Few-body quantum method in a $d$-dimensional space

Abstract

In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of an external field. This method is conceptually simple, although, due to the presence of the external field, its numerical implementation can become rather cumbersome, especially when the system is highly confined. In the second method the external field is not used, and it simply considers the spatial dimension $d$ as a parameter that changes continuously between the ordinary integer values. In this way the numerical effort is absorbed in a modified strength of the centrifugal barrier. Then the technique required to obtain the wave function of the confined system is precisely the same as needed in ordinary three dimensional calculations without any confinement potential. The case of a two-body system squeezed from three to two dimensions is considered, and used to provide a translation between all the quantities in the two methods. Finally we point out perspectives for applications on more particles, different spatial dimensions, and other confinement potentials.

To be published in Physics Letters A

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Cited by in corpus (11)

• Three identical bosons: Properties in non-integer dimensions and in external fields
• Confinement of two-body systems and calculations in $d$ dimensions
• D-dimensional three-body bound-state problem with zero range interactions
• Efimov effect in non-integer dimensions induced by an external field
• Cold atom-dimer reaction rates with ${}^4$He, ${}^{6,7}$Li and ${}^{23}$Na
• 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
• Emergence of N-body tunable interactions in universal few-atom system