We report extensive numerical studies of the dynamics of a classical particle in an anharmonic one-dimensional potential while it is harmonically coupled to three different many-particle systems. The studies address the comparatively simpler dynamical problem when the energy of the anharmonic oscillator is sufficiently low. The first model is one in which the many-particle system is a chain of harmonic oscillators that have nearest-neighbor harmonic interactions. The anharmonic oscillator is connected to every harmonic oscillator via harmonic springs. The second model is identical to the first except that each oscillator is subjected to an additional one-body harmonic potential. The third model is identical to the second except that the nearest-neighbor couplings between the individual harmonic oscillators are absent, i.e., the oscillators are decoupled with respect to one another. In the first model we find that the lowest frequency of the anharmonic oscillator, while possessing a lower bound, increases as $\ensuremath{\omega}\ensuremath{\propto}\sqrt{\mathrm{NK}},$ where $N$ is the number of oscillators in the bath and $K$ is the force constant describing the strength of interaction between the anharmonic oscillator and the interacting harmonic many-body system. In the second model we find aspects of dynamical correlations as seen in the canonical ensemble and a dominant frequency that increases as $\sqrt{\mathrm{NK}}.$ We recover the dynamical correlations of the anharmonic oscillator as obtained within the framework of a canonical ensemble [S. Sen, R. S. Sinkovits, and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996)] in the third model for sufficiently many harmonic oscillators. We comment briefly on an alternate way to correctly model heat baths for numerical studies on the dynamics of physical systems using canonical ensembles.We report extensive numerical studies of the dynamics of a classical particle in an anharmonic one-dimensional potential while it is harmonically coupled to three different many-particle systems. The studies address the comparatively simpler dynamical problem when the energy of the anharmonic oscillator is sufficiently low. The first model is one in which the many-particle system is a chain of harmonic oscillators that have nearest-neighbor harmonic interactions. The anharmonic oscillator is connected to every harmonic oscillator via harmonic springs. The second model is identical to the first except that each oscillator is subjected to an additional one-body harmonic potential. The third model is identical to the second except that the nearest-neighbor couplings between the individual harmonic oscillators are absent, i.e., the oscillators are decoupled with respect to one another. In the first model we find that the lowest frequency of the anharmonic oscillator, while possessing a lower bound, increases as $\ensuremath{\omega}\ensuremath{\propto}\sqrt{\mathrm{NK}},$ where $N$ is the number of oscillators in the bath and $K$ is the force constant describing the strength of interaction between the anharmonic oscillator and the interacting harmonic many-body system. In the second model we find aspects of dynamical correlations as seen in the canonical ensemble and a dominant frequency that increases as $\sqrt{\mathrm{NK}}.$ We recover the dynamical correlations of the anharmonic oscillator as obtained within the framework of a canonical ensemble [S. Sen, R. S. Sinkovits, and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996)] in the third model for sufficiently many harmonic oscillators. We comment briefly on an alternate way to correctly model heat baths for numerical studies on the dynamics of physical systems using canonical ensembles.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJan 1, 19989 citations

THE THREE-DIMENSIONAL HARMONIC OSCILLATOR

WORLD SCIENTIFIC eBooksJun 1, 20050 citations

The theory of the anharmonic oscillator

K. S. Viswanathan

Proceedings of the Indian Academy of Sciences - Section ASep 1, 195710 citations

Observation of quantum oscillations in the extreme weak anharmonic limit

A. Théry, B. Neukelmance, B Hue +7 more

We investigate a granular aluminium quantum circuit with an anharmonicity of the order of its decoherence rate in a three-dimensional microwave cavity. We perform single qubitlike manipulations such as Rabi oscillations and Ramsey fringes. Our findings, supported by quantitative numerical modeling, show that a very weakly anharmonic oscillator can also display quantum oscillations outside the qubit regime. These oscillations are hard to disambiguate from qubit oscillations in time domain measurements for a single driving frequency. This sheds light on recent findings for material superconducting quantum bits. Our platform shows in addition large magnetic field resilience which could find applications for quantum enhanced dark matter search.We investigate a granular aluminium quantum circuit with an anharmonicity of the order of its decoherence rate in a three-dimensional microwave cavity. We perform single qubitlike manipulations such as Rabi oscillations and Ramsey fringes. Our findings, supported by quantitative numerical modeling, show that a very weakly anharmonic oscillator can also display quantum oscillations outside the qubit regime. These oscillations are hard to disambiguate from qubit oscillations in time domain measurements for a single driving frequency. This sheds light on recent findings for material superconducting quantum bits. Our platform shows in addition large magnetic field resilience which could find applications for quantum enhanced dark matter search.

arXiv:2401.04227Physical review. B./Physical review. BFeb 14, 20246 citations

The One-Dimensional Harmonic Oscillator

John P. Lowe, Kirk A. Peterson

Elsevier eBooksJan 1, 20061 citation

N

is the number of oscillators in the bath and

K

is the force constant describing the strength of interaction between the anharmonic oscillator and the interacting harmonic many-body system. In the second model we find aspects of dynamical correlations as seen in the canonical ensemble and a dominant frequency that increases as

\sqrt{\mathrm{NK}}.

We recover the dynamical correlations of the anharmonic oscillator as obtained within the framework of a canonical ensemble [S. Sen, R. S. Sinkovits, and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996)] in the third model for sufficiently many harmonic oscillators. We comment briefly on an alternate way to correctly model heat baths for numerical studies on the dynamics of physical systems using canonical ensembles.