### Abstract

Original language | English |
---|---|

Pages (from-to) | 1551-1572 |

Number of pages | 22 |

Journal | Foundations of Physics |

Volume | 46 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2016 |

### Keywords

- Classical limit
- Foundations of quantum mechanics
- Quantum-classical hybrids
- Semiclassical physics

### Cite this

*Foundations of Physics*,

*46*(12), 1551-1572. https://doi.org/10.1007/s10701-016-0028-5

}

*Foundations of Physics*, vol. 46, no. 12, pp. 1551-1572. https://doi.org/10.1007/s10701-016-0028-5

**Classical-quantum limits.** / Oliynyk, Todd A.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Classical-quantum limits

AU - Oliynyk, Todd A.

PY - 2016/12

Y1 - 2016/12

N2 - 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.

AB - 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.

KW - Classical limit

KW - Foundations of quantum mechanics

KW - Quantum-classical hybrids

KW - Semiclassical physics

UR - http://www.scopus.com/inward/record.url?scp=84975450745&partnerID=8YFLogxK

U2 - 10.1007/s10701-016-0028-5

DO - 10.1007/s10701-016-0028-5

M3 - Article

VL - 46

SP - 1551

EP - 1572

JO - Foundations of Physics

JF - Foundations of Physics

SN - 0015-9018

IS - 12

ER -