https://doi.org/10.1140/epjd/s10053-025-01090-y
Research - Photon
Time-dependent oscillators with asymptotically increasing mass: classical and coherent state dynamics
Department of Physics, Faculty of Engineering and Natural Sciences, Hitit University, 19030, Çorum, Türkiye
Received:
20
August
2025
Accepted:
27
October
2025
Published online:
5
November
2025
In this study, we investigate the classical and quantum dynamics of a harmonic oscillator with a mass that increases over time and asymptotically approaches a finite limit. The mass evolution is modeled by a logistic-type growth law, which leads to the disappearance of the effective damping in the longtime limit. Two scenarios are considered: (i) the case of a constant spring constant, corresponding to a parametric oscillator with decreasing frequency, and (ii) the case of a constant natural frequency, where the stiffness increases proportionally with the mass. In the classical regime, we derive the exact equations of motion, analyze phase-space trajectories, and examine the time evolution of the total energy. In both cases, as 
, the oscillator approaches a stable periodic motion with constant energy. In the quantum regime, we employ the SU(1,1) coherent state formalism to obtain semiclassical equations of motion and compare them with the classical results. The analytical results obtained are supported by numerical simulations.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
