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 [Formula: see text] 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 [Formula: see text] while in the strong coupling regime it diverges to infinity as [Formula: see text]. We demonstrate it for selected examples of the dissipation mechanisms defined by the memory kernel [Formula: see text] 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 [Formula: see text] of the dissipation function [Formula: see text] at time [Formula: see text] or at the memory time [Formula: see text] which characterizes the degree of non-Markovianity of the Brownian particle dynamics. The impact of low temperature is also presented.