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arXiv · 2501.03199

Visualizing quantum entanglement in Bose-Einstein condensates without state vectors

Russell B. Thompson
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Abstract

Ring polymer self-consistent field theory is used to calculate the critical temperatures and heat capacities of an ideal Bose gas for an order of magnitude more particles than previously reported. A lambda-transition indicative of Bose-Einstein condensation is observed as expected. Using a known proof of spatial mode entanglement in Bose-Einstein condensates, a relationship between boson exchange and quantum entanglement is established. This is done without the use of state vectors, since ring polymer quantum theory uses instead a thermal degree of freedom, sometimes called the "imaginary time", to map classical statistical mechanics onto non-relativistic quantum mechanics through the theorems of density functional theory. It is shown that quantum phenomena, such as Bose-Einstein condensation, boson exchange, entanglement and contextuality, can be visualized in terms of merging and separating ring polymer threads in thermal-space. A possible extension to fermions is mentioned.

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Russell B. Thompson. 2025-01-06. Visualizing quantum entanglement in Bose-Einstein condensates without state vectors. https://doi.org/10.1007/s10773-024-05880-99777f00d-b86d-453b-b024-5c9c68c18891

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