveling of positive quantum dynamics
NASA Astrophysics Data System (ADS)
Caiaffa, Matteo; Smirne, Andrea; Bassi, Angelo
2017-06-01
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems, and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a generalization of QSD, which also applies to positive, but not completely positive evolutions. The rate and the action of the diffusive processes involved in the unraveling are obtained by applying a proper transformation to the operators which define the master equation. The unraveling is first defined for semigroup dynamics and then extended to a definite class of time-dependent generators. We test our approach on a prototypical model for the description of exciton transfer, keeping track of relevant phenomena, which are instead disregarded within the standard, completely positive framework.
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations We compare Wiener chaos and stochastic collocation methods for linear advection-reaction...ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 nonlinear stochastic PDEs (SPDEs), nonlocal SPDEs, Navier...3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations Report Title We compare Wiener chaos and stochastic collocation methods for linear
Statistical validation of stochastic models
Hunter, N.F.; Barney, P.; Paez, T.L.; Ferregut, C.; Perez, L.
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Stochasticity, heterogeneity, and variance in longevity in human populations.
Hartemink, Nienke; Missov, Trifon I; Caswell, Hal
2017-04-01
Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751-1899), France (1816-1903), and Italy (1872-1899), and also for a selection of period data for the same countries. Heterogeneity in mortality is described by the gamma-Gompertz-Makeham model, in which a gamma distributed "frailty" modifies a baseline Gompertz-Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age×frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time
Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations
NASA Astrophysics Data System (ADS)
Terragni, F.; Carretero, M.; Capasso, V.; Bonilla, L. L.
2016-02-01
A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014), 10.1103/PhysRevE.90.062716]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble-averaged stochastic descriptions.
Network Analysis with Stochastic Grammars
2015-09-17
a variety of ways on a lower level. For a grammar , each phase is essentially a Task and a network attack is, at the highest level, a five Task...NETIVORK ANALYSIS \\\\’ITH STOCHASTIC GRAMMARS DISSERTATION Alan C. Lin, Maj , USAF AFIT-ENG-DS-15-S-014 DEPARTMENT OF THE AIR FORCE AIR...subject to copyright protection in the United States. AFIT-ENG-DS-15-S-014 NETWORK ANALYSIS WITH STOCHASTIC GRAMMARS DISSERTATION Presented
Stochastic roots of growth phenomena
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
Some Topics in Stochastic Control
2010-10-14
Flows of Diffeomorphisms , (viii)Feller and Stability Properties of the Nonlinear Filter, (ix) Particle filter methods for Atmospheric and Oceanic data... Diffeomorphisms , Bernoulli, 16 (2010), no. 1, 91- -113. 5. A. Budhiraja, P. Dupuis and V. Maroulas. Variational Representations for Continuous Time...treat a setting with state dependent rates. 16 C.III. Large Deviations for Stochastic Flows of Diffeomorphisms [11]. Stochastic flows of diffeomorphisms
Stochastic Models of Polymer Systems
2016-01-01
Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title...field limit of a dynamical model for polymer systems, Science China Mathematics, (11 2012): 0. doi: TOTAL: 1 Number of Non Peer-Reviewed Conference
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian; Majda, Andrew J.
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Phenomenology of stochastic exponential growth
NASA Astrophysics Data System (ADS)
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
The stochastic dance of early HIV infection
NASA Astrophysics Data System (ADS)
Merrill, Stephen J.
2005-12-01
The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for the immune response, the dance predicts that the immune response will be also in a variable state of readiness and capability for this task of adaptation. The description of the stochastic dance of HIV here will use the tools of stochastic models, and for the most part, simulation. The justification for this approach is that the early stages and the development of HIV diversity require that the model to be able to describe both individual sample path and patient-to-patient variability. In addition, as early viral dynamics are best described using branching processes, the explosive growth of these models both predicts high variability and rapid response of HIV to changes in system parameters.In this paper, a basic viral growth model based on a time dependent continuous-time branching process is used to describe the growth of HIV infected cells in the macrophage and lymphocyte populations. Immigration from the reservoir population is added to the basic model to describe the incubation time distribution. This distribution is deduced directly from the modeling assumptions and the model of viral growth. A system of two branching processes, one in the infected macrophage population and one in the infected lymphocyte population is used to provide a description of the relationship between the development of HIV diversity as it relates to tropism (host cell preference). The role of the immune
Brennan J. M.; Blaskiewicz, M.; Mernick, K.
2012-05-20
The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.
NASA Astrophysics Data System (ADS)
McDonnell, Mark D.; Amblard, Pierre-Olivier; Stocks, Nigel G.
2009-01-01
We introduce and define the concept of a stochastic pooling network (SPN), as a model for sensor systems where redundancy and two forms of 'noise'—lossy compression and randomness—interact in surprising ways. Our approach to analysing SPNs is information theoretic. We define an SPN as a network with multiple nodes that each produce noisy and compressed measurements of the same information. An SPN must combine all these measurements into a single further compressed network output, in a way dictated solely by naturally occurring physical properties—i.e. pooling—and yet cause no (or negligible) reduction in mutual information. This means that SPNs exhibit redundancy reduction as an emergent property of pooling. The SPN concept is applicable to examples in biological neural coding, nanoelectronics, distributed sensor networks, digital beamforming arrays, image processing, multiaccess communication networks and social networks. In most cases the randomness is assumed to be unavoidably present rather than deliberately introduced. We illustrate the central properties of SPNs for several case studies, where pooling occurs by summation, including nodes that are noisy scalar quantizers, and nodes with conditionally Poisson statistics. Other emergent properties of SPNs and some unsolved problems are also briefly discussed.
Stochastic processes in gravitropism.
Meroz, Yasmine; Bastien, Renaud
2014-01-01
In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles) to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i) dynamic sensing, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification, and integration of the signal. (ii) The role of the cytoskeleton in signal-to-noise modulation and (iii) in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
Kazeroonian, Atefeh; Fröhlich, Fabian; Raue, Andreas; Theis, Fabian J; Hasenauer, Jan
2016-01-01
Gene expression, signal transduction and many other cellular processes are subject to stochastic fluctuations. The analysis of these stochastic chemical kinetics is important for understanding cell-to-cell variability and its functional implications, but it is also challenging. A multitude of exact and approximate descriptions of stochastic chemical kinetics have been developed, however, tools to automatically generate the descriptions and compare their accuracy and computational efficiency are missing. In this manuscript we introduced CERENA, a toolbox for the analysis of stochastic chemical kinetics using Approximations of the Chemical Master Equation solution statistics. CERENA implements stochastic simulation algorithms and the finite state projection for microscopic descriptions of processes, the system size expansion and moment equations for meso- and macroscopic descriptions, as well as the novel conditional moment equations for a hybrid description. This unique collection of descriptions in a single toolbox facilitates the selection of appropriate modeling approaches. Unlike other software packages, the implementation of CERENA is completely general and allows, e.g., for time-dependent propensities and non-mass action kinetics. By providing SBML import, symbolic model generation and simulation using MEX-files, CERENA is user-friendly and computationally efficient. The availability of forward and adjoint sensitivity analyses allows for further studies such as parameter estimation and uncertainty analysis. The MATLAB code implementing CERENA is freely available from http://cerenadevelopers.github.io/CERENA/.
Stochastic tools hidden behind the empirical dielectric relaxation laws.
Stanislavsky, Aleksander; Weron, Karina
2017-03-01
The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of 'structures with variations' (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools-by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.
A new stochastic systems approach to structural integrity
NASA Technical Reports Server (NTRS)
Provan, James W.; Farhangdoost, Khalil
1994-01-01
This paper develops improved stochastic models for the description of a large variety of fatigue crack growth phenomena that occur in components of considerable importance to the functionality and reliability of complex engineering structures. In essence, the models are based on the McGill-Markov and Closure-Lognormal stochastic processes. Not only do these models have the capability of predicting the statistical dispersion of crack growth rates, they also, by incorporating the concept of crack closure, have the capability of transferring stochastic crack growth properties measured under ideal laboratory conditions to situations of industrial significance, such as those occurring under adverse loading and/or environmental conditions. The primary data required in order to be in a position to estimate the pertinent parameters of these stochastic models are obtained from a statistically significant number of replicate tests. In this paper, both the theory and the experimental technique are illustrated using a Ti-6Al-4V alloy. Finally, important structural integrity, reliability, availability and maintainability concepts are developed and illustrated.
Stochastic tools hidden behind the empirical dielectric relaxation laws
NASA Astrophysics Data System (ADS)
Stanislavsky, Aleksander; Weron, Karina
2017-03-01
The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of ‘structures with variations’ (Goldenfield and Kadanoff 1999 Science 284 87–9) require application of such mathematical tools—by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.
NASA Astrophysics Data System (ADS)
Van Mieghem, P.; van de Bovenkamp, R.
2013-03-01
Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent α. For three basic classes of graphs, the Erdős-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents α. Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory.
A non-Markovian model of avalanche gain statistics for a solid-state photomultiplier
NASA Technical Reports Server (NTRS)
Laviolette, Randall A.; Stapelbroek, M. G.
1989-01-01
A solid-state photomultiplier (SSPM) capable of continously detecting individual photons of wavelength between 0.4 and 28 microns has recently been disclosed (Petroff et al., 1987). The initial response of the SSPM to single photon is a fast, high-amplitude current pulse of between 10,000 and 100,000 electrons. A phenomenological model of the SSPM avalanche process is presented which successfully predicts the shape of the observed pulse-amplitude distribution by including small history-dependent effects on the carrier transport. The model clarifies the consequences of the electric field strength and the scattering of the electrons for the development of the avalanche in the SSPM.
Electron Pumping under Non-Markovian Dissipation: The Role of the Self-Consistent Field
NASA Astrophysics Data System (ADS)
Grossmann, Frank; Sakurai, Atsunori; Tanimura, Yoshitaka
2016-03-01
Focusing on electron transport through a periodically driven resonant tunneling diode, we study the generation of a non-vanishing dc-current by applying symmetry breaking external ac fields with phase difference φ in a statically unbiased system. The effect of an environment is investigated using the system-bath Hamiltonian represented by the electron system coupled to harmonic oscillator modes with a Drude-Lorentz spectral density. To carry out simulations, we use the hierarchal equations of motion approach in the Wigner representation including a self-consistently constructed electric field that is determined from the electron distribution using the Poisson equation. We show that the maximal pumping current at a phase difference near φ = π/2 is strongly influenced by the system-bath coupling strength. The effect of dissipation is diminished if the self-consistent part of the potential is ignored.
Publisher's Note: Non-Markovian dynamics of a qubit [Phys. Rev. A 73, 012111 (2006)
NASA Astrophysics Data System (ADS)
Maniscalco, Sabrina; Petruccione, Franceso
2006-02-01
This paper was published online on 24 January 2006 with an incorrect electronic address in the first author’s byline footnote. The electronic address for the first author should read “sabrina.maniscalco@utu.fi.” The byline footnote has been corrected as of 26 January 2006. The byline footnote is correct in the printed version of the journal.
Publisher's Note: Non-Markovian dynamics of a qubit [Phys. Rev. A 73, 012111 (2006)
Maniscalco, Sabrina; Petruccione, Franceso
2006-02-15
This paper was published online on 24 January 2006 with an incorrect electronic address in the first author's byline footnote. The electronic address for the first author should read 'sabrina.maniscalco at utu.fi'. The byline footnote has been corrected as of 26 January 2006. The byline footnote is correct in the printed version of the journal.
Non-Markovian Line Shapes of Physisorbed Atoms on a Crystal.
1987-04-01
8217 - . "." "."." ", , " - .""." " "".""."" .’ " "" " . ’ "-". " "" " "" " "" / " ’" ’.’’= 0* I e~mz& ’V-PWTNW’L~~~~~~~~iwflmrlr wS.npq RVI %"PL Mswq M, WVn ~ vin M-Mr ml -UWnin-N-%l.- - 0 N
A non-Markovian model of avalanche gain statistics for a solid-state photomultiplier
NASA Technical Reports Server (NTRS)
Laviolette, Randall A.; Stapelbroek, M. G.
1989-01-01
A solid-state photomultiplier (SSPM) capable of continously detecting individual photons of wavelength between 0.4 and 28 microns has recently been disclosed (Petroff et al., 1987). The initial response of the SSPM to single photon is a fast, high-amplitude current pulse of between 10,000 and 100,000 electrons. A phenomenological model of the SSPM avalanche process is presented which successfully predicts the shape of the observed pulse-amplitude distribution by including small history-dependent effects on the carrier transport. The model clarifies the consequences of the electric field strength and the scattering of the electrons for the development of the avalanche in the SSPM.
Capture-recapture studies for multiple strata including non-markovian transitions
Brownie, C.; Hines, J.E.; Nichols, J.D.; Pollock, K.H.; Hestbeck, J.B.
1993-01-01
We consider capture-recapture studies where release and recapture data are available from each of a number of strata on every capture occasion. Strata may, for example, be geographic locations or physiological states. Movement of animals among strata occurs with unknown probabilities, and estimation of these unknown transition probabilities is the objective. We describe a computer routine for carrying out the analysis under a model that assumes Markovian transitions and under reduced parameter versions of this model. We also introduce models that relax the Markovian assumption and allow 'memory' to operate (i.e., allow dependence of the transition probabilities on the previous state). For these models, we sugg st an analysis based on a conditional likelihood approach. Methods are illustrated with data from a large study on Canada geese (Branta canadensis) banded in three geographic regions. The assumption of Markovian transitions is rejected convincingly for these data, emphasizing the importance of the more general models that allow memory.
Self-similarity and non-Markovian behavior in traded stock volumes
NASA Astrophysics Data System (ADS)
Brown, Frank R.; Pravica, David; Bier, Martin
2015-11-01
The volume traded daily for 17 stocks is followed over a period of about half a century. We look at the volume of stocks traded in a certain time interval (day, week, month) and analyze how long that traded volume keeps monotonically increasing or decreasing. On all three times scales we find that the sequence of traded volumes behaves neither like a sequence of independent and identically distributed variables, nor like a Markov sequence. A compressed exponential survival function with the same parameters at all timescales is firmly established. A day with an increase (decrease) of traded volume is most likely followed by a day with a decrease (increase) of traded volume. We show how the apparent self-similarity results because the small day-to-day anticorrelation carries over when larger time intervals are considered. The observed small anticorrelation can be explained as a consequence of market forces and trader reactions.
NASA Astrophysics Data System (ADS)
Sultana, Tahmina; Takagi, Hiroaki; Morimatsu, Miki; Teramoto, Hiroshi; Li, Chun-Biu; Sako, Yasushi; Komatsuzaki, Tamiki
2013-12-01
We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ˜3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.
Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits
NASA Astrophysics Data System (ADS)
Barnes, Edwin; Rudner, Mark S.; Martins, Frederico; Malinowski, Filip K.; Marcus, Charles M.; Kuemmeth, Ferdinand
2016-03-01
The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and 1 /ωα charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
Segmentation of stochastic images with a stochastic random walker method.
Pätz, Torben; Preusser, Tobias
2012-05-01
We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.
Paszek, Pawel
2007-07-01
Intrinsic stochasticity plays an essential role in gene regulation because of a small number of involved molecules of DNA, mRNA and protein of a given species. To better understand this phenomenon, small gene regulatory systems are mathematically modeled as systems of coupled chemical reactions, but the existing exact description utilizing a Chapman-Kolmogorov equation or simulation algorithms is limited and inefficient. The present work considers a much more efficient yet accurate modeling approach, which allows analyzing stochasticity in the system in the terms of the underlying distribution function. We depart from the analysis of a single gene regulatory module to find that the mRNA and protein variance is decomposable into additive terms resulting from respective sources of stochasticity. This variance decomposition is asserted by constructing two approximations to the exact stochastic description: First, the continuous approximation, which considers only the stochasticity due to the intermittent gene activity. Second, the mixed approximation, which in addition attributes stochasticity to the mRNA transcription/decay process. Considered approximations yield systems of first order partial differential equations for the underlying distribution function, which can be efficiently solved using developed numerical methods. Single cell simulations and numerical two-dimensional mRNA-protein stationary distribution functions are presented to confirm accuracy of approximating models.
Stacking with stochastic cooling
NASA Astrophysics Data System (ADS)
Caspers, Fritz; Möhl, Dieter
2004-10-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105 the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some considerations to the 'azimuthal' schemes.
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Accelerated stochastic diffusion processes
NASA Astrophysics Data System (ADS)
Garbaczewski, Piotr
1990-07-01
We give a purely probabilistic demonstration that all effects of non-random (external, conservative) forces on the diffusion process can be encoded in the Nelson ansatz for the second Newton law. Each random path of the process together with a probabilistic weight carries a phase accumulation (complex valued) weight. Random path summation (integration) of these weights leads to the transition probability density and transition amplitude respectively between two spatial points in a given time interval. The Bohm-Vigier, Fenyes-Nelson-Guerra and Feynman descriptions of the quantum particle behaviours are in fact equivalent.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Enhanced algorithms for stochastic programming
Krishna, A.S.
1993-09-01
In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean of a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Stochastic simulation in systems biology
Székely, Tamás; Burrage, Kevin
2014-01-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503
NASA Astrophysics Data System (ADS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-10-01
We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form "crater"-"peak +crater "-"peak" are demonstrated by numerical simulation. An analytical investigation of such P bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.
General no-go condition for stochastic pumping.
Maes, Christian; Netocný, Karel; Thomas, Simi R
2010-06-21
The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemomechanical molecular configurations. Pumping refers to generating a net current, e.g., per period in the time dependence, through a cycle of consecutive states. The work of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are, in general, modified with a multiplicative factor when this time dependence is turned on.
General no-go condition for stochastic pumping
NASA Astrophysics Data System (ADS)
Maes, Christian; Netočný, Karel; Thomas, Simi R.
2010-06-01
The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemomechanical molecular configurations. Pumping refers to generating a net current, e.g., per period in the time dependence, through a cycle of consecutive states. The work of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are, in general, modified with a multiplicative factor when this time dependence is turned on.
Mixed quantal-semiquantal dynamics with stochastic particles for backreaction
Ando, Koji
2014-10-14
A mixed quantal-semiquantal theory is presented in which the semiquantal squeezed-state wave packet describes the heavy degrees of freedom. Starting from the mean-field equations of motion that are naturally derived from the time-dependent variational principle, we introduce the stochastic particle description for both the quantal and semiquantal parts in an aim to take into account the interparticle correlation, in particular the “quantum backreaction” beyond the mean-field approximation. A numerical application on a model of O{sub 2} scattering from a Pt surface demonstrates that the proposed scheme gives correct asymptotic behavior of the scattering probability, with improvement over the mixed quantum-classical scheme with Bohmian particles, which is comprehended by comparing the Bohmian and the stochastic trajectories.
Toward Stochastic Parameterization Based on Profiler Measurements of Vertical Velocity
NASA Astrophysics Data System (ADS)
Penland, C.; Koepke, A.; Williams, C. R.
2016-12-01
Parameterizations in General Circulation Models (GCMs) that account for uncertainty due to both unresolved, sub-grid scale processes and errors in assumptions made in the formulation of the parameterization itself are needed to represent the full probability distribution function of resolved processes in the model. In this study, we develop a probabilistic description of vertical velocity based on profiler data collected at Darwin during the time period November 2005 to February 2006. Data collected at one-minute resolution are analyzed at the one-minute, ten-minute and hourly timescales, including fits to the Stochastically-Generated Skew (SGS) distributions. The SGS distributions are associated with linear dynamics, including correlated additive and multiplicative noise. As expected, we find that the stochastic approximation to nonlinear dynamics becomes more appropriate as the timescale is increased by coarse-graining.
Stochastic sensitivity of a bistable energy model for visual perception
NASA Astrophysics Data System (ADS)
Pisarchik, Alexander N.; Bashkirtseva, Irina; Ryashko, Lev
2017-01-01
Modern trends in physiology, psychology and cognitive neuroscience suggest that noise is an essential component of brain functionality and self-organization. With adequate noise the brain as a complex dynamical system can easily access different ordered states and improve signal detection for decision-making by preventing deadlocks. Using a stochastic sensitivity function approach, we analyze how sensitive equilibrium points are to Gaussian noise in a bistable energy model often used for qualitative description of visual perception. The probability distribution of noise-induced transitions between two coexisting percepts is calculated at different noise intensity and system stability. Stochastic squeezing of the hysteresis range and its transition from positive (bistable regime) to negative (intermittency regime) are demonstrated as the noise intensity increases. The hysteresis is more sensitive to noise in the system with higher stability.