M.S. Theses
Permanent URI for this collection
Browse
Browsing M.S. Theses by Subject "Bose-Einstein condensation."
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Aspects of finite size effects on Bose-Einstein condensation(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.) Seymen, Sema.; Turgut, Teoman.In this thesis, the number of particles calculations of Pathria for a 3 dimensional box is shortly reviewed. After that, the works of Toms and Kirsten which use the Mellin Barnes integral representation and heat kernel approximation to calculate the partition function summation is reviewed. Toms and Kirsten's approach is worked out in d dimension to calculate some thermodynamic quantities such as the number of particles, internal energy, heat capacity at constant volume and constant pressure, isothermal compressibility, adiabatic compressibility etc. The discontinuity of the heat capacity and the derivative of the heat capacity around the critical temperature is investigated. The results are checked at the bulk level to see that at d = 3 they are consistent with the ones given in Pathria. Lastly, the results are generalized to ps for s = 2k case and also an expression for the discontinuity of the heat capacity at constant volume is written.Item Bose-Einstein condensation on a Reimannian manifolds with nonnegative Ricci curvature(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.) Tapramaz, Ferzan.; Turgut, Osman Teoman.In this thesis, the properties of the Bose-Einstein condensation in at spaces are reviewed. Three dimensional weakly interacting Bose systems are examined by using the Bogoliubov approximation. The heat kernel of the Laplace operator is introduced. The Bose-Einstein condensation for an ideal gas and for a weakly interacting gas in the nonrelativistic limit on a Riemannian manifold with nonnegative Ricci curvature is studied using the heat kernel and eigenvalue estimates of the Laplace operator. The Bose gas is assumed to obey the Neumann boundary conditions. Behaviour of the chemical potential at low temperatures is described. Bounds for the depletion of the condensate and for the critical temperature of an ideal Bose system are derived in the thermodynamic limit. We observed that the condensation does not take place in two dimensions, however it is formed in three dimenions which is consistent with the at space results. In the case of dilute gases on a compact Riemannian manifold, Bogoliubov theory is applied. The ground state of a dilute Bose system is analyzed using the heat kernel methods. Specifically, the depletion of the condensate is estimated at absolute zero temperature. For finite volumes, we concluded that the condensate exists in two dimensions for weakly interacting gases. We also analyzed the depletion of the condensate at finite temperatures. Inconsistency of the Bogoliubov approximation in the thermodynamic limit is shown using heat kernel methods. Justification of the c-number substitution on a manifold is given.Item Finite size effects on the Bose-Einstein condensation(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2014., 2014.) Doğan, Ebru.; Turgut, Osman Teoman.In this thesis, the nite size e ects for the Bose-Einstein condensation are investigated. The application of the Poisson summation method on the ideal Bose gas (both for relativistic and non-relativistic cases) is studied. The Bose gas is assumed to be enclosed in a cubical nite enclosure with periodic boundary conditions. The Bogoliubov theory for the weakly interacting Bose gas is reviewed and an expression for the ground state energy in terms of the heat kernel is obtained. We observed that a well known result of the ground state energy is obtainable via an alternative method. Then for the zero temperature case, the depletion of the condensate is treated with the heat kernel analysis combined with the Poisson summation method. The results show that for such con guration, nite size corrections turn out to be of order 1=L2. Finally, for the zero temperature case, the ground state energy is analysed by scaling the heat kernel. This yields nite size corrections of order 1=L, a result which shows the necessity of a more elaborate treatment for more accurate results.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.