Dissipative Bohmian mechanics within the Caldirola-Kanai framework: A trajectory analysis of wave-packet dynamics in viscid media

TL;DR

This paper explores how a hypothetical quantum viscid medium affects wave-packet dynamics using Bohmian mechanics within the Caldirola-Kanai framework, revealing localization effects and quantum-classical correspondence through analytical and numerical analysis.

Contribution

It provides a novel Bohmian trajectory analysis of quantum friction effects in viscid media modeled by the Caldirola-Kanai Hamiltonian, including new insights into wave-packet behavior.

Findings

Localization by quantum freezing observed in wave packets

Quantum-classical correspondence demonstrated in viscid media

Numerical simulations confirmed analytical results

Abstract

Classical viscid media are quite common in our everyday life. However, we are not used to find such media in quantum mechanics, and much less to analyze their effects on the dynamics of quantum systems. In this regard, the Caldirola-Kanai time-dependent Hamiltonian constitutes an appealing model, accounting for friction without including environmental fluctuations (as it happens, for example, with quantum Brownian motion). Here, a Bohmian analysis of the associated friction dynamics is provided in order to understand how a hypothetical, purely quantum viscid medium would act on a wave packet from a (quantum) hydrodynamic viewpoint. To this purpose, a series of paradigmatic contexts have been chosen, such as the free particle, the motion under the action of a linear potential, the harmonic oscillator, or the superposition of two coherent wave packets. Apart from their analyticity, these examples illustrate interesting emerging behaviors, such as localization by "quantum freezing" or a particular type of quantum-classical correspondence. The reliability of the results analytically determined has been checked by means of numerical simulations, which has served to investigate other problems lacking of such analyticity (e.g., the coherent superpositions).