The Kanai–Caldirola propagator in the de Broglie–Bohm theory

Tilbi, A; Boudjedaa, T.; Merad, M.; Chétouani, L.

doi:10.1088/0031-8949/75/4/018

Cited by 7 publications

(9 citation statements)

References 14 publications

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“…The results obtained in this paper contradict the previous claims [23,24] that the CK Lagrangian is not valid for the Bateman oscillators but instead it represents a different dynamical system in which mass increases or decreases exponentially in time. As a result of this contradiction, derivations of the Kanai-Caldirola propagator in the de Broglie-Bohm theory [28], which are based on the CK Lagrangian with its mass being time-dependent [29], must be taken with caution.…”

Section: Discussionmentioning

confidence: 99%

Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

Vestal

Musielak

2021

Physics

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The Lagrange formalism is developed for Bateman oscillators, which includes both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, the corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed.

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Section: Discussionmentioning

confidence: 99%

Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

Vestal

Musielak

2021

Physics

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“…Ten years later, Shojai and Shojai analyzed [32] the problem of friction of two-level system transition by reformulating such a problem in Bohmian terms. At a more practical level, Tilbi et al [33] used Bohmian mechanics to derive an expression of the Caldirola-Kanai propagator starting from the Feynman path integral approach. In this regard, apart from offering a Bohmian description of dissipative systems within the Caldirola-Kanai context, another purpose of this 2 work is to establish a general hydrodynamic dissipative framework (within this model) where the use of transformations that make the system to satisfy the uncertainty relations [8,[16][17][18] is not necessary.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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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).

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“…In this regard, the first study was carried out about 22 years ago by Vandyck, who investigated the decay of the harmonic oscillator eigenstates, lossing the energy [18]. Also, Tilbi and others used Bohmian mechanics to derive an expression for the damping harmonic oscillator, albeit in the Feynman path integral approach [19].…”

Section: Introductionmentioning

confidence: 99%

Langevin equation for a dissipative macroscopic quantum system: Bohmian theory versus quantum mechanics

Naeij

Shafiee

2019

Quantum Stud.: Math. Found.

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In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the system using two approaches: Quantum Mechanics and Bohmian Theory. Our results show that the predictions of the two theories are inherently different in real conditions. Nevertheless, the Langevin equation obtained by Bohmian approach could be reduced to the quantum one, when the vibrational frequency of the central system is high enough compared to the frequency of the environmental particles.

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The Kanai–Caldirola propagator in the de Broglie–Bohm theory

Cited by 7 publications

References 14 publications

Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions

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

Langevin equation for a dissipative macroscopic quantum system: Bohmian theory versus quantum mechanics

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