A comparison between classical and Bohmian quantum chaos
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909319201554432 |
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| author | Tzemos, Athanasios C. Contopoulos, George |
| author_facet | Tzemos, Athanasios C. Contopoulos, George |
| contents | We study the emergence of chaos in a 2d system corresponding to a classical Hamiltonian system $V= \frac{1}{2}(ω_x^2x^2+ω_y^2y^2)+εxy^2$ consisting of two interacting harmonic oscillators and compare the classical and the Bohmian quantum trajectories for increasing values of $ε$. In particular we present an initial quantum state composed of two coherent states in $x$ and $y$, which in the absence of interaction produces ordered trajectories (Lissajous figures) and an initial state which contains {both chaotic and ordered} trajectories for $ε=0$. In both cases we find that, in general, Bohmian trajectories become chaotic in the long run, but chaos emerges at times which depend on the strength of the interaction between the oscillators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A comparison between classical and Bohmian quantum chaos Tzemos, Athanasios C. Contopoulos, George Quantum Physics Mathematical Physics Chaotic Dynamics We study the emergence of chaos in a 2d system corresponding to a classical Hamiltonian system $V= \frac{1}{2}(ω_x^2x^2+ω_y^2y^2)+εxy^2$ consisting of two interacting harmonic oscillators and compare the classical and the Bohmian quantum trajectories for increasing values of $ε$. In particular we present an initial quantum state composed of two coherent states in $x$ and $y$, which in the absence of interaction produces ordered trajectories (Lissajous figures) and an initial state which contains {both chaotic and ordered} trajectories for $ε=0$. In both cases we find that, in general, Bohmian trajectories become chaotic in the long run, but chaos emerges at times which depend on the strength of the interaction between the oscillators. |
| title | A comparison between classical and Bohmian quantum chaos |
| topic | Quantum Physics Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2409.12056 |