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International Journal of Modern Physics B

TWO ONE-DIMENSIONAL INTERACTING PARTICLES IN A HARMONIC TRAP

Bo-Bo Wei

Published Jul 20, 2009• 3 citations
Publisher

Abstract

In this brief report, two one-dimensional interacting particles interacting with a delta interaction in a harmonic trap is discussed. For strong interactions, we derive the asymptotic expressions for all the energy levels. In addition, the variational method is used to obtain asymptotic ground state energy and wave function. The variational results are compared with the exact solution and they turn out to agree very well.

DOI
10.1142/s0217979209053345

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In this brief report, two one-dimensional interacting particles interacting with a delta interaction in a harmonic trap is discussed. For strong interactions, we derive the asymptotic expressions for all the energy levels. In addition, the variational method is used to obtain asymptotic ground state energy and wave function. The variational results are compared with the exact solution and they turn out to agree very well.
We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.