# Stochastic Bohmian mechanics within the Schr\"{o}dinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

## TL;DR

This paper develops a stochastic Bohmian framework within the Schr"{o}dinger-Langevin equation to analyze wave-packet dynamics in dissipative environments, revealing how thermal fluctuations influence quantum trajectories and transport properties.

## Contribution

It introduces a Bohmian stochastic approach to the Schr"{o}dinger-Langevin equation, providing new insights into wave-packet behavior under thermal fluctuations in dissipative media.

## Key findings

- Derived quantum and classical diffusion coefficients.
- Analyzed thermal arrival times in linear potentials.
- Computed transmission and dwell times in a parabolic barrier.

## Abstract

A Bohmian analysis of the so-called Schr\"{o}dinger-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 Schr\"{o}dinger-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.