Speaker
Description
Most natural phenomena evolve through non-equilibrium pathways following non-linear dynamics involving the crossing of a potential energy barrier. During these processes the systems transit from one state to another. We intend to understand in detail the significance of these states, their positions, and associated intrinsic fluctuations. As these systems are inevitably subjected to environmental noise, there appears complexity in studying their behavior. We focus on analyzing the rate of diffusion-controlled transport in these complex systems under pertinent conditions. We implemented distinctions in the characteristics of the concerned states by altering their positions and the level of noise or diffusion coefficients linked to them. It has been observed that the variation of the reference point position and the diffusion coefficients have significant impacts on the rate. Our investigations unveil very important and critical aspects of the characteristic roles of the initial and final states in diffusion-controlled kinetics. We continued to develop an understanding of these fundamental transport phenomena where periodic force is involved. This is a particular scenario where the constructive interplay of noise and the non-linearity of the system comes into effect in the presence of appropriate conditions. The phenomenon is termed stochastic resonance. We explored the significance of the state dependence in stochastic resonance which manifests in many natural and designed processes, starting from climate systems to chemical reactions1-3. We developed a completely analytical theory in the adiabatic limit and a semi-analytical approach for the general case for stochastic resonance considering state-dependent diffusion. The theoretical findings are substantiated with numerical simulation results. The results of our studies not only enrich the fundamental understanding of diffusion-controlled kinetics but also indicate the paths to developing advantageous technologies based on optimizing the conditions of transport.
References:
[1] H. Grabert, P. Hänggi and I. Oppenheim, Physica A 117, 300-16 (1983)
[2] N.K. Vitanov and K.N. Vitanov, Comput. Math. Appl. 68, 962-71 (2014)
[3] M. Das and H. Kantz, Phys. Rev. E 101, 062145 (2020)
