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Simulated annealing‐based optimal control over tunneling process through SDWP and E ckart barrier: A momentum basis representation
Author(s) -
Talukder Srijeeta,
Chaudhury Pinaki,
Ghosh Subhasree
Publication year - 2017
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25388
Subject(s) - quantum tunnelling , position and momentum space , rectangular potential barrier , momentum (technical analysis) , wave function , basis (linear algebra) , physics , space (punctuation) , electric field , chemistry , quantum mechanics , mathematics , geometry , linguistics , philosophy , finance , economics
For a reaction to proceed via tunneling mechanism, it is essential that the reactants will cross the potential barrier ( E P ), where its initial energy ( E 0 ) is below the potential barrier E P . Tunneling probability τ is defined as the probability of having momentum higher than k m , wherek m = ( 2 m E P ). In the momentum basis representation, τ can be directly calculated by integrating | ψ ( k ) | 2from the limit k m to infinity, where ψ ( k ) is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as τ =∑k i = k m∞ | ψ ( k i ) | 2. 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.