Simulated annealing‐based optimal control over tunneling process through SDWP and Eckart barrier: A momentum basis representation |
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| Authors: | Srijeeta Talukder Pinaki Chaudhury Subhasree Ghosh |
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| Institution: | 1. Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, India;2. Department of Chemistry, University of Calcutta, Kolkata, India;3. Department of Chemistry, Serampore College, Hooghly, India |
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| Abstract: | For a reaction to proceed via tunneling mechanism, it is essential that the reactants will cross the potential barrier (EP), where its initial energy (E0) is below the potential barrier EP. Tunneling probability τ is defined as the probability of having momentum higher than km, where  . In the momentum basis representation, τ can be directly calculated by integrating  from the limit km to infinity, where  is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as  . Our target here is to increase this τ by applying a polychromatic field, so that the reaction rate can be enhanced. By applying Simulated Annealing technique we have designed some polychromatic electric fields, spatially symmetric and asymmetric type, which enhances the tunneling rate in symmetric double well system and Eckart barrier confined in an infinite well. |
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| Keywords: | Eckart barrier momentum representation SDWP simulated annealing tunneling probability |
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. In the momentum basis representation, τ can be directly calculated by integrating 
from the limit km to infinity, where 
is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as 
. Our target here is to increase this τ by applying a polychromatic field, so that the reaction rate can be enhanced. By applying Simulated Annealing technique we have designed some polychromatic electric fields, spatially symmetric and asymmetric type, which enhances the tunneling rate in symmetric double well system and Eckart barrier confined in an infinite well.