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)similar to c ln(1/c) while in the strong coupling regime it diverges to infinity as E(c)similar to root 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.

Automated summary

Experimentalists have achieved temperatures very close to absolute zero, where quantum effects and fluctuations play a dominant role. The study shows that the energy of particles changes differently with increasing coupling strength, and the impact of dissipation models on energy is also varied.