Threshold expansion formula of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> bosons in a finite volume from a variational approach

Abstract

In present work, we show how the threshold expansion formula of $N$ identical bosons in finite volume may be derived by iterations of Faddeev-type coupled dynamical equations. The energy shift of $N$-boson system near threshold is dominated by zero momenta mode of $N$-body amplitudes with all particles nearly static. The dominant zero momenta mode and subleading nonzero momenta mode contributions are connected through finite volume Faddeev-type coupled dynamical equations. Eliminating nonzero momenta modes by iterations ultimately yields an analytic expression that can be solved by threshold expansion.

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