Freeing Semiclassical Field Theory of the UV Catastrophe and Cutoff Dependence
Dr Piotr Deuar
The Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
Semiclassical matter wave descriptions are the widespread method of choice for nonperturbative and thermal phenomena in ultracold gases. This is because for large and realistic systems, only this "classical field" approach remains tractable. However, calculations are continuously harassed by the twin plagues of an ultraviolet catastrophe, and the resulting dependence on a technical parameter - the cutoff. The problems are particularly severe in 2D and 3D.
We have developed a modified classical field that no longer suffers from these problems, but whose computational efficiency scales the same way as standard classical field methods. To achieve this, an SGPE-like reservoir coupling is mustered to act as a constraint on the high-energy part of the system. The key to avoiding the UV divergence is then to preserve the quantum properties of this constraining reservoir coupling. Examples in 1D and 3D will be given, including the famous case of collective modes that have previously eluded accurate description with classical fields
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