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Browsing Fizik by Author "Akant, Levent."
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Item Boundary effects on Bose-Einstein condensation in ultra-static space-times(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.) Ertuğrul, Emine.; Akant, Levent.In this theses relativistic boson anti-boson system, inside d dimensional box B with volume V and surface area A, which is a sub-manifold of d dimensional manifold M is studied. Mellin-Barnes Transformations and short time asymptotic of heat kernel are used as mathematical tools. Both Neumann and Dirichlet boundary conditions are considered. Analysis are done for the free energy and charge. Charge is expressed as a function of temperature. E ects of boundaries on temperature is calculated perturbatively. Same methods are employed for studying the neutral gas; free energy and number of particles are studied and again the e ect of boundary on temperature is calculated. Apart from these, upper and lower bounds for depletion coe cient of ideal relativistic bose gas in thermodynamic limit is given with the help of Li-Yau and Colbois-Maerten bounds.Item Geometric formulation of lagrangian mechanics and symmetries(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.) Türeli, Sina.; Akant, Levent.We start the thesis by covering the geometric formulation of time-independent and time-dependent Lagrangian mechanics and the concept of dynamical symmetry. Then we give two applications. First we review and tie together the results given between alternative Lagrangians, constants of motion and symmetries using Cartan 2-forms. Then it is followed by theory of connections and geometric mechanics applied to the Dirac monopole problem.Item Introduction to open quantum systems(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.) Erciyas, Abdurrahman.; Akant, Levent.The purpose of this study is to introduce open quantum systems to the reader. The study should not be taken as a comprehensive resource on the subject. In the study, some of the fundamental concepts of quantum mechanics have been given with a di erent point of view; thus, it is intended to take the reader beyond the orthodox attitude of standard quantum mechanics. Here, we will start with the introduction of basic tools to understand the open quantum systems. In the study, system-plusreservoir model, which is the most fundamental model to understand the nature of open systems, will be introduced. Then, quantum evolutions will be generalized and how non-unitary evolution will be de ned will be shown. In this study, only markovian open systems will be introduced. Finally, the example of quantum harmonic oscillator, which is isomorphic to most quantum systems, will be given as a physical example for explaining the dynamics of open systems.Item Kinetic theory in k=0 Friedmann-Robertson-Walker cosmology(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.) Tülümen, Nimet.; Akant, Levent.In the thesis we calculated Boltzmann Equation in RW metric. After that in the at space-like slices we showed that for RW metric it is not possible to nd any equilibrium solutions. However we looked for the equilibrium solutions in the two limits when mass goes to zero and when mass goes to in nity. Then we applied these result to the Bose-Einstein and to the Fermi-Dirac statistics for nding the equilibrium solution in the limits. Finally in the Bose-Einstein Condensation we calculated critical temperature.Item Non - relativistic bose gas in curved background(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.) Debir, Birses.; Akant, Levent.In this thesis we focus on the Bose-Einstein Condensation of a pure Bose gas con ned in a box placed near the horizon. Then, we formulate the nite size e ects in the limit m ! 0. We look for the number of excited particles, as well as free energy and entropy. During these processes, we used the Heat kernel expansion and the Mellin Barnes transform.Item Nonrelativistic limit of Bose-Einstein condensation in a static spacetime(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.) İşeri, İslam Çağrı.; Akant, Levent.Nonrelativistic limit of thermodynamics of noninteracting Bose field in curved background is investigated via a post-Newtonian approach. In large but finite c limit matter becomes nonrelativistic whereas the geometry stays unchanged. Mellin trans form and heat kernel techniques lead to asymptotics of thermodynamic variables that are used to analyze the gravitational effects on Bose Einstein Condensation in static background. For finite volume, particle density-temperature relation is obtained which include gravitational corrections to the classical expression. Boundary effects due to gravitation are also examined and the results are found to be reduced to usual Minkowski space ones in the absence of gravitation in the thermodynamic limit.Item Quantum phenomena and shape dynamics(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.) Dündar, Furkan Semih.; Akant, Levent.; Arık, Metin.In this thesis, we considered quantum phenomena (Unruh effect) in Shape Dy namics, version of Bohmian Mechanics that is compatible with Mach’s Principle, and a solution (gravitational collapse of a spherically symmetric thin shell of dust) of Shape Dynamics. First, it is interesting that we proved the existence of Unruh radiation in Shape Dynamics where there is no Lorentz symmetry and no unbounded flat space. In order to detect the existence of Unruh effect we used an Unruh-DeWitt detector. Second, a toy model for Shape Dynamics that is suitable for particle interactions is considered. It brings three constraints for solutions: Energy constraint, angular mo mentum constraint and dilational momentum constraint. We applied these constraints to particle variables of Bohmian Mechanics and obtained a constrained Bohmian Me chanics that is Machian. Third, we considered a spherically symmetric thins shell of dust in Shape Dynamics in a space manifold which is [0,1]×S2. We calculated the symplectic form and its inverse. The phase space variables turned out to be the coordinate radius and total momentum of the shell, the expectation value of the trace of the metric momentum, and the volume of the space. We laid the foundations for future research.Item Thermodynamical properties of bosons and fermions for lattice motivated dispersion relationships(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2023., 2023) Güner, Metin Mehmet.; Akant, Levent.; Arık, Metin.In this thesis, we have studied the coupled simple harmonic oscillator physics of one-dimensional strings, for acoustical phonons, and n-dimensional physics for the optical case (for arbitrary n). For the acoustical modes, we have calculated only the Bosonic Simple Harmonic Oscillator (BSHO), for the optical mode, we have included both BSHO and Fermionic Simple Harmonic Oscillator (FSHO). For the optical modes, for both BSHO’s and FSHO’s, we have found that the problem is reduced to the physics of a single oscillator with a partial vibration frequency. For the FSHO’s in the optical cases, we have encountered the presence of negative temperatures for all n. In both cases, we have discovered the presence of correct asymptotical behavior as T → 0 and T → ∞. In the acoustical case, we have used Mellin Transform and a summation formula due to Euler to calculate the partition function and the thermodynamical properties thereof. Again we have obtained the correct asymptotical behavior as T → 0 and T →∞. We note that whenever possible, we have included more than one method of calculation and obtained similar results.