A Velocity-Dependent Threshold for Quantum Coherence in Open Systems.

This work introduces a velocity-dependent threshold,v_char, as a critical parameter for quantum coherence in open systems. This characteristic velocity arises when the system’s intrinsic dynamical timescale,T_dyn, becomes comparable to its velocity-dependent environmental decoherence timescale,T_coh(v). The concept is analyzed for free particles and confined systems. For decoherence mechanisms where the rate increases with velocity,v >> v_charsignifies decoherence dominance, while forv << v_char, coherent evolution should prevail. Expressions forv_charare derived under collisional decoherence and a thermal photon-induced decoherence model where the rateΓ_photon = Λ_γ T³ v. Experimental frameworks (trapped ions, BEC interferometry, nanomechanical resonators), considering practical feasibility such as cryogenic tuning, are proposed. This investigation suggests velocity control as a means for managing quantum coherence, primarily within the Markovian approximation, and notes the need for further study in non-Markovian regimes.