Browsing by Subject "Quantum"
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Item Dynamical refinement in loop quantum gravity(2015-08) Hassan, Syed Asif; Matzner, Richard A. (Richard Alfred), 1942-; Dicus, Duane A; Freed, Daniel S; Morrison, Philip J; Weinberg, StevenIn Loop Quantum Gravity, a quantum state of the gravitational field has a semiclassical interpretation as a three-dimensional lattice discretization of space. We explore the possibility that the scale of the lattice is only as fine as it needs to be in order to carry the dominant frequency excitations of the auxiliary fields living on the lattice, by considering graph-changing transition amplitudes in the context of a pure gravity quantum theory. We define regular graphs that correspond to closed spatial slices of FLRW spacetime in a novel way, with coherent state labels that correspond to physical observables. This correspondence is obtained using the novel concept of a pseudoregular polyhedron which affords a dimensionless volume to surface area ratio in terms of the number of faces of the polyhedron. We normalize these regular graph states using a new method, employing a saddle point approximation based on the valence of the nodes rather than the large-scale semiclassical limit to obtain a result that holds in the quantum limit. Finally we employ the EPRL spin foam model to obtain a transition amplitude between single-node graphs of arbitrary valence that is valid in both the semiclassical and quantum regimes, using an improved method of normalizing the amplitude. We find that if we fix the scale factor and the fiducial volume of space the amplitude favors final states with infinitely large valence.Item Electronic correlations in few layer graphene(2011-12) Zhang, Fan, 1983-; MacDonald, Allan H.In this thesis we investigate the electronic band structures and the correlations in chirally (ABC) stacked N-layer graphene with N ≥ 2. We use ab initio density-functional theory and k · p theory to fit the parameters of a p-band tightbinding model. External potential differences between top and bottom layers are strongly screened by charge transfer but still open an energy gap at overall neutrality. Perpendicular magnetic field drives the system into the quantum Hall region with 4N-fold zero energy Landau levels. We predict that Coulomb interactions spontaneously break the SU(4N) symmetry and drive quantum Hall effects at all integer fillings n from −2N to 2N with exotic spin and pseudospin polarizations. Based on mean-field theory and perturbative renormalization group analysis, we predict that the ground state of bilayer graphene spontaneously breaks inversion symmetry for arbitrarily weak electron-electron interactions and conclude that this instability is not suppressed by quantum fluctuations but that, because of trigonal warping, it may occur only in high quality suspended bilayers. Remarkably flat conduction and valence bands that touch at charge neutrality point and Bloch states with large pseudospin chirality combine to make the bilayer graphene gapless band state strongly susceptible to a family of broken symmetry states in which each spinvalley flavor spontaneously transfers charge between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We further analyze how these competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using response and edge state signatures to identify the character of the bilayer ground state experimentally. We demonstrate that similar insulating broken symmetry states and spontaneous topological orders also occur in bilayer’s thicker cousins, chirally stacked multilayer graphene systems.