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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 eigenstate solutions of Schrodinger equation with noncentral generalized oscillator potential by extended Nikiforov-Uvarov method(Elsevier, 2021) Karayer, Hale; Demirhan, DoganExact eigenstate solutions of Schrodinger equation for a generalized oscillator system that includes, as special cases; ring shaped oscillator potential and isotropic harmonic oscillator potential are examined in an analytical treatment by using extended Nikiforov Uvarov method. Radial and angular parts of the Schrodinger equation for the relevant potential can be systematically solved in the same manner. Moreover the relation between the eigenfunction solutions for this potential and Heun polynomials are presented. (C) 2021 Elsevier B.V. All rights reserved.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 Exact analytical solution of Schrodinger equation for a generalized noncentral potential(Springer Heidelberg, 2022) Karayer, Hale; Demirhan, DoganAnalytical eigenstate solution of Schrodinger equation for a modified ring-shaped oscillator potential is presented by using extended Nikiforov Uvarov method in cylindrical coordinates. The potential is a generalized form of ring-shaped oscillator potential, double-ring-shaped potential, double-ring-shaped harmonic oscillator potential, some extended class of Smorodinsky-Winternitz potentials, double-ring-shaped Coulomb oscillator potential and anisotropic ring-shaped oscillator potential. Bound-state solutions of the Schrodinger equation are obtained in terms of biconfluent Heun polynomials.Öğe A Fractal Approach To the Distribution Function of a Paramagnetic System(Springer, 1995) Bueyuekkilic, Fevzi; Demirhan, DoganA similarity between the random walk problem and a paramagnetic system has been established. The distribution functions of the stationary states have been obtained by making the Tsallis entropy a maximum, belonging to the statistical ensemble of a paramagnetic system, under suitable constraints using the variational methods. The asymptotic form of the distribution of the magnetic moments has been determined from the behaviour of the Levy distribution. For the paramagnetic system which has been considered as the fractally structured system, following the way used by Alemany and Zanette [1] Tsallis q index has been related to the fractal dimension and the interval of the values of q has also been determined.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 Investigation of the behavior of an Ising metamagnet under the influence of a field using Glauber dynamics(Elsevier Science Bv, 2007) Gulpinar, Gul; Demirhan, Dogan; Buyukkilic, FevzlIn this study, the kinetics of the Ising metamagnet where the interlayer interactions are ferromagnetic has been investigated under the mean field approximation. In describing the kinetics of the system, Glauber stochastic dynamics in the presence of an external field which performs time-dependent oscillations, has been utilized. Obtained results could be identified by two distinct types: the asymmetric solutions oscillating in the vicinity of finite values where the lattice magnetization has different values and the symmetric solutions being zero where the sublattice magnetizations are equal to each other. On the other hand, it has been observed that in the case where the system's initial state has a homogenous magnetization it exhibits two different periodical behaviors in the course of time. (c) 2007 Elsevier B.V. All rights reserved.Öğe Investigation of the Bose-Einstein condensation based on fractality using fractional mathematics(Iop Publishing Ltd, 2010) Sirin, Hueseyin; Ertik, Hueseyin; Bueyuekkilic, Fevzi; Demirhan, DoganAlthough atomic Bose gases are investigated in the dilute gas regime, the physical properties of the Bose-Einstein condensates are affected by interparticle interactions and the fractal nature of the space where the Bose systems are evolving. Theoretical predictions of the traditional Bose-Einstein thermostatistics do not account for the deviations from the experimental results, which are related to internal energy, specific heat, transition temperature, etc. On the other hand, in this study, fractional calculus is introduced where effects of the fractality of space are taken into account. Meanwhile, the order of the fractional derivative a is handled as a measure of the fractality of space. In this content, some improvements which take into account the effects of the fractal nature of the system are made in the standard physical results of the Bose-Einstein condensation phenomena. As an example, for the dilute atomic gas Li-7, the measured transition temperature of Bose-Einstein condensation could be obtained for the value of alpha approximate to 0.976, and one could predict that the interparticle interactions have a weak attractive nature consistent with experiment (Bradley et al 1995 Phys. Rev. Lett. 75 1687). Thus, a fractional mathematical theory is established in coherence with experimental results of Bose-Einstein condensation.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]
