Random-Matrix Approach to Transition-State Theory

TL;DR

This paper uses random matrix theory to model complex systems with barriers, deriving a universal transition probability formula that generalizes transition-state theory for large systems and thick barriers.

Contribution

It introduces a random-matrix model to derive a universal transition probability, extending transition-state theory to complex, high-dimensional systems.

Findings

Derived a universal transition probability formula

Connected random matrix models with transition-state theory

Showed independence of tunneling process formation and decay for thick barriers

Abstract

To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of large matrix dimension. We calculate the average probability for transition from scattering channel coupled to the first Hamiltonian to a scattering channel coupled to the second Hamiltonian. Using only the assumption that the sum of transmission coefficients of channels coupled to the second Hamiltonian is large we retrieve transition-state theory in its general form. For tunneling through a very thick barrier independence of formation and decay of the tunneling process hold more generally.