Eur. Phys. J. Plus (2019) 134: 311
https://doi.org/10.1140/epjp/i2019-12672-4

Regular Article

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

¹ Department of Physics, University of Qom, Ghadir Blvd., 371614-6611, Qom, Iran
² Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

^* e-mail: vmousavi@qom.ac.ir

Received: 13 December 2018
Accepted: 8 April 2019
Published online: 28 June 2019

Abstract

A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. If a time-dependent Gaussian ansatz for the probability density is assumed, the effect of thermal fluctuations together with thermal wave packets leads to Bohmian stochastic trajectories. From this trajectory based analysis, quantum and classical diffusion coefficients for free particles, thermal arrival times for a linear potential and transmission probabilities and characteristic times, such as arrival and dwell times for a parabolic repeller, are then presented and discussed.