Three identical bosons: Properties in non-integer dimensions and in external fields

• URL: http://arxiv.org/abs/2007.15900v1
• Date: Fri, 31 Jul 2020 08:32:49 GMT
• Title: Three identical bosons: Properties in non-integer dimensions and in external fields
• Authors: E. Garrido and A.S. Jensen
• Abstract summary: Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. An alternative is provided by use of the dimension $d$ as a parameter that changes continuously within the range $2leq d leq 3$. The simplicity of the $d$-calculations is exploited to investigate the evolution of three-body states after progressive confinement.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. Such a squeezing can be obtained by means of an external confining potential acting along a single axis. However, this procedure can be numerically demanding, or even undoable, especially for large squeezed scenarios. An alternative is provided by use of the dimension $d$ as a parameter that changes continuously within the range $2\leq d \leq 3$. The simplicity of the $d$-calculations is exploited to investigate the evolution of three-body states after progressive confinement. The case of three identical spinless bosons with relative $s$-waves in 3D, and a harmonic oscillator squeezing potential is considered. We compare results from the two methods and provide a translation between them, relating dimension, squeezing length, and wave functions from both methods. All calculations are then possible entirely within the simpler $d$-method, but simultaneously providing the equivalent geometry with the external potential.

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