Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 48, Issue 11, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/48/11/115304
Keywords
quantum time of arrival; first passage problem; quantum measurement
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Funding
- CSIR, India [09/028(0839)/2011-EMR-I]
- UGC-UPE (University of Calcutta)
- DST
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Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is the time of arrival (TOA) of the particle at the detector ? Within the paradigm of the measurement postulate of quantum mechanics, one can use the idea of projective measurements to define the TOA. We consider a setup where a detector keeps making instantaneous measurements at regular finite time intervals until it detects the particle at time t, which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.
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