Please use this identifier to cite or link to this item:
Title: 1D tight-binding models render quantum first passage time “Speakable”
Authors: Ranjith, V.
Kumar, N.
Keywords: Tunneling time
Time in quantum mechanics
Issue Date: Dec-2015
Publisher: Springer Verlag
Citation: International Journal of Theoretical Physics, 2015, Vol. 54, p4204-4213
Abstract: The calculation of First Passage Time (moreover, even its probability density in time) has so far been generally viewed as an ill-posed problem in the domain of quantum mechanics. The reasons can be summarily seen in the fact that the quantum probabilities in general do not satisfy the Kolmogorov sum rule: the probabilities for entering and non-entering of Feynman paths into a given region of space-time do not in general add up to unity, much owing to the interference of alternative paths. In the present work, it is pointed out that a special case exists (within quantum framework), in which, by design, there exists one and only one available path (i.e., door-way) to mediate the (first) passage –no alternative path to interfere with. Further, it is identified that a popular family of quantum systems – namely the 1d tight binding Hamiltonian systems – falls under this special category. For these model quantum systems, the first passage time distributions are obtained analytically by suitably applying a method originally devised for classical (stochastic) mechanics (by Schroedinger in 1915). This result is interesting especially given the fact that the tight binding models are extensively used in describing everyday phenomena in condense matter physics.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 0020-7748 (Print)
1572-9575 (Online)
Alternative Location:
Copyright: 2014 Springer
Appears in Collections:Research Papers (TP)

Files in This Item:
File Description SizeFormat 
  Restricted Access
Restriced Access374.38 kBAdobe PDFView/Open Request a copy

Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.