KAN-based trial wavefunctions reach about 1 percent ground-state energy accuracy for one-dimensional trapped bosons at roughly 10 times lower cost per training step than MLP-based wavefunctions, aided by a transferable two-body cusp term.
Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
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abstract
We consider trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. The exact ground state energy and wave function are identified in closed form together with a rich phase diagram, unveiled by Monte Carlo methods, with crossovers between different regimes. A trapped McGuire quantum soliton describes the attractive case. Weak repulsion results in an incompressible Laughlin-like fluid with flat density, well reproduced by a Gross-Pitaevskii equation with long-range interactions. Higher repulsion induces Friedel oscillation and the eventual formation of a Wigner crystal.
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Kolmogorov-Arnold Wavefunctions
KAN-based trial wavefunctions reach about 1 percent ground-state energy accuracy for one-dimensional trapped bosons at roughly 10 times lower cost per training step than MLP-based wavefunctions, aided by a transferable two-body cusp term.