Stochastic process emerged from lattice fermion systems by repeated measurements and large-time limit

TL;DR

This paper demonstrates that repeated long-time measurements on lattice fermion systems lead to the emergence of a stochastic process, specifically the symmetric simple exclusion process, independent of the system's potential and interactions.

Contribution

It introduces a new scaling regime where measurement effects and Hamiltonian dynamics balance, resulting in the emergence of a classical stochastic process from quantum many-body systems.

Findings

The symmetric simple exclusion process (SSEP) emerges from repeated measurements.

Emergence of SSEP is independent of potential and interactions.

Long-time measurement scaling leads to classical stochastic dynamics.

Abstract

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.