We propose a dynamical quantum mechanical model to investigate the behavior of localized bound states embedded in a continuously decaying dissipative background field. Reconciling quantum mechanics with general relativity at microscopic scales remains one of the central challenges in theoretical physics. Within the proposed framework, the internalstructure of a bound system continuously responds to the dissipative evolution of its surrounding background. We show that the resulting dynamical resistance can be interpreted, through the equivalence principle, as an effective local gravitational field, thereby giving rise to an emergent spacetime geometry and an intrinsic relativistic time redshift. Based on this framework, we derive a time-dependent (non-autonomous) redshift Schrödinger equation describing the evolution of quantum bound states in a dissipative background. We further demonstrate that, in the deeply bound-state limit, the induced time dilation suppresses the quantum tunneling rate, leading to the spontaneous emergence of Hawking-like quantum radiation. The proposed model provides a unified dynamical framework linking dissipative environmental evolution, effective gravitational fields, relativistic time dilation, and quantum emission processes within non-equilibrium quantum systems, and suggests a possible microscopic route toward the emergence of gravitational phenomena from quantum dynamics.
Liu et al. (Fri,) studied this question.