On the connection between the Wigner and the Bohm quantum formalism

Morandi, Omar

doi:10.1016/j.physleta.2022.128223

Cited by 4 publications

(2 citation statements)

References 45 publications

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“…This property is typically interpreted as the expression of the non-local nature of the quantum motion. Various representations of the particle evolution in which the quantum motion is represented by using a language derived from the classical mechanics, as for example the Wigner quasi-distribution function or the complex classical mechanics, share a similar interpretation [44][45][46][47][48][49][50]. In the framework of the so called classical wave function formalism, a comparison between the quantum Bohm trajectories obtained by the interference of Gaussian packets and their classical limit, is discussed in [36].…”

Section: Test Case: Reflecting Gaussian Wavementioning

confidence: 99%

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

Morandi¹

2022

J. Phys. A: Math. Theor.

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The phase of a single valued wave function with local zeros (nodes), is globally represented by a function connecting different branches of Riemann sheets. We investigate the mathematical limitations and the loss of regularity associated to such a global representation of the quantum phase. Our study is based on a geometrical description of the dynamics of one-dimensional quantum systems. We develop a mathematical model based on the Bohm formalism of quantum mechanics where the quantum dynamics is described in terms of horizontal lifts associated to a Ehresmann connection. We express the non triviality of the bundle in terms of holonomy along loops delimited by Bohm trajectories. We assume that the nodes of the wave function form a discrete set of points in the spacetime and we show that the connection becomes singular on this set. We perform a local study of the behaviour of the Bohm trajectories around the singularities and we provide a control on the Bohm potential by deriving semi-analytical expressions for the particle trajectories. We express the total phase rotation along a loop in terms of the derivative of the quantum current evaluated on the set of nodes inside the loop.

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Section: Test Case: Reflecting Gaussian Wavementioning

confidence: 99%

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

Morandi¹

2022

J. Phys. A: Math. Theor.

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“…A general introduction ot the Wigner formalism can be found in books and reviews [15][16][17][18]. Mathematical properties and relevant asymptotic regimes associated to the Wigner formalism, have been also subjects of extended studies [36][37][38][39][40]. The optical geometry limit shares some similarity with the semi-classical limit in quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Phase space propagation of waves in nonhomogeneous media: corrections beyond the optical geometry limit

Morandi

2024

J. Phys. A: Math. Theor.

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We investigate the corrections to the optical geometry approximation for waves traveling in non homogeneous media. We model the wave propagation in dispersive and non dispersive materials in terms of the phase space Wigner-Weyl formalism. The ray tracing optical geometry limit is introduced visually by numerical tests. We solve the exact Wigner propagation equation for 1D non dispersive materials. We discuss the connection of the Wigner-Weyl description of waves with the particle-wave duality phenomenon in quantum mechanics.

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Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

Morandi

2024

Physics Letters A

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On the connection between the Wigner and the Bohm quantum formalism

Cited by 4 publications

References 45 publications

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

Geometric phase of quantum wave function and singularities of Bohm dynamics in a one-dimensional system

Phase space propagation of waves in nonhomogeneous media: corrections beyond the optical geometry limit

Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

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