A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation

The Schrödinger–Langevin equation with and without thermal fluctuations

“…proportional to the particle velocity). A nonlinear friction can be obtained by extending Kostin derivation to a nonlinear coupling [28,29]. The SLE exhibits interesting properties: unitarity is preserved at all times [24], the uncertainty principle is always satisfied 2 [31,32,33] and the superposition principle is violated due to the nonlinearities (which might not be a problem per se for dissipative equations [34,35]).…”

Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

“…1(b), the final wave function is in excellent agreement with the ground state wave function in Eq. (15). [70][71][72][73][74], these Bohmian trajectories follow the main features of the evolving probability density, and they finally become stationary.…”

“…In addition, this equation has been propagated for obtaining the ground states of several one-dimensional quantum systems [13]. Moreover, the nonlinear Schrödinger-Langevin equation has been generalized for quantum processes in the presence of nonlinear friction and a heat bath [14], and a non-Markovian nonlinear Schrödinger-Langevin equation has been derived from the system-plus-bath approach [15].…”

Trajectory description of the quantum–classical transition for wave packet interference

“…Recently, dissipative Bohmian trajectories have been analyzed within the Caldirola-Kanai framework [27]. In addition, the nonlinear Schrödinger-Langevin equation has been generalized for quantum processes in the presence of nonlinear friction and a heat bath [28,29], and this equation has been solved for the ground state of quantum systems by propagating quantum trajectories [30,31]. Remarkable progress has been made in the development and application of real-valued quantum trajectories for providing an analytical, interpretative, and computational framework for quantum dynamical problems [3,[32][33][34][35].…”