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Diffusion in a two-dimensional energy landscape in the presence of dynamical correlations and validity of random walk model

Acharya, S and Bagchi, B (2023) Diffusion in a two-dimensional energy landscape in the presence of dynamical correlations and validity of random walk model. In: Physical Review E, 107 (2).

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Official URL: https://10.1103/PhysRevE.107.024127


Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and it also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and simulations of a tagged particle moving on a two-dimensional periodic potential energy surface, both in the presence and absence of noise. Langevin dynamics simulations at multiple temperatures are carried out to obtain the diffusion coefficient of a solute particle. Friction is varied from zero to large values. Diffusive motion emerges in the limit of a long time, even in the absence of noise. Noise destroys the correlations and increases diffusion at small friction. Diffusion thus exhibits a nonmonotonic friction dependence at the intermediate value of the damping, ultimately converging to our theoretically predicted value. The latter is obtained using the well-established relationship between diffusion and random walk. An excellent agreement is obtained between theory and simulations in the high-friction limit but not so in the intermediate regime. We explain the deviation in the low- to intermediate-friction regime using the modified random walk theory. The rate of escape from one cell to another is obtained from the multidimensional rate theory of Langer. We find that enhanced dimensionality plays an important role. To quantify the effects of noise on the potential-imposed coherence on the trajectories, we calculate the Lyapunov exponent. At small friction values, the Lyapunov exponent mimics the friction dependence of the rate. © 2023 American Physical Society.

Item Type: Journal Article
Publication: Physical Review E
Publisher: American Physical Society
Additional Information: The copyright of this article belongs to American Physical Society.
Keywords: Differential equations; Diffusion; Lyapunov functions; Lyapunov methods; Molecular dynamics; Potential energy; Quantum chemistry; Random processes; Statistical mechanics; Dynamical correlations; Energy landscape; Energy surface; Lyapunov exponent; Periodic potentials; Potential-energy surfaces; Protein foldings; Random walk modeling; Tagged particle; Two-dimensional; Friction
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Date Deposited: 10 Mar 2023 10:15
Last Modified: 10 Mar 2023 10:15
URI: https://eprints.iisc.ac.in/id/eprint/80927

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