non-Markovian Approach Research Articles

Non-Markovian dynamics of mixed fermionic-bosonic systems: Rotating-wave-approximation coupling

Employing quadratic fermionic and bosonic Hamiltonians for collective and internal subsystems with a linear rotating-wave-approximation coupling, we studied the role of heat-bath statistics on the dynamics of the collective motion. The master equations for the collective occupation number derived directly from the quadratic Hamiltonians and within the Non-Markovian Langevin approach are discussed and their solutions are obtained. Because of the different nature of the heat-bath statistics, the path to equilibrium or the relaxation time is affected as shown in the numerical calculations.

Non-Markovian dynamics of fully coupled fermionic and bosonic oscillators

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.

Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model

One long-standing 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 derivie a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schr\"odinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.

Estimating first-passage time distributions from weighted ensemble simulations and non-Markovian analyses.

First-passage times (FPTs) are widely used to characterize stochastic processes such as chemical reactions, protein folding, diffusion processes or triggering a stock option. In previous work (Suarez et al., JCTC 2014;10:2658-2667), we demonstrated a non-Markovian analysis approach that, with a sufficient subset of history information, yields unbiased mean first-passage times from weighted-ensemble (WE) simulations. The estimation of the distribution of the first-passage times is, however, a more ambitious goal since it cannot be obtained by direct observation in WE trajectories. Likewise, a large number of events would be required to make a good estimation of the distribution from a regular "brute force" simulation. Here, we show how the previously developed non-Markovian analysis can generate approximate, but highly accurate, FPT distributions from WE data. The analysis can also be applied to any other unbiased trajectories, such as from standard molecular dynamics simulations. The present study employs a range of systems with independent verification of the distributions to demonstrate the success and limitations of the approach. By comparison to a standard Markov analysis, the non-Markovian approach is less sensitive to the user-defined discretization of configuration space.

Rejuvenation effects on the grid environment performance with response time delays using Monte Carlo simulation

Grid computing is an evolutionary technological achievement that takes advantages of wide area communication and large scale resource sharing. Although there are several advantages, grid does not guaranty stableness of resources due to their resources’ nature, diverse failures and error conditions that may appear. Consequently, grid dependability issues arise. In this paper, a grid computing environment with star topology and direct access to resources is considered, which consists of a Resource Management System (RMS) and distributed Root Nodes (RNs). The distributed RNs are considered either as operational or as failed, though the RMS is susceptible to resource exhaustion, which can lead to software failures. The response waiting time from a distributed RN is also taken under consideration. A software rejuvenation to counteract RMS resource exhaustion is adopted, and its effect on grid environment performance is studied extensively. A non-Markovian approach is considered to model the system’s evolution in time and to evaluate the proposed performance measures. Due to the complicated structure of the system, analytic formulas for the proposed measures are not available, thus Monte Carlo simulation methods are employed.

Extension of the non-Markovian Energy-Corrected Sudden model to the case of parallel and perpendicular infrared bands

The non-Markovian Energy-Corrected Sudden approach [J. Buldyreva and L. Bonamy, Phys. Rev. A 60, 370 (1999)] previously developed for wide-band rototranslational Raman spectra of linear rotors is extended to the case of infrared absorption by linear molecules with stretching and bending modes. Basic relations such as detailed balance and double-sided sum rules for the rotational relaxation matrix are easily satisfied owing to the specific choice of a symmetric metric in the Liouville space. A single set of model parameters deduced from experimental widths of isolated isotropic Raman lines enables calculations of line-shape characteristics and full spectra up to the far wings. Applications to the important but quite complex example of pure carbon dioxide indicate the crucial role of the frequency dependence in the relaxation operator even for calculations of isolated-line characteristics.

Communication: Quantum dynamics in classical spin baths

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.

Reconstruction of the environmental correlation function from single-emitter photon statistics: A non-Markovian approach

We consider the two-level system approximation of a single emitter driven by a continuous laser pump and simultaneously coupled to the electromagnetic vacuum and to a thermal reservoir beyond the Markovian approximation. We discuss the connection between a rigorous microscopic theory and the phenomenological spectral diffusion approach, used to model the interaction of the emitter with the thermal bath, and obtained analytic expressions relating the thermal correlation function to the single emitter photon statistics.

Rational Automata Networks: A Non-Markovian Modeling Approach

A new class of non-Markovian models is introduced that results from the combination of stochastic automata networks and a very general class of stochastic processes, namely, rational arrival processes, which are derived from matrix exponential distributions. It is shown that the modeling formalism allows a compact representation of complex models with large state spaces. The resulting stochastic process is non-Markovian, but it can be analyzed with numerical techniques like a Markov chain, and the results at the level of the automata are stochastic distributions that can be used to compute standard performance and dependability results. The model class includes stochastic automata networks with phase-type distributed and correlated event times and also includes models that have a finite state space but cannot be represented by finite Markov chains. The paper introduces the model class, shows how the descriptor matrix can be represented in compact form, presents some example models, and outlines methods to analyze the new models.

Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency

We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale.

Fermionic stochastic Schrödinger equation and master equation: An open-system model

This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schr\"{o}dinger equation (SSE), called fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model and the N-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.

Line mixing in Raman scattering spectra of CO2 modelled by a non-Markovian Energy-Corrected Sudden approach

Non-Markovian Energy-Corrected Sudden modelling of room-temperature CO2 Raman scattering spectra up to the far wing is revisited and completed for gas densities between 1 and 45 amagat. The model parameters are fitted on an extended set of low-pressure isolated line widths including very high values of the rotational quantum number J and well reproduce the decreasing of line broadening for the experimentally studied J-values. From calculations of the absolute-intensity rototranslational spectrum at 23 amagat, it is shown that the traditional adiabaticity factor of De Pristo gives a more coherent description of low-pressure line widths and high-pressure wing intensities than the two-parameter factor of Birnbaum–Cohen. A simple qualitative correction of the ECS-modelled intensities for the induced and cross allowed-induced scattering appears to be insufficient to match the experimental data in the spectral wing. Theoretical spectral shapes are also calculated for the O-Q-S branches of vibrotational ν1 and 2ν2 Raman bands and compared to experimental results in the density range 1–45 amagat.

Spin decoherence in graphene quantum dots due to hyperfine interaction

Carbon based systems are prominent candidates for a solid-state spin-qubit due to weak spin-orbit and hyperfine interactions in combination with a low natural abundance of spin carrying isotopes. We consider the effect of the hyperfine interaction on the coherence of an electron-spin localized in a graphene quantum dot. It is known, that the hyperfine interaction in these systems is anisotropic promising interesting physics. We calculate the dynamics of an electron spin surrounded by a bath of nuclear spins in a non-Markovian approach using a generalized master equation. Considering a general form of the hyperfine interaction, we are able to extend the range of validity of our results to other systems beyond graphene. For large external magnetic fields, we find within Born approximation that the electron spin state is conserved up to small corrections, which oscillate with a frequency determined by the hyperfine interaction. The amplitude of these oscillations decays with a power law, where its initial value depends on the specific form of the anisotropy. Analyzing this in more detail, we identify two distinct classes of anisotropy, which can be both found in graphene depending on the orientation of the external magnetic field with respect to the carbon layer.

Non-Markovian evolution approach to structural modeling of material fracture

The new multiscale non-Markov evolution modeling approach for damage accumulation and fracture processes of polycrystalline and ultra fine grained materials is proven by experimental results at nanoscale. Microstructural parameters are estimated by an atomic-force scanning probe in situ during the deformation. The non-Marcov evolution in the approach means taking into account the history of each element on a certain structure. The ultimate state of the current level controls the transfer on the next level of the whole structure. The main difficulty of traditional multiscale modeling is the determination of the ultimate states due to the parameters. This new approach presumes it is possible to restrict the current state of a material to only one control factor of nanostructure order. The new approach of defect behavior modeling allows the simulation of materials under a wide range of external influence, including low and high temperature and other environmental factors, almost without any faults.

Laser control in open quantum systems: preliminary analysis toward the Cope rearrangement control in methyl-cyclopentadienylcarboxylate dimer

We present a preliminary simulation toward the control of theCope rearrangement of themost stable isomer of methyl-cyclopentadienylcarboxylate dimer. An experimental investigation of the dimerization of methyl-cyclopentadienylcarboxylate has been carried out. It shows that the most stable isomer of the dimer, the Thiele’s ester, is the major product of the dimerization. The simulation takes it as the initial state for the further control of the Cope reaction. The aim of the simulation is to examine the possibility of laser control to form the target product, not detected during the dimerization. The relevant stationary states have been characterized at the DFT B3LYP level, particularly the Cope transition state in which the dimer is connected only by a single bond r1. A minimum energy potential surface has been computed in a two-dimensional subspace of two bounds r2 and r3 which achieve the dimerization and have a very high weight in the reaction path from the Cope TS to the two adducts. Quantum wave packet optimal control simulation has been studied in a one-dimensionalmodel using an active coordinate r_= r3 - r2 which nearly corresponds to the reaction path. The stability of the optimal field against dissipation is examined by a non-Markovian master equation approach, which is perturbative in the system-bath coupling but without limitation on the strength of the field.

Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at high dissipation there is a difference which is likely to be measured at any temperature.

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise.

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

Dust particles in typical laboratory plasma become charged largely by collecting electrons and/or ions. Most of the theoretical studies in dusty plasma assume that the grain charge remains constant even though it fluctuates due to the discrete nature of the charge. The rates of ions and electrons absorption depend on the grain charge, hence its temporal evolution. Stochastic charging model based on the standard Langevin equation assumes that the underlying process is Markovian. In this work, the memory effect in dust charging dynamics is incorporated using fractional calculus formalism. The resulting fractional Langevin equation is solved to obtain the amplitude and correlation function for the dust charge fluctuation. It is shown that the effects of ion-neutral collisions can be interpreted in phenomenological sense through the nonlocal fractional order derivative.

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima—Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.

Use of Metadynamics in the Design of isoDGR-Based αvβ3 Antagonists To Fine-Tune the Conformational Ensemble

The integrin family of cell-adhesion receptors regulates cellular functions crucial to the initiation, progression, and metastasis of solid tumors. In particular, integrin avb3 plays a key role in endothelial cell survival and migration during tumor angiogenesis. It is therefore gaining increasing importance as a drug target in antiangiogenic cancer therapy. The sequence Arg-Gly-Asp (RGD), which is contained in natural avb3 interactors, such as vitronectin, fibronectin, fibrinogen, osteopontin, and tenascin, is by far the most prominent ligand to promote specific cell adhesion through stimulation. This sequence is therefore attractive as a lead for the development of different integrin antagonists. Recent biochemical studies showed that deamidation of the NGR sequence gives rise to isoDGR, a new avb3-binding motif. This sequence constitutes a novel class of peptidic integrin ligands and paves the way to drug-design studies with a focus on the synthesis and characterization of a new generation of isoDGR-based macrocycles. For the design of low-molecular-mass isoDGR-containing molecules, an accurate determination of their biologically active conformation is a prerequisite. The presence of the b bond induces high flexibility in isoDGR-containing macrocycles and thus augments the range of accessible interconverting conformations. However, the identification of relevant conformations that might affect binding affinity is challenging for standard spectroscopic and diffraction techniques. Atomistic simulations, such as molecular dynamics (MD), replica-exchange molecular dynamics (REMD), and Monte Carlo (MC) simulations, can complement experimental data. However, they often fail to generate reliable equilibrium conformations because of the rugged and complex nature of the free-energy surface (FES) that is accessible to the system. As a consequence, computational sampling is often relegated to some local, unrealistic minima, which compromise subsequent docking studies. As computational drug design becomes increasingly reliant on virtual screening and on high-throughput 3D modeling, the need for fast and accurate computational methods for sampling of the ensemble of energetically accessible conformations is warranted. In this context, several techniques, including the local-elevation method, taboo search, the Wang–Landau method, adaptive force bias, conformational flooding, umbrella sampling, weighted histogram techniques, transitionstate theory, and path sampling, have been developed to address the sampling problem, through either reconstruction of the free energy or the direct acceleration of events that might happen on a long timescale (“rare events”). Related to these methods, metadynamics (MetaD) has emerged as a powerful coarse-grained non-Markovian molecular-dynamics approach for the acceleration of rare events and the efficient and rapid computation of multidimensional free-energy surfaces as a function of a restricted number of degrees of freedom, named collective variables (CVs). If the CVs are appropriately chosen for the system under investigation, MetaD directly provides a good estimate of the free energy of the system projected into the CVs (see the Supporting Information for details). Notably, the free energy is not immediately deducible by other sampling methods, such as umbrella sampling, in which the free-energy profile is not obtained directly from the simulations and requires an additional computational step, such as the weighted histogram analysis method (WHAM). In this study, we developed a protocol based on the combination of MetaD and docking simulations to analyze the conformations and the avb3-binding properties of isoDGR-containing cyclopeptides and to predict the conformational effects of chemical modifications and discriminate binders from nonbinders in silico. To investigate the conformational equilibrium of RGD-, DGR-, and isoDGRcontaining cyclopeptides (cyclization mode involving cysteine side chains) and to exhaustively explore their FESs, we performed well-temperedMetaD simulations, for which we chose Gly f and y angles as CVs (Figure 1; for simulation details, see the Supporting Information). As it lacks a side chain, Gly has large conformational freedom around its backbone dihedral angles. Therefore, Gly can explore a considerably larger area in the Ramachandran energy diagram than any other amino acid, and occupies five [*] Dr. A. Spitaleri, Dr. M. Ghitti, Dr. S. Mari, Dr. G. Musco Dulbecco Telethon Institute, Biomolecular NMR Laboratory c/o Center of Genomic and Bioinformatics S. Raffaele Scientific Institute via Olgettina 58, 20132 Milan (Italy) Fax: (+39)02-2643-4153 E-mail: giovanna.musco@hsr.it