A new Langevin equation with a field-dependent kernel is proposed to deal with bottomless systems. The corresponding Fokker-Planck equation is shown to be a diffusion-type equation and is solved analytically at any finite fictitious time. The solution generally depends on the choice of initial distribution and has no equilibrium limit. An interesting connection to the ordinary Feynman measure, which in this case is not normalizable, is clarified.
ASJC Scopus subject areas
- Nuclear and High Energy Physics