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1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''

Ranjith, V and Kumar, N (2015) 1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''. In: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 54 (12). pp. 4204-4213.

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Official URL: http://dx.doi.org/10.1007/s10773-014-2385-1


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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the SPRINGER/PLENUM PUBLISHERS, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords: Quantum first-passage time; Arrival time; Tunneling time; Time in quantum mechanics
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 02 Dec 2015 08:23
Last Modified: 02 Dec 2015 08:23
URI: http://eprints.iisc.ac.in/id/eprint/52834

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