Statistical theory of self-similarly distributed fields
Copyright policy )Statistical theory of self-similarly distributed fields
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.
10 pages, 2 figures. Accepted for publication in Physics Letters A. DOI 10.1016/j.physleta.2009.08.070
- National Academy of Sciences of Ukraine Ukraine
- Institute of Applied Physics Ukraine
- Sumy State University Ukraine
Statistical Mechanics (cond-mat.stat-mech), deformation, Fractional processes, including fractional Brownian motion, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, field theory, Strong interaction, including quantum chromodynamics, generating functional, Jackson derivative, Quantum dynamics and nonequilibrium statistical mechanics (general), Interacting particle systems in time-dependent statistical mechanics, Quantum groups and related algebraic methods applied to problems in quantum theory, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Condensed Matter - Statistical Mechanics
Statistical Mechanics (cond-mat.stat-mech), deformation, Fractional processes, including fractional Brownian motion, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, field theory, Strong interaction, including quantum chromodynamics, generating functional, Jackson derivative, Quantum dynamics and nonequilibrium statistical mechanics (general), Interacting particle systems in time-dependent statistical mechanics, Quantum groups and related algebraic methods applied to problems in quantum theory, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Condensed Matter - Statistical Mechanics
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