The classical-quantum limit

• URL: http://arxiv.org/abs/2310.18271v2
• Date: Thu, 28 Nov 2024 05:26:10 GMT
• Title: The classical-quantum limit
• Authors: Isaac Layton, Jonathan Oppenheim,
• Abstract summary: The standard notion of a classical limit, represented schematically by $hbarrightarrow 0$, provides a method for approximating a quantum system by a classical one. Denoting the decoherence time $tau$, we demonstrate that a double scaling limit in which $hbar rightarrow 0$ and $tau rightarrow 0$ remains fixed leads to an irreversible open-system evolution.
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• Abstract: 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 $\tau$, we demonstrate that a double scaling limit in which $\hbar \rightarrow 0$ and $\tau \rightarrow 0$ such that the ratio $E_f =\hbar /\tau$ 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.

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