Rate processes with dynamical disorder: a direct variational approach.
28 May 2006-Journal of Chemical Physics (American Institute of Physics)-Vol. 124, Iss: 20, pp 204111-204111
TL;DR: Using path integral approach, variational approximations to the calculation of survival probability for rate processes with dynamical disorder are developed and both upper and lower bounds to the survival probability are derived using Jensen's inequality.
Abstract: Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen’s inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.
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TL;DR: The simulations show that the tracer can undergo normal yet non-Gaussian diffusion under certain circumstances, e.g., when the polymers with traps are frozen in space and the volume fraction and the binding strength of the traps are moderate.
Abstract: We use molecular dynamics simulations to investigate the tracer diffusion in a sea of polymers with specific binding zones for the tracer. These binding zones act as traps. Our simulations show that the tracer can undergo normal yet non-Gaussian diffusion under certain circumstances, e.g., when the polymers with traps are frozen in space and the volume fraction and the binding strength of the traps are moderate. In this case, as the tracer moves, it experiences a heterogeneous environment and exhibits confined continuous time random walk (CTRW) like motion resulting in a non-Gaussian behavior. Also the long time dynamics becomes subdiffusive as the number or the binding strength of the traps increases. However, if the polymers are mobile then the tracer dynamics is Gaussian but could be normal or subdiffusive depending on the number and the binding strength of the traps. In addition, with increasing binding strength and number of polymer traps, the probability of the tracer being trapped increases. On the other hand, removing the binding zones does not result in trapping, even at comparatively high crowding. Our simulations also show that the trapping probability increases with the increasing size of the tracer and for a bigger tracer with the frozen polymer background the dynamics is only weakly non-Gaussian but highly subdiffusive. Our observations are in the same spirit as found in many recent experiments on tracer diffusion in polymeric materials and question the validity of using Gaussian theory to describe diffusion in a crowded environment in general.
43 citations
TL;DR: In this article, the authors examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environment, and the expression for the Kramers' mean escape time from low activity holds only in the limit of low activity.
Abstract: Spontaneous persistent motions driven by active processes play a central role in maintaining living cells far from equilibrium. In the majority of research studies, the steady state dynamics of an active system has been described in terms of an effective temperature. By contrast, we have examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environment. The expression for the mean escape time from the activity-induced rugged energy landscape holds only in the limit of low activity and the mean escape time from the rugged energy landscape increases with activity. The precise form of the active correlation will determine whether the mean escape time will depend on the persistence time or not. The activity-induced rugged energy landscape approach also allows an estimate of the non-equilibrium effective diffusivity characterizing the slow diffusive motion of the tagged particle due to activity. On the other hand, in a dilute environment, high activity augments the diffusion of the tagged particle. The enhanced diffusion can be attributed to an effective temperature higher than the ambient temperature and this is used to calculate the Kramers' mean escape time, which decreases with activity. Our results have direct relevance to recent experiments on tagged particle diffusion in condensed phases.
32 citations
TL;DR: In this paper, a flexible Gaussian chain with internal friction was used to analyze the intra-chain reconfiguration and loop formation times for all three topology classes namely, end-to-end, endto-interior and interior-tointerior.
Abstract: In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This friction is termed as internal friction in the literature. Using a flexible Gaussian chain with internal friction we analyze the intra-chain reconfiguration and loop formation times for all three topology classes namely end-to-end, end-to-interior and interior-to-interior. In a nutshell, bypassing expensive simulations we show how simple models like that of Rouse and Zimm can support the single molecule experiment and computer simulation results on intra-chain diffusion coefficients, looping time and even can predict the effects of tail length on the looping time.
22 citations
TL;DR: Weber et al. as mentioned in this paper theoretically investigated the looping dynamics of a linear chain immersed in a viscoelastic fluid and showed that the mean square displacement of the center of mass of the chain scales as t 1 / 2.
Abstract: We theoretically investigate the looping dynamics of a linear chain immersed in a viscoelastic fluid. The dynamics of the chain is governed by a Rouse model with a fractional memory kernel recently proposed by Weber et al. [S.C. Weber, J.A. Theriot, A.J. Spakowitz, Phys. Rev. E 82 (2010) 011913]. Using the Wilemski–Fixman [G. Wilemski, M. Fixman, J. Chem. Phys. 60 (1974) 866] formalism we calculate the looping time for a chain in a viscoelastic fluid where the mean square displacement of the center of mass of the chain scales as t 1 / 2 . We observe that the looping time is faster for the chain in a viscoelastic fluid than for a Rouse chain in a Newtonian fluid up to a chain length and above this chain length the trend is reversed. Also no stable scaling of the looping time with the length of the chain seems to exist for the chain in a viscoelastic fluid.
21 citations
TL;DR: In this article, the authors used molecular dynamics simulations to investigate tracer diffusion in a sea of polymers with specific binding zones for the tracer, and they showed that the tracers can undergo normal yet non-Gaussian diffusion under certain circumstances, e.
Abstract: We use molecular dynamics simulations to investigate the tracer diffusion in a sea of polymers with specific binding zones for the tracer. These binding zones act as traps. Our simulations show that the tracer can undergo normal yet non-Gaussian diffusion under certain circumstances, e.g, when the polymers with traps are frozen in space and the volume fraction and the binding strength of the traps are moderate. In this case, as the tracer moves, it experiences a heterogeneous environment and exhibits confined continuous time random walk (CTRW) like motion resulting a non-Gaussian behavior. Also the long time dynamics becomes subdiffusive as the number or the binding strength of the traps increases. However, if the polymers are mobile then the tracer dynamics is Gaussian but could be normal or subdiffusive depending on the number and the binding strength of the traps. In addition, with increasing binding strength and the number of the polymer traps, the probability of the tracer being trapped increases. On the other hand, removing the binding zones does not result trapping, even at comparatively high crowding. Our simulations also show that the trapping probability increases with the increasing size of the tracer and for a bigger tracer with the frozen polymer background the dynamics is only weakly non-Gaussian but highly subdiffusive. Our observations are in the same spirit as found in many recent experiments on tracer diffusion in polymeric materials and questions the validity of Gaussian theory to describe diffusion in crowded environment in general.
21 citations
References
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TL;DR: In this article, a discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method for quantum reactive scattering.
Abstract: A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S‐matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)] for quantum reactive scattering. (It can also be readily used for quantum eigenvalue problems.) The primary novel feature is that this DVR gives an extremely simple kinetic energy matrix (the potential energy matrix is diagonal, as in all DVRs) which is in a sense ‘‘universal,’’ i.e., independent of any explicit reference to an underlying set of basis functions; it can, in fact, be derived as an infinite limit using different basis functions. An energy truncation procedure allows the DVR grid points to be adapted naturally to the shape of any given potential energy surface. Application to the benchmark collinear H+H2→H2+H reaction shows that convergence in the reaction probabilities is achieved with only about 15% more DVR grid points than the number of conventional basis functions used in previous S‐matrix Kohn...
1,575 citations
Book•
19 Jul 2006
TL;DR: In this paper, the Duru-Kleinert method was used to solve the problem of path integral formulas for singular potentials in the Coulomb system, and the solution of further path integrals in polymers and Particle Orbits in multiply connected connected spaces.
Abstract: Fundamentals Path Integrals - Elementary Properties and Simple Solutions External Sources, Correlations, and Perturbation Theory Semiclassical Time Evolution Amplitude Variational Perturbation Theory Path Integrals with Topological Constrainsts Many Particle Orbits - Statistics and Second Quantization Path Integrals in Spherical Coordinates Fixed-Energy Amplitude and Wave Functions Spaces with Curvature and Torsion Schrodinger Equation in General Metric-Affine Spaces New Path Integral Formula for Singular Potentials Path Integral of Coulomb System Solution of Further Path Integrals by the Duru-Kleinert Method Path Integrals in Polymer Physics Polymers and Particle Orbits in Multiply Connected Spaces Tunneling Nonequilibrium Quantum Statistics Relativistic Particle Orbits Path Integrals and Financial Markets.
1,077 citations
Book•
01 Jan 2005
TL;DR: In this article, a path integral and holomorphic formalism for quantum mechanics is proposed, where path integrals are fermions and quantization is performed by path integral in phase space.
Abstract: 1. Gaussian integrals 2. Path integral in quantum mechanics 3. Partition function and spectrum 4. Classical and quantum statistical physics 5. Path integrals and quantization 6. Path integral and holomorphic formalism 7. Path integrals: fermions 8. Barrier penetration: semi-classical approximation 9. Quantum evolution and scattering matrix 10. Path integrals in phase space QUANTUM MECHANICS: MINIMAL BACKGROUND A1 Hilbert space and operators A2 Quantum evolution, symmetries and density matrix A3 Position and momentum. Scrodinger equation
736 citations
367 citations