  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.
