  It is known that in quantum theory, measurements may suppress Hamiltonian
dynamics of a system. A famous example is the `Quantum Zeno Effect'. This is
the phenomena that if one repeats the measurements many times asking whether
the system is in the same state as the one at the initial time until the fixed
measurement time, then survival probability tends to 1 by taking the
measurement interval to 0. This is the case for fixed measurement time. It is
known that if one takes measurement time infinite at appropriate scaling,
`Quantum Zeno Effect' does not occur and the effect of Hamiltonian dynamics
emerges (Facchi and Ligabo 2017). In the present paper, we consider the long
time repeated measurements and the dynamics of quantum many body systems in the
scaling where the effect of measurements and dynamics are balanced. We show
that the stochastic process, called symmetric simple exclusion process (SSEP),
is obtained from the repeated and long time measurements of configuration of
particles in finite lattice fermion systems. The emerging stochastic process is
independent of potential and interaction of the underlying Hamiltonian of the
system.
