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

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.

arXiv commentAccepted for publication in The European Physical Journal Plus

References in corpus (16)

• Fast optimal frictionless atom cooling in harmonic traps
• Applied Bohmian Mechanics
• The Schrödinger-Langevin equation with and without thermal fluctuations
• Inverted Oscillator
• Dynamics of Tunneling Ionization using Bohmian Mechanics
• Factorization method and new potentials from the inverted oscillator
• Dissipative tunneling by means of scaled trajectories
• Decoherence at zero temperature
• Weak value of Dwell time for Quantum Dissipative spin-1/2 System
• On the unique mapping relationship between initial and final quantum states
• Time-Dependent Gaussian Solution for the Kostin Equation around Classical Trajectories
• Time in dissipative tunneling: subtleties and applications
• Quantum surface diffusion in Bohmian Mechanics
• The effect of dissipation on quantum transmission resonance
• Hartman effect and dissipative quantum systems
• Bohmian transmission and reflection dwell times without trajectory sampling

Cited by in corpus (6)

• Dissipative quantum backflow
• Dissipative two-identical-particle systems: diffraction and interference
• On non-linear Schrödinger equations for open quantum systems
• Mean square displacement of a free quantum particle in a thermal state
• Stochastic Bohmian and Scaled Trajectories
• Momentum-space decoherence of distinguishable and identical particles in the Caldeira-Leggett formalism