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A Bohmian analysis of the so-called Schr\"{o}dinger-Langevin or Kostinnonlinear differential equation is provided to study how thermal fluctuationsof the environment affects the dynamics of the wave packet from a quantumhydrodynamical point of view. In this way, after obtaining theSchr\"{o}dinger-Langevin-Bohm equation from the Kostin equation its applicationto simple but physically insightful systems such as the Brownian-Bohmianmotion, motion in a gravity field and transmission through a parabolic repelleris studied. % If a time-dependent Gaussian ansatz for the probability densityis assumed, the effect of thermal fluctuations together with thermal wavepackets leads to Bohmian stochastic trajectories. From this trajectory basedanalysis, quantum and classical diffusion coefficients for free particles,thermal arrival times for a linear potential and transmission probabilities andcharacteristic times such as arrival and dwell times for a parabolic repellerare then presented and discussed.

the european physical journal plus

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