Related papers: Random-Matrix Approach to Transition-State Theory

Random-Matrix Approach to Transition-State Theory

URL: http://arxiv.org/abs/2202.04914v2
Date: Mon, 2 May 2022 08:01:06 GMT
Title: Random-Matrix Approach to Transition-State Theory
Authors: H. A. Weidenm\"uller
Abstract summary: We calculate the average probability for transition from scattering channel coupled to the first Hamiltonian to a scattering channel coupled to the second Hamiltonian. For tunneling through a very thick barrier independence of formation and decay of the tunneling process hold more generally.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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.

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