Time reversed states in barrier tunneling

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 149; p. 115680
• Main Authors: Meena, Kanchan, Singha Deo, P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2023
• Subjects: Analytical continuation; Density of States; Evanescent modes; Larmor clock; Local partial density of States; Tunneling current; Local partial density of States; Evanescent modes; Density of States; Tunneling current; Larmor clock; Analytical continuation
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2023.115680

Tunneling, though a physical reality, is shrouded in mystery. Wave packets cannot be constructed under the barrier and group velocity cannot be defined. The tunneling particle can be observed on either side of the barrier but its properties under the barrier has never been probed due to several problems related to quantum measurement. We show that there are ways to bypass these problems in mesoscopic systems and one can even derive an expression for the quantum mechanical current under the barrier. A general scheme is developed to derive this expression for any arbitrary system. One can use mesoscopic phenomena to subject the expression to several theoretical and experimental cross checks. For demonstration we consider an ideal 1D quantum ring with Aharonov–Bohm flux Φ, connected to a reservoir. It gives clear evidence that propagation occur under the barrier resulting in a current that can be measured non-invasively and theoretically cross checked. Time reversed states play a role but there is no evidence of violation of causality. The evanescent states are known to be largely stable and robust against phase fluctuations making them a possible candidate for device applications and so formalizing the current under the barrier is important.