Out-of-Equilibrium Quantum Dynamics

Abstract

We present three general frameworks to describe the dynamics of quantum many-particle systems under continuous observation. In Sect. 4.1, we formulate the dynamics conditioned on the number of quantum jump events, which we term as the full-counting dynamics. We apply it to an exactly solvable model of noninteracting fermions and analyze its out-of-equilibrium dynamics after the quench. We find non-local and chiral propagation of correlations beyond the Lieb-Robinson bound. The unique features originate from the non-Hermiticity of the continuously monitored dynamics and do not appear in the corresponding closed systems or the ensemble-averaged dissipative dynamics. In Sect. 4.2, we formulate the thermalization and heating dynamics in generic many-body systems under measurements. Employing the eigenstate thermalization hypothesis, we show that a generic (nonintegrable) many-body system will thermalize at a single-trajectory level under continuous observation. We provide numerical evidence of our findings by studying specific nonintegrable models that are relevant to state-of-the-art experimental setups in ultracold gases. In Sect. 4.3, we formulate the diffusive dynamics under a minimally destructive spatial observation. We derive the many-body stochastic Schrödinger equation for indistinguishable particles under continuous position measurement. We show that the measurement indistinguishability of particles results in complete suppression of relative positional decoherence, leading to persistent correlations in transport dynamics under measurement. We apply the theory of minimally destructive spatial observation to a setup of ultracold atoms in an optical lattice. In Sect. 4.4, we discuss possible experimental realizations of our theoretical studies presented in this chapter. Finally, we conclude this chapter with an outlook in Sect. 4.5.