Description |
Imagine an experiment where a quantum-mechanical particle is released from
some fixed region inside a box. On one side of the box there is a screen
with detectors which click as soon as the particle "arrives" at the screen. One expects that the time of arrival of the particle is a stochastic variable and it is interesting to ask for it's probability distribution.
This is similar to asking for the distribution of the time of absorption of Brownian particle at some point. In this talk, an attempt will be made to explain why the quantum problem is subtle, and our recent attempts at understanding this in a framework where repeated projective measurements
are made to detect the particle. This leads to a non-unitary time evolution
of the wave-function of the particle, and we show that this is well described by an effective non-Hermitiian Hamiltonian. For some simple lattice models, we find power-law tails for the probability that the particle survives detection up to some time.
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