Abstract
We studied one-dimensional systems formed by N identical particles confined in a harmonic trap and subject to an inverse power-law interaction potential ~ |x|−d. The correlation properties of a Wigner molecule with the lowest energy are investigated in terms of their dependence on the number N and the power d, including the limit as d → 0. There are N-particle Wigner molecules with properties such that their correlations are mainly manifested in the N lowest natural orbitals. The values of the control parameters of the system at which such states appear are identified. The properties of Wigner molecules formed in the limit as d approaches infinity are also revealed.Graphical abstract
Highlights
Soon after the birth of quantum mechanics, the study of quantum correlations began to attract significant research attention
Within the framework of the harmonic approximation (HA), we studied the properties of the Wigner molecule formed by N identical particles confined in a harmonic trap and interacting via the inverse power-law potential |x|−d
Our results show the dependencies of the degree of correlation on d for the N -particle Wigner molecule ground-state in a wide range of values of N
Summary
Soon after the birth of quantum mechanics, the study of quantum correlations began to attract significant research attention. Other well-known examples of artificially created systems exhibiting long-range interactions are quantum dots [27,28] and systems of electromagnetically trapped ions [29]. Such systems exhibit a variety of strongly correlated states. It provides an effective procedure for the analysis of the special case as d → 0.
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