The incommensurate charge density wave states (CDWs) can exhibit steady motion in the flow limit after depinning, behaving as a nonequilibrium system with time-dependent states. Since the moving CDW, like an electric current, breaks both time-reversal and inversion symmetries, one may speculate the emergence of nonreciprocal nonlinear responses from such motion. However, the moving CDW order parameter is intrinsically time-dependent in the lab frame, and it is known to be challenging to evaluate the responses of such a time-varying system. In this work, following the principle of Galilean relativity, we resolve this time-dependent hard problem in the lab frame by mapping the system to the comoving frame with static CDW states through the Galilean transformation. We explicitly show that the nonreciprocal nonlinear responses would be generated by the movement of CDW states through violating Galilean relativity.

不相称的电荷密度波态 （CDW） 在去固定后可以在流动极限中表现出稳定的运动，表现为具有时间依赖性状态的非平衡系统。由于移动的 CDW 就像电流一样，打破了时间反转和反转对称性，因此可以推测这种运动会出现非互易非线性响应。然而，移动 CDW 阶次参数在实验室框架中本质上是瞬态的，众所周知，评估这种时变系统的响应具有挑战性。在这项工作中，遵循伽利略相对论原理，我们通过伽利略变换将系统映射到具有静态 CDW 状态的共动坐标系，从而在实验室坐标系中解决了这个依赖于时间的难题。我们明确表明，非互易非线性响应将由 CDW 状态的运动通过违反伽利略相对论而产生。