Browsing by Subject "Lattice theory."
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Item Open Access Hard spin mean field theory of 3D stacked-triangular-lattice system(1994) Akgüç, Gürsoy BozkurtClosed form solution of ‘Hard spin mean field theory’ is constructed and applied to ‘Three dimensional stacked-triangular-system’. The phase diagram of this system is examined. ‘Free energy’ is calculated to reveal the thermodynamically stable state in the phase diagram. A new second order phase transition line is found near the zero external magnetic field. Strong evidence is found for the tricriticality point behaviour in the multicritical region.Item Open Access The lattice of periods of a group action and its topology(2006) Acan, HüseyinIn this thesis, we study the topology of the poset obtained by removing the greatest and least elements of lattice of periods of a group action. For a G-set X where G is a finite group, the lattice of periods is defined as the image of the map from the subgroup lattice of G to the partition lattice of X which sends a subgroup H of G to the partition of X whose blocks are the H-orbits of X. We study the homotopy type of the associated simplicial complex. When the group G belongs to one of the families dihedral group of order 2n , dihedral group of order 2p n where p is an odd prime, semi-dihedral group, or quaternion group and the set X is transitive, we find the homotopy type of the corresponding poset. If G is the dihedral group of order 2n or one of semidihedral and quaternion groups, we find that the homotopy type of the complex is either contractible or has the homotopy type of three points. In the case of dihedral group of order 2p n , the associated complex is either contractible or it has the homotopy type of p points or it has the homotopy type of p + 1 points.Item Open Access Quantum gases in rotating optical lattices(2010) Umucalılar, Rifat OnurThe thesis is structured into two main parts so as to cover bosons and fermions in rotating optical lattices separately. In the first part, after a brief introduction to ultracold atoms in optical lattices, we review the single-particle physics for the lowest (s) band of a periodic potential under an artificial magnetic field created by rotation. Next, we discuss rotational effects on the first excited (p) band of the lattice, extending the methods available for the lowest band. We conclude the first part with a discussion of many-body physics in rotating lattice systems using a mean-field approach and investigate how the transition boundary between superfluid and Mott insulator phases is affected by the single-particle spectrum. In this context, we also examine a possible coexistent phase of Mott insulator and bosonic fractional quantum Hall states, appearing for certain system parameters near the Mott insulator lobes in the phase diagram. The second part starts with the proposal of a realization and detection scheme for the so-called topological Hofstadter insulator, which basically reveals the single-particle spectrum discussed before. The scheme depends on a measurement of the density profile for noninteracting fermions in a rotating optical lattice with a superimposed harmonic trapping potential. This method also allows one to measure the quantized Hall conductance, a feature which appears when the Fermi energy lies in an energy gap of the lattice potential. Finally, we explore the Bardeen-Cooper-Schrieffer type of pairing of fermionic atoms in optical lattices under an artificial magnetic field by paying special attention to single-particle degeneracies and present our results for the vortex lattice structure of the paired fermionic superfluid phase.