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Theory of One-Dimensional Bosons in Harmonic Traps(1)

正人大矢

We consider a one-dimensional system of repulsive δ-interacting bosons trapped in a harmonic potential. For all values of the coupling strength, we derive expressions of the wave functions and ground-state energies of two, three, four-body systems.

Jan 31, 20060 citations

調和トラップ中の1次元ボース系の理論(4)

正人大矢

We consider a one-dimensional two-level system of repulsive δ-interacting bosons trapped in a harmonic potential. For all values of the coupling strength, we derive expressions of the wave functions of three, four, five, six-body systems.

Mar 24, 20090 citations

調和トラップ中の1次元ボース系の理論(5)

正人大矢

We consider a one-dimensional system of δ-interacting bosons trapped in harmonic potential. For the repulsive and attractive interaction, we derive expressions of ground-state wave functions, excited-state wavefunctions and their energe eigenvaluess of two-body systems.

Nov 29, 20100 citations

Construction of Analytical Many-Body Wave Functions for Correlated Bosons in a Harmonic Trap

Ioannis Brouzos, Peter Schmelcher

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.

arXiv:1108.1354Physical Review LettersJan 24, 201247 citations

TWO ONE-DIMENSIONAL INTERACTING PARTICLES IN A HARMONIC TRAP

Bo-Bo Wei

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.

International Journal of Modern Physics BJul 20, 20093 citations

Ground State of a One-Dimensional Many-Boson System

Deok Kyo Lee

The ground state of a one-dimensional system of many bosons interacting through a repulsive $\ensuremath{\delta}$-function potential is studied when the coupling parameter $\ensuremath{\gamma}$ of the system is small. The procedure is based on the variational analysis in the Bijl-Dingle-Jastrow wave-function space. The ground-state energy, determined in a series form in powers of ${\ensuremath{\gamma}}^{\frac{1}{2}}$ and truncated after the third leading term, is found to be in fair agreement with exact results of Lieb and Liniger over a range of the coupling parameter extending up to $\ensuremath{\gamma}=6$. Two slightly different approaches are considered, and they are shown to be equivalent.The ground state of a one-dimensional system of many bosons interacting through a repulsive $\ensuremath{\delta}$-function potential is studied when the coupling parameter $\ensuremath{\gamma}$ of the system is small. The procedure is based on the variational analysis in the Bijl-Dingle-Jastrow wave-function space. The ground-state energy, determined in a series form in powers of ${\ensuremath{\gamma}}^{\frac{1}{2}}$ and truncated after the third leading term, is found to be in fair agreement with exact results of Lieb and Liniger over a range of the coupling parameter extending up to $\ensuremath{\gamma}=6$. Two slightly different approaches are considered, and they are shown to be equivalent.

Physical Review AJan 1, 197113 citations

Theory of One-Dimensional Bosons in Harmonic Traps(2)

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Theory of One-Dimensional Bosons in Harmonic Traps(2)

Abstract

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