Quantum Dynamics under continuous projective measurements: non-Hermitian
description and the continuous space limit
- URL: http://arxiv.org/abs/2012.01196v3
- Date: Mon, 28 Dec 2020 08:52:35 GMT
- Title: Quantum Dynamics under continuous projective measurements: non-Hermitian
description and the continuous space limit
- Authors: Varun Dubey and Cedric Bernardin and Abhishek Dhar
- Abstract summary: The time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol.
For a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The problem of the time of arrival of a quantum system in a specified state
is considered in the framework of the repeated measurement protocol and in
particular the limit of continuous measurements is discussed. It is shown that
for a particular choice of system-detector coupling, the Zeno effect is avoided
and the system can be described effectively by a non-Hermitian effective
Hamiltonian. As a specific example we consider the evolution of a quantum
particle on a one-dimensional lattice that is subjected to position
measurements at a specific site. By solving the corresponding non-Hermitian
wave function evolution equation, we present analytic closed-form results on
the survival probability and the first arrival time distribution. Finally we
discuss the limit of vanishing lattice spacing and show that this leads to a
continuum description where the particle evolves via the free Schrodinger
equation with complex Robin boundary conditions at the detector site. Several
interesting physical results for this dynamics are presented.
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