Statistical theory of self-similarly distributed fields |
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Authors: | Alexander Olemskoi Irina Shuda |
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Institution: | a Institute of Applied Physics, National Academy of Sciences of Ukraine, 58, Petropavlovskaya St., 40030 Sumy, Ukraine b Sumy State University, 2, Rimskii-Korsakov St., 40007 Sumy, Ukraine |
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Abstract: | A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With such a choice, the role of a fluctuating order parameter is shown to play deformed logarithm of the amplitude of a hydrodynamic mode. Within the harmonic approach, deformed partition function and moments of the order parameter of lower powers are found. A set of equations for the generating functional is obtained to take into account constraints and symmetry of the statistical system. |
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Keywords: | 02 20 Uw 05 30 Pr 12 40 Ee |
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