Energy of a free Brownian particle coupled to thermal vacuum.

Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary. In such a regime quantum effects and fluctuations start to play a dominant role. In this context we study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum, i.e. thermostat in the limiting case of absolute zero temperature. We analyze the average energy $$E=E(c)$$ of the particle from a weak to strong interaction strength c between the particle and thermal vacuum. The impact of various dissipation mechanisms is considered. In the weak coupling regime the energy tends to zero as $$E(c) \sim c\, \ln {(1/c)}$$ while in the strong coupling regime it diverges to infinity as $$E(c) \sim \sqrt{c}$$ . We demonstrate it for selected examples of the dissipation mechanisms defined by the memory kernel $$\gamma (t)$$ of the Generalized Langevin Equation. We reveal how at a fixed value of c the energy E(c) depends on the dissipation model: one has to compare values of the derivative $$\gamma '(t)$$ of the dissipation function $$\gamma (t)$$ at time $$t=0$$ or at the memory time $$t=\tau _c$$ which characterizes the degree of non-Markovianity of the Brownian particle dynamics. The impact of low temperature is also presented.