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

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 $2\le d\le 3$. 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.

13 pages, to be published in Physical Review Research

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Observation of the Efimovian Expansion in Scale Invariant Fermi Gases
• Efimov trimers under strong confinement
• Efimov effect in $D$ spatial dimensions in $AAB$ systems
• Analytic solutions of topologically disjoint systems
• Weakly bound states of two- and three-boson systems in the crossover from two to three dimension
• Squeezing the Efimov effect
• Few-body quantum method in a $d$-dimensional space
• Confinement of two-body systems and calculations in $d$ dimensions
• Correlated Gaussian Approach to Anisotropic Resonantly Interacting Few-Body Systems

Cited by in corpus (8)

• D-dimensional three-body bound-state problem with zero range interactions
• Efimov effect in non-integer dimensions induced by an external field
• Three-body continuum states and Efimov physics in non-integer geometry
• Confinement of $N$-body systems and non-integer dimensions
• Two-body continuum states in non-integer geometry
• Efimov effect evaporation after confinement
• Tuning of Efimov states in non-integer dimensions
• Reliability of the Born-Oppenheimer approximation in noninteger dimensions