Role of $PT$-symmetry in understanding Hartman effect

Hasan, Mohd.; Singh, Vibhav Narayan; Mandal, Bhabani Prasad

doi:10.48550/arxiv.2004.14815

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Generalized Hartman Effect1

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2020

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“…This is to be noted that the result represented by Eq. 15 have been found in [10,11] for real 'unit cell' potential and in [26,27] for P T -symmetric 'unit cell' potential. In all these cases, the 'unit cell' potentials show Hartman effect.…”

Section: Generalized Hartman Effectmentioning

confidence: 84%

General(ized) Hartman effect

Hasan,

Mandal

2020

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In this letter we prove explicitly that if Hartman effect exists for an arbitrary 'unit cell' potential, then it also exist for a periodic system constructed using the same 'unit cell' potential repeatedly. We further show that if Hartman effect exists, the tunneling time in the limiting case of a sufficiently thick 'unit cell' potential is same as that of its periodic system. This is true for any arbitrary value of the intervening gap between the consecutive 'unit cell' of the periodic system. Thus generalized Hartman effect always occurs for a general potential constructed using multiple copies of single potential which shows Hartman effect.

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