Three-body scattering area for particles with infinite or zero scattering length in two dimensions

• URL: http://arxiv.org/abs/2402.02202v2
• Date: Sun, 28 Apr 2024 06:51:45 GMT
• Title: Three-body scattering area for particles with infinite or zero scattering length in two dimensions
• Authors: Junjie Liang, Shina Tan,
• Abstract summary: We find that the ground state energy per particle of a zero-temperature dilute Bose gas with finite-range interactions is approximately $frachbar2 D 6mrho2$. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$.
• Score: 3.345575993695074
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter $D$ is defined. The dimension of $D$ is length squared, and we call $D$ three-body scattering area. We find that the ground state energy per particle of a zero-temperature dilute Bose gas with these interactions is approximately $\frac{\hbar^2 D }{6m}\rho^2$, where $\rho$ is the number density of the bosons, $m$ is the mass of each boson, and $\hbar$ is Planck's constant over $2\pi$. Such a Bose gas is stable at $D\geq 0$ in the thermodynamic limit, and metastable at $D<0$ in the harmonic trap if the number of bosons is less than $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{m\omega |D|}}$, where $\omega$ is the angular frequency of the harmonic trap. If the two-body interaction supports bound states, $D$ typically acquires a negative imaginary part, and we find the relation between this imaginary part and the amplitudes of the pair-boson production processes. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$.

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