The classical-quantum limit
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915037873963008 |
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| author | Layton, Isaac Oppenheim, Jonathan |
| author_facet | Layton, Isaac Oppenheim, Jonathan |
| contents | The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modelling the decoherence of a subsystem by its environment. Denoting the decoherence time $τ$, we demonstrate that a double scaling limit in which $\hbar \rightarrow 0$ and $τ\rightarrow 0$ such that the ratio $E_f =\hbar /τ$ remains fixed leads to an irreversible open-system evolution with well-defined classical and quantum subsystems. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi and Glauber-Sudarshan quasiprobability distributions may all be mapped in the above double scaling limit to the same completely-positive classical-quantum generator. This provides a regime in which one can study effective and consistent classical-quantum dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_18271 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The classical-quantum limit Layton, Isaac Oppenheim, Jonathan Quantum Physics Mesoscale and Nanoscale Physics The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modelling the decoherence of a subsystem by its environment. Denoting the decoherence time $τ$, we demonstrate that a double scaling limit in which $\hbar \rightarrow 0$ and $τ\rightarrow 0$ such that the ratio $E_f =\hbar /τ$ remains fixed leads to an irreversible open-system evolution with well-defined classical and quantum subsystems. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi and Glauber-Sudarshan quasiprobability distributions may all be mapped in the above double scaling limit to the same completely-positive classical-quantum generator. This provides a regime in which one can study effective and consistent classical-quantum dynamics. |
| title | The classical-quantum limit |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2310.18271 |