The effect of stochastic barrier fluctuation on semiclassical transmission probability and Shannon entropy of a symmetric double well potential. Issue 17 (13th August 2018)

• Record Type: Journal Article
• Authors: Naskar, Pulak; Talukder, Srijeeta; Chaudhury, Pinaki; Ghosh, Subhasree
• Is Part Of: International journal of quantum chemistry. Volume 118:Issue 17(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-08-13
• Subjects: barrier fluctuation -- Hellmann–Feynman energy -- Shannon entropy -- TDFGH -- transmission probability; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.25667
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: Stochastic fluctuation of barrier height and width of a symmetric double well plays a very significant role in the corresponding dynamics by increasing the semiclassical transmission probability and Shannon entropy of the system. The population of the system has been observed to be spread into several under barrier states starting from the Ψ L or Ψ R [ Ψ L, R = 1 2 ( Ψ + ± Ψ − ), where Ψ + and Ψ − are the wave functions describing the two lowest degenerate states] in presence of the stochastic fluctuation. This distribution over several states is manifested by steady increase in Shannon entropy. However, any arbitrary value of the stochastic fluctuation cannot increase the populations of the upper energy states and consequently no gain in the net value of Shannon entropy results. There is an optimum frequency for which the Shannon entropy passes through a maximum, which is also found out in this work. We have also calculated the semiclassical WKB like transmission probability as a function of time and it is clear that the random fluctuation of barrier causes the transmission probability to increase to a significant amount. As the total energy of the system remains below the potential barrier, this transmission probability is equivalent to tunneling probability. It has been clearly shown that if the fluctuation is made to be periodic (without changing the frequency and magnitude of the fluctuation) it cannot effect any significant change in the overall dynamics. Abstract : Periodic fluctuation of barrier has almost no effect on a proton moving in a symmetric double well potential, whereas a random fluctuation can make the system to spread its population in higher energy levels. Consequently, Shannon entropy, H‐F energy and semiclassical tunneling probability are also increased in case of random fluctuation of the barrier. Moreover, there is an optimum fluctuation frequency for which each of the above properties go through a maximum.