Correlated Gaussian approach to anisotropic resonantly interacting few-body systems

Abstract

Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical approaches are necessary for addressing dimensional transitions. The Fully-Correlated Gaussian method provides a variational description of the fewbody real-space wavefunction. By placing the particles in a harmonic trap, the system can be described at various degrees of anisotropy by squeezing the confinement. Through this approach, configurations of two and three identical bosons as well as heteronuclear (Cs-Cs-Li and K-K-Rb) systems are described during a continuous deformation from three to one dimension. We find that the changes in binding energies between integer dimensional cases exhibit a universal behavior akin to that seen in avoided crossings or Zeldovich rearrangement. arXiv:1805.12488v1 [cond-mat.quant-gas] 31 May 2018

Three identical bosons: Properties in noninteger dimensions and in external fields

“…To deal with such a huge number of crossings is very time-consuming and makes this method rather inefficient close to two dimensions. Towards this limit the method of correlated Gaussians [4] might, for example, be used, although the advantage of very similar basis functions would then also disappear. The choice is then between using different methods in the two limits or the same method with inherent loss of efficiency in one of the limits.…”

“…Being more specific, and focusing on three-body systems, N = 3, the total three-body wave function in d dimensions is obtained in this work by solving the Faddeev equations leading to the Schrödinger equation, (4). In particular, the wave function is written as…”

“…Together with the dimension, d, the properties depend also on the number of particles [3]. However, so far only the d dependence of the relative motion of the simplest systems has been studied by various methods [4][5][6]. Two particles squeezed between integer dimensions are obviously the simplest case, but beside its inherent interest, it is also necessary in investigations of three particles.…”

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

“…Together with the dimension, d, the properties depend as well on the number of particles [3]. However, so far only the d-dependence of the relative motion of the simplest systems has been studied by various methods [4][5][6]. Two particles squeezed between integer dimensions are obviously the simplest case, but beside its inherent interest, it is also necessary in investigations of three particles.…”

Efimov effect in non-integer dimensions induced by an external field

“…The neces-sary relation to ordinary physics of integer-based dimensions is also available [31,33]. The translation involves an external deformed field [35], which is shown to be equivalent to the non-integer dimensional treatment [34]. Thus, we can employ the simple method and interpret in terms of a deformed external one-body field.…”