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Connection between two- and three-body systems in an oscillator trap and D-dimensional calculations

AuthorsGarrido, Eduardo
Issue Date16-Oct-2017
CitationCritical Stability of Quantum Few-Body Systems (2017)
AbstractIn this work we investigate three-body systems when the dimension changes in a continuous way from three (3D) to two (2D) dimensions. This amounts to confining the particles into a narrower and narrower layer, such that, eventually, when the layer has zero width, the particles are forced to move in 2D. In practice, this can be done by putting the particles under the effect of an external trap potential confining the particles in the space. In particular, this can be done by means of a harmonic oscillator potential in the z-coordinate. For two-body systems the numerical implementation of the external field is simple, and it does not present particular problems. However, for three-body systems, although conceptually the procedure is exactly the same, the numerical difficulties increase when the frequency of the harmonic oscillator increases. In fact, for very large frequencies, i.e., when approaching 2D, the method is quite inefficient. For this reason, in this work we propose to implement the confinement of the particles, not by means of an external potential, but by introducing the dimension d as a parameter in the Schrödinger (or Faddeev) equations to be solved. The dimension is then allowed to take non-integer values within the range 2 ¿ d ¿ 3. The purpose of this work is twofold. First, we want to see the connection between the two confinement methods mentioned above. It is necessary to see the equivalence between a given value of the confining harmonic oscillator frequency and the dimension d describing the same physical situation. Once this is done, we shall use the second method, which is numerically much simpler, to investigate the Efimov states in mass imbalanced systems, focusing in particular on how those states disappear when increasing the confinement of the particles.
Appears in Collections:(CFMAC-IEM) Comunicaciones congresos
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