Classical-quantum limits

Abstract

We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multi-particle Schrödinger equations. The limit equations obtained by this procedure, which we refer to as the classical-quantum limit, govern the interaction between classical and quantum systems, and they possess many desirable properties that are inherited in the limit from the multi-particle quantum system. As an application, we use the classical-quantum limit equations to identify the source of the non-local signalling that is known to occur in the classical-quantum hybrid scheme of Hall and Reginatto. We also derive the first order correction to the classical-quantum limit equation to obtain a fully consistent first order approximation to the Schrödinger equation that should be accurate for modeling the interaction between particles of disparate mass in the regime where the particles with the larger masses are effectively classical.

Material added to address referee comments. Agrees with the published version

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Cited by in corpus (6)

• The classical-quantum limit
• Canonical bracket in quantum-classical hybrid systems
• When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
• Vindication of entanglement-based witnesses of non-classicality in hybrid systems
• Classical Dynamics from Self-Consistency Equations in Quantum Mechanics -- Extended Version
• Entanglement of Classical and Quantum Short-Range Dynamics in Mean-Field Systems