Threshold-controlled fractional dissipation in open quantum systems

Non-Markovian environments often exhibit power-law memory and intermittent activation, features that cannot be captured by standard Lindblad dynamics. We introduce a threshold-controlled fractional dissipation model in which decoherence is regulated by a sigmoid-type activation function driven by a set of classical control variables representing activation strength, modulation, and threshold level. Combined with a fractional power-law memory kernel, this structure allows dissipation to switch on smoothly whenever an effective activation parameter exceeds its threshold. The resulting dynamics define a controlled interpolation between unitary evolution, standard Lindblad dissipation, and fractional non-Markovian behaviour. Application to a single qubit demonstrates threshold-induced dissipation onset and power-law decoherence, capturing physical scenarios such as switching noise, feedback-driven dissipation, and intermittent environmental coupling. The framework offers a compact and physically motivated tool for studying memory-controlled quantum evolution.