Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

We numerically investigate the quantum transport in a coupled kicked rotors with $\mathcal{PT}$-symmetric potential. find that spontaneous $\mathcal{PT}$-symmetry breaking of wavefunctions emerges when amplitude imaginary part complex potential is beyond threshold value, which can be modulated by coupling strength effectively. In regime breaking, particles driven periodical kicks move unidirectionally momentum space, indicating emergence directed current. Meanwhile, increasing strength, we transition from ballistic energy diffusion to kind modified where width wavepacket also increases time power law. Our findings suggest decoherence effect induced interplay between inter-particle and non-Hermitian driving responsible for these particular behaviors.