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Öğe 2-d Finite barrier rectangular quantum dots I: Schrodinger description(Elsevier Science Bv, 2014) Ata, Engin; Demirhan, Dogan; Buyukkilic, FevziThe bound state energy levels of a finite barrier rectangular shaped quantum dot are obtained using a transfer matrix method and imposing parity and rotation symmetries of the dot on the wavefunction. Energy relations containing potential depth, dot size and effective masses are found in the 2-fold degenerate quantized transcendental equations. (C) 2014 Elsevier B.V. All rights reserved.Öğe 2-d finite barrier rectangular quantum dots II: Dirac description(Elsevier Science Bv, 2015) Ata, Engin; Demirhan, Dogan; Buyukkilic, FevziThe Schrodinger description of 2-d finite barrier rectangular quantum dots [1] expanded to Dirac description through transfer matrices and reflection and rotation symmetries of the dot system. Inexactness of wave vector components of spinors is then reduced to two relations which lead to two different bispinors and four quantized transcendental energy relations corresponding to even-even, odd-odd and even-odd, odd-even factorizing functions of each bispinor. In order to show the spin effect on the dot energy levels, the solutions of the transcendental relations of the Schrodinger and Dirac descriptions are plotted. (C) 2014 Elsevier B.V. All rights reserved.Öğe Analytical solution of the local fractional Klein-Gordon equation for generalized Hulthen potential(Scientific Technical Research Council Turkey-Tubitak, 2017) Karayer, Hasibe Hale; Demirhan, Ahmet Dogan; Buyukkilic, FevziThe one-dimensional Klein Gordon (KG) equation is investigated in the domain of conformable fractional calculus for one-dimensional scalar potential, namely generalized Hulthen potential. The conformable fractional calculus is based on conformable fractional derivative, which is the most natural definition in noninteger order calculus. Fractional order differential equations can be solved analytically by means of this derivative operator. We obtained exact eigenvalue and eigenfunction solutions of the local fractional KG equation and investigated the evolution of relativistic effects in correspondence with the fractional order.Öğe Analytical solutions of conformable time, space, and time space fractional KdV equations(Scientific Technical Research Council Turkey-Tubitak, 2018) Karayer, Hasibe Hale; Demirhan, Ahmet Dogan; Buyukkilic, FevziIn this study, we consider the Korteweg de Vries (KdV) equation for solitary waves in the domain of conformable fractional calculus. By means of this fractional theory, we obtain exact solutions for time, space, and time space fractional KdV equations and demonstrate our results graphically according to the fractional order of the related equations. Furthermore, we report that the fractional order in the solution of the time fractional KdV equation is associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of time fractional KdV and Burgers KdV equations.Öğe The effect of competition between the frequency of the field and the frequency of the spin flipping on the kinetics of Ising metanlagnet(Elsevier Science Bv, 2009) Gulpinar, Gul; Demirhan, Dogan; Buyukkilic, FevziWe consider the effect of a variable representing the competition between the frequency of the field and the frequency of the spin flipping (Omega) on the dynamics of the metamagnetic Ising model in a cubic lattice under the presence of a time varying (oscillating) external magnetic field. The system is modelled with a formalism of master equation at a mean-field level. The time averaged staggered magnetization (M(s)) acts as the order parameter and divides temperature field plane into three regions: anti-ferromagnetic, paramagnetic and coexistence of anti-ferromagnetic and paramagnetic phases. It is observed that the topology of the dynamical phase diagram depends strongly on Omega as well as the ratio between interlayer and intralayer couplings. (c) 2008 Elsevier B.V. All rights reserved.Öğe The effect of time fractality on the transition coefficients: Historical Stern-Gerlach experiment revisited(Pergamon-Elsevier Science Ltd, 2011) Sirin, Huseyin; Buyukkilic, Fevzi; Ertik, Huseyin; Demirhan, DoganIn this article, the influence of time discreteness on the transition coefficients is investigated within the framework of time fractional development of quantum systems which has been developed recently by the present authors [22]. In this formalism, fractional mathematics which is a powerful tool to study the non-Markovian and non-Gaussian properties of physical processes is used in order to obtain time fractional evolution operator and transition probability. They are given in terms of Mittag-Leffler function which plays an important role in the mathematical structure as well as the physical interpretation of the phenomena under investigation. In order to place the presented formalism on a concrete basis, historical Stern-Gerlach experiment has been revisited with the purpose of studying transition coefficients which have a non-Markovian feature. The effect of the time fractionalization has been clearly illustrated in the figures via fractional derivative order (C) 2010 Elsevier Ltd. All rights reserved.Öğe Fractional differential and integral operations via cumulative approach(Wiley, 2019) Buyukkilic, Fevzi; Bayrakdar, Zahide Ok; Demirhan, DoganIn this study, a fractal operator model of cumulative processes is described. Accordingly, differential and integral operators of the fractional calculus are derived by the fractal operator model of a cumulative process. In order to exhibit the relation between our cumulative approach and fractional calculus, vertical motion of a body is handled within these frameworks. Thereby, regard to our assessments, the underlying physical mechanism of the success of the fractional differintegral operators in describing stochastic complex systems is uncovered to some extent.Öğe Investigation of heat capacities of proteins by statistical mechanical methods(Elsevier Science Bv, 2007) Oylumluoglu, Gorkem; Buyukkilic, Fevzi; Demirhan, DoganIn this study additional heat capacity of the proteins in water dissociation have been investigated by statistical mechanical methods. For this purpose, taking electric field E and total dipole moment M as thermodynamical variables and starting with the first law of thermodynamics, an expression which reveals the thermodynamical relation between additional heat capacity in effective electric field Delta C-E and additional heat capacity at the constant total dipole moment Delta C-M, has been obtained. It is found that, difference between the heat capacities depends linearly on temperature. To establish the hydration effect during the folding and unfolding of the proteins, physical properties of the apolar dissociation have been used [G. Oylumluoglu, et al, Physica A 361 (2006) 255-262]. In the thermodynamical investigation of the protein system, in order to introduce the chemical potential mu (here it takes place of pH), one has to consider the system as a macro-canonical ensemble. In this study, the macro-canonical ensemble is obtained from the canonical ensemble. In this approach the proteins are taken in a heat bath, and also it is supposed that the system is in a particle reservoir. When this reservoir reaches to an equilibrium the number of particles take an average value. In this study, with the purpose of revealing the additional effect to the heat capacity, the partition functions of the proteins obtained in single protein molecule approach are taken. In this way, additional free energy has been related to heat capacities. Calculating the heat capacity Delta C-E and taking the heat capacity at constant total dipole moment Delta C-M from the experimental data, the outcomes of the performed calculations have been investigated for Myoglobin and other proteins. (c) 2006 Elsevier B.V. All rights reserved.Öğe A particular solution of Heun equation for Hulthen and Woods-Saxon potentials(Wiley-V C H Verlag Gmbh, 2014) Karayer, Hale; Demirhan, Dogan; Buyukkilic, FevziIn this article a particular solution of Heun equation is derived by making use of the Nikiforov-Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrodinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods-Saxon potentials).Öğe Relativistic energy-dispersion relations of 2D rectangular lattices(World Scientific Publ Co Pte Ltd, 2017) Ata, Engin; Demirhan, Dogan; Buyukkilic, FevziAn exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V-0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.Öğe Relaxation dynamics of iron-group dihalides(American Physical Soc, 2007) Gulpinar, Gul; Demirhan, Dogan; Buyukkilic, FevziIn this study, the relaxation dynamics of iron-group dihalides by making use of spin-1/2 metamagnetic Ising model has been formulated by the method of thermodynamics of irreversible processes. Using a molecular field approximation for the magnetic Gibbs energy, the magnetic Gibbs energy production in the irreversible process is calculated and time derivatives of the order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager's theory of irreversible thermodynamics. Two relaxation times are calculated and their temperature variances are examined. Moreover, the phase transition behaviors of the relaxation times are also obtained anaytically via the critical exponents.Öğe A thermostatistical approach to protein structures(Elsevier Science Bv, 2008) Oylumluoglu, Gorkem; Buyukkilic, Fevzi; Demirhan, DoganIn this study, the relation between the additional heat capacities of proteins have been obtained. The expressions for the increments of enthalpy Delta H, entropy Delta S and Gibbs energy Delta G which are encountered in the dissolving of the proteins in water, have been calculated. Partition functions of proteins are related to the macrothermodynamical quantities with the help of free energies. In order to endeavour the structure of the proteins, the theoretical calculations of thermostatistical mechanics are fitted to the data of experimental results. (c) 2007 Elsevier B.V. All rights reserved.Öğe Time fractional development of quantum systems(Amer Inst Physics, 2010) Ertik, Huseyin; Demirhan, Dogan; Sirin, Huseyin; Buyukkilic, FevziIn this study, the effect of time fractionalization on the development of quantum systems is taken under consideration by making use of fractional calculus. In this context, a Mittag-Leffler function is introduced as an important mathematical tool in the generalization of the evolution operator. In order to investigate the time fractional evolution of the quantum (nano) systems, time fractional forms of motion are obtained for a Schrodinger equation and a Heisenberg equation. As an application of the concomitant formalism, the wave functions, energy eigenvalues, and probability densities of the potential well and harmonic oscillator are time fractionally obtained via the fractional derivative order a, which is a measure of the fractality of time. In the case alpha=1, where time becomes homogenous and continuous, traditional physical conclusions are recovered. Since energy and time are conjugate to each other, the fractional derivative order a is relevant to time. It is understood that the fractionalization of time gives rise to energy fluctuations of the quantum (nano) systems. (C) 2010 American Institute of Physics. [doi:10.1063/1.3464492]
