Path integrals, spontaneous localisation, and the classical limit

We recall that in order to obtain the classical limit of quantum mechanics one needs to take the \(\hbar\rightarrow 0\) limit. In addition, one also needs an explanation for the absence of macroscopic quantum superposition of position states. One possible explanation for the latter is the Ghirardi-R...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Bhatt, Bhavya, Manish Ram Chander, Patil, Raj, Mishra, Ruchira, Nahar, Shlok, Singh, Tejinder P
Format: Article
Language:English
Subjects:
Density
Integrals
Liouville equations
Localization
Quantum mechanics
Quantum physics
Quantum theory
Superposition (mathematics)
Online Access:Get full text
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Summary:We recall that in order to obtain the classical limit of quantum mechanics one needs to take the \(\hbar\rightarrow 0\) limit. In addition, one also needs an explanation for the absence of macroscopic quantum superposition of position states. One possible explanation for the latter is the Ghirardi-Rimini-Weber (GRW) model of spontaneous localisation. Here we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. (Such a formulation has been derived earlier by Pearle and Soucek; we provide two new derivations of their result). We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral. Thus we provide a rigorous demonstration of the quantum to classical transition.
ISSN:2331-8422
DOI:10.48550/arxiv.1808.04178