Statistical theory of self-similarly distributed fields

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• 作者：Alex ; er Olemskoi ; Irina Shuda
• 关键词：Field theory ; Generating functional ; Jackson derivative ; Deformation
• 刊名：Physics Letters A
• 出版年：2009
• 出版时间：26 October 2009
• 年：2009
• 卷：373
• 期：44
• 页码：4012-4016
• 全文大小：193 K

文摘

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.