Star exponentials and Wigner functions for time-dependent harmonic oscillators

• URL: http://arxiv.org/abs/2503.06384v1
• Date: Sun, 09 Mar 2025 01:43:07 GMT
• Title: Star exponentials and Wigner functions for time-dependent harmonic oscillators
• Authors: Jasel Berra-Montiel, Daniel Contreras-Bear, Alberto Molgado, Mar Sanchez-Cordova,
• Abstract summary: We explore the connection between the star exponential and the propagators constructed through the path integral formalism.<n>By introducing a judicious time variable, we recovered a time-dependent phase function associated with the Lewis-Riesenfeld construction of the standard Schr"odinger picture.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore the connection between the star exponential, naturally emerging within the context of deformation quantization, and the propagators constructed through the path integral formalism. In particular, the Fourier-Dirichlet expansion of the star exponential implies a distinctive quantization of the Lewis-Riesenfeld invariant. Further, by introducing a judicious time variable, we recovered a time-dependent phase function associated with the Lewis-Riesenfeld construction of the standard Schr\"odinger picture. In particular, we applied our results to the cases of the Caldirola-Kanai and the time-dependent frequency harmonic oscillators, recovering relevant results previously reported in the literature.

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