Ph.D. Theses
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Browsing Ph.D. Theses 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 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.