Quantum Dynamics under Competing Strong and Weak Measurements

A quantum system interacting with its environment is often described by a Lindblad master equation under the Markov assumption, capturing both coherent and dissipative dynamics. When the coherent and dissipative terms are time-independent, the system generally evolves toward a unique nonequilibrium steady state, independent of the initial conditions. In contrast, purely unitary evolution can be directed into specific states using local projective measurements followed by feedback operations. In this talk, we will explore the interplay between these two mechanisms in the context of a competition between strong, projective measurements and weaker, environment-induced measurements. Focusing on the nonequilibrium many-body dynamics of interacting spins, we will examine how this competition shapes the driven dissipative many-body evolution.