Quantum dynamics of non-Hermitian many-body Landau-Zener models

Non-Hermiticity in quantum systems has unlocked a variety of exotic phenomena in topological systems with no counterparts in Hermitian physics. The quantum systems often considered are time-independent and the non-Hermiticity can be engineered via controlled gain and loss. In contrast, the investigations of explicitly time-dependent quantum systems are limited. Recently, the simplest time-dependent non-Hermitian parity-time ($\mathcal{PT}$) symmetric variants of the Landau-Zener (LZ) model have been explored. Here, we introduce and outline a framework to solve a class of non-Hermitian many-body Hamiltonians linearly driven in time. Such models have practical implications and can describe the dynamics of multi-species bosonic systems. Moreover, we observe the emergence of a new conservation law, which is unique to this class of Hamiltonians that reveals a pair-production mechanism of a non-Hermitian origin. Our findings will open new avenues for more emergent phenomena in explicitly time-dependent non-Hermitian quantum systems.