arXiv subjects

Irina Shuda

Publications and source records attributed to Irina Shuda.

4 recordsLinked to original sources

arXiv2010

Generalization of multifractal theory within quantum calculus

On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation $τ_q=D_q(q-1)$. We find equation for set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and porous surface condensates are considered as examples. Keywords:Multifractal set; Deformation; Power series.

cond-mat.stat-mech↗

arXiv2009

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.

cond-mat.stat-mech↗

arXiv2009

Supersymmetry representation of Bose-Einstein condensation of fermion pairs

We consider supersymmetry field theory with supercomponents being the square root of the Bose condensate density, the amplitude of its fluctuations and Grassmannian fields related to the Fermi particles density. The fermion number is demonstrated to be conserved in degenerated Fermi-Bose mixtures with unbroken supersymmetry when the system is invariant with respect to inversion of the time arrow. We show the supersymmetry breaking allows one to derive field equations describing behavior of real Bose-Fermi mixtures. Solution of related field equations reveals the cooling of homogeneously distributed fermions gives first spontaneous rise to strong inhomogeneous fluctuations, while the Bose condensate appears at a lower temperature dependent of the fermion density.

cond-mat.stat-mech↗

arXiv2009

Multifractal theory within quantum calculus

Within framework of the quantum calculus, we represent the partition function and the mass exponent of a multifractal, as well as the average of random variables distributed over self-similar set, on the basis of the deformed expansion in powers of the difference $q-1$. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes known relation $τ_q=D_q(q-1)$. We find the physical average related to the escort probability in terms of the deformed expansion as well. It is demonstrated the mass exponent can acquire a singularity that relates to a phase transition of the multifractal set in the course of its deformation.

cond-mat.stat-mech↗