Nonequilibrium Quantum Brownian Motion

Every realistic quantum mechanical system is an open one as long as we define the whole collection of the all other ones to be its environment, whose interaction strength with the system that attracts our interests would varies but never vanishes thoroughly. Although being complex and uncontrollable for most of the times, when its influence on the dynamics of system alone is of the only importance the environment could be mathematically simulated or constructed by simplified statistical models of which the simple harmonic oscillator bath being an excellent one since typical environments such as electromagnetic field and phonon field are themselves sets of quantum harmonic oscillators. After all, to investigate the most fundamental laws of physics one has to focus his mind, if the errors introduced by simplification and modeling are acceptable, to the key point of the matter, namely the system of interests.Advances in two distinguished areas intrigued our mind to this research of nonequilibrium Brownian motion. O ne of the advances, dealing with complex systems and networks, is called the theorem of landscape and flux which at nonequilibrium steady state can illustrate the mechanisms that probability theory or the second law of thermodynamics cannot completely explain because of the breakdown of detail balance and the net curl flux thus caused. Its success in biological and chemical systems by considering the key concept of nonlocal flux sheds lights on one possible understanding of another nonlocal quantity named entanglement in 1935 that has confused the most brilliant brains in the universe ever since as well as ours. Unambiguously they are two different nonlocal concepts, but some argument that the imaginary part of quantum coherence quantified by one special off-diagonal element in the density matrix would be a function of nonequilibriumness draws pretty much attention from us back into the similarity instead of the difference of the two kind of nonlocal quantities. The other advance in physics that seems more relative to the investigation of nonequilibrium Brownian motion is the time-dependent coupling of Brownian particles in the research of entanglement survival in hot temperature limit that produced amazing results. Nonequilibriumness in another form enhancing the entanglement tempted physicists and engineers and we wonder whether it’s possible to realize that fantasy in the form of nonequilibrium steady state.Some discussion of the technics in quantifying entanglement is provided and it seems that few is satisfying. We thus guess that under current comprehension of entanglement and by means of current technics nonequilibriumness in steady state may probably be trivial in enhancing entanglement thus the nonlocalities in global flux and entanglement may be absolutely irrelevant. But we are still far from drawing any scientific conclusion about this, since we can even not unambiguously quantify entanglement in a continuous variable bipartite system in nonequilibrium quantum steady state, which as a result seems to be one of the most interesting and profound topics in theoretical physics and quantum engineering and information.