Nonequilibrium stationary states of quantum non-Hermitian lattice models

We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing appropriate open quantum system. focus on the steady states of such for both fermionic and bosonic systems. Surprisingly, key features spatial structures state cannot simply understood from Hamiltonian alone. Using 1D Hatano-Nelson model as a paradigmatic example, we that has marked sensitivity to boundary conditions. This dependence however is qualitatively quantitatively distinct skin effect, no simple connection topology. Further, particle statistics play unexpected role: steady-state density profile dramatically different fermions versus bosons. Our work highlights role fluctuations realizations dynamics, provides starting point future engineered