The generalized Schrodinger-Langevin equation

In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrodinger-Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. (C) 2014 Elsevier Inc. All rights reserved.