Small coupling strength is not the necessary condition for strong-coupling effects to disappear

Lots of dynamics of microscopic systems are described by the Langevin equation that contains no terms depending on the interaction between the system and the environment, although the system energy scale is comparable to that of the interaction. One might guess that this weak-coupling feature originates from a small coupling strength. But the small coupling strength limit is unreasonable because it leads the system to evolve deterministically with decoupled from the environment. In this presentation, we show the condition for strong-coupling effects to disappear regardless of the coupling strength. For this purpose, we consider a strongly-coupled system evolving deterministically coupled to the bath particles in the Langevin thermostat. By taking the limit as the relaxation time of the bath goes to zero, we derive the stochastic equation of motion for the reduced dynamics. This equation contains two interaction-dependent terms, (i) an additional potential and (ii) an effective damping tensor. By revealing the condition where the conventional weakly-coupled Langevin equation is restored even with a finite coupling strength, we confirm that a small coupling is not the necessary condition for strong-coupling effects to vanish. We verify our result numerically in systems with various forms of the interaction potential. We show that when the condition is satisfied, the interaction form has no influence on the equation of motion for the reduced system.