  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.
