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**Dissipative effect and tunneling time.**
*(English)*
Zbl 1241.82055

Summary: The quantum Langevin equation is studied for a dissipative system using the approach due to G. W. Ford, J. T. Lewis and R. F. O’Connell [“Dissipative quantum tunneling: quantum Langevin equation approach”, Phys. Lett., A 128, No. 1–2, 29–34 (1988; doi:10.1016/0375-9601(88)91037-7)]. Here, we have considered the inverted harmonic oscillator potential and calculated the effect of dissipation on tunneling time, group delay, and the self-interference term. A critical value of the friction coefficient has been determined for which the self-interference term vanishes. This approach sheds new light on understanding the ion transport at nanoscale.

### MSC:

82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |

82C27 | Dynamic critical phenomena in statistical mechanics |

82D80 | Statistical mechanics of nanostructures and nanoparticles |

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\textit{S. Bhattacharya} and \textit{S. Roy}, Adv. Math. Phys. 2011, Article ID 138358, 13 p. (2011; Zbl 1241.82055)

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### References:

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