UNLABELLED: The Langevin equation is universally applied to describe noise in physical systems of all kinds. To derive it, rather than postulate it, one has to introduce a noise source such as an environment or "reservoir". The solution requires that at some initial time the reservoir is in equilibrium and uncorrelated with the system. This is unphysical and, moreover, in the quantum mechanical case leads to inconsistencies. The way to overcome this anomaly is to consider the equilibrium of system and noise source combined. Then the resulting time-dependent equations for the correlation of various operators can be given. To find out whether they can be reproduced by a Langevin equation, the result is applied to the explicitly solvable system of a harmonic oscillator in a harmonic bath. CONCLUSION: Langevin cannot describe quantum noise but belongs to the realm of mesoscopic physics.
The Langevin equation is universally applied to describe noise in physical systems of all kinds. In order to derive it, rather than postulating it, one has to introduce a noise source such as an environment or “reservoir”. The solution requires that at some initial time the reservoir is in equilibrium and uncorrelated with the system. This is unphysical and moreover, in the quantum mechanical case leads to inconsistencies. The way to overcome this anomaly is by considering the equilibrium of system and noise source combined. The resulting equations for the time dependent correlations between various operators can be computed. In order to find out whether the Langevin equation is able to reproduce the result we consider the explicitly solvable system of a harmonic oscillator in a harmonic bath. Conclusion: Langevin cannot describe quantum noise but belongs to the realm of mesoscopic physics.