Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--
arXiv:1408.3885 · doi:10.1093/ptep/ptu138
Abstract
Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter , a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by . To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined.
arXiv comment19 pages, no figure, version accepted for publication in Progress of Theoretical and Experimental Physics
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