Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis thermostatistics. The generalized partition functions, internal energies, free energies and temperature factor (or Debye-Waller factor) are calculated. It has also been observed that the temperature factor is dependent on the non-extensive parameter q which behaves like a scale parameter in the harmonic oscillator model. As $q\to 1$, we also show that these approximations agree with the result of Gaussian network model.Comment: 8 pages, 2 figure

Precision cosmology as a test for statistics

We compute the shift in the epoch of matter-radiation equality due to the possible existence of a different statistical (non-extensive) background. The shift is mainly caused by a different neutrino-photon temperature ratio. We then consider the prospects to use future large galaxy surveys and cosmic microwave background measurements to constrain the degree of non-extensivity of the universe.Comment: to appear in Physica

Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis

We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1-q)<<1, in terms of the factorization approach. Two methods agree under certain conditions.Comment: Clarifications and new references. Version to appear in Phys.Lett.

Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic double-well potential are investigated by this method

q-thermostatistics and the analytical treatment of the ideal Fermi gas

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis' literature.Comment: v2: comparison with conventional results and validity of approximations clarified, typos corrected; accepted for publication in Physica

Quantal distribution functions in non-extensive statistics and an early universe test revisited

Within the context of non-extensive thermostatistics, we use the factorization approximation to study a recently proposed early universe test. A very restrictive bound upon the non-extensive parameter is presented: $|q-1| < 4.01 \times 10^{-3}$.Comment: 4 pages, prl revtex style, no figures. To appear in Physica A, 199

Solution of Schrodinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation

Exact solutions of the Schrodinger equation for two different potentials are presented by using the extended Nikiforov-Uvarov method. The first one is the inverse square root potential which is a long-range potential and the second one is a combination of Coulomb, linear, and harmonic potentials which is often used to describe quarkonium. Eigenstate solutions are obtained in a systematicway without using any ansatz or transformation. Eigenfunctions for considered potentials are given in terms of biconfluent Heun polynomials. Published by AIP Publishing.Kirklareli UniversityKirklareli University [KLUBAP142]This work has been supported by Kirklareli University under the Research Project No. KLUBAP142.WOS:0004339503000312-s2.0-8504696294

Solutions of local fractional sine-Gordon equations

In this paper, we study sine-Gordon equation in order to obtain exact solitary wave solutions in the domain of fractional calculus. By using the definition of conformable fractional derivative, we obtain analytical solutions of time, space and time-space fractional sine-Gordon equations. We analyze graphically the effect of fractional order on evolution of the kink and antikink type solitons.WOS:0004585665000042-s2.0-8504096626