Physics
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Item Learning and Enhancing Important Fluctuations in Model Hamiltonian Systems(2019) Cisneros, Freddy Alexis; Tiwary, Pratyush; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we discuss the need for enhanced sampling methods, namely to allow the simulation to sample hard to reach microstates of the system, allowing us to make better approximations of thermodynamic observables obtained from a simulation. To do this, we first introduce three enhanced sampling methods that can be applied Monte Carlo simulations with emphasis on the $2d$ Ising model. These three enhanced sampling methods are Wang-Landau sampling, a Variational Approach to Monte Carlo simulations developed by Yantao Wu and Roberto Car, and the Predictive Reweighted Autoencoded Variational Bayes for Enhanced Sampling (pRAVE) method which was developed by our group. After introducing these three methods we then apply pRAVE to the $2d$ Ising model in the absence of an external magnetic field. Using pRAVE we explore the relative importance of the net magnetic moment to the average nearest neighbor interaction energy, and the average second nearest neighbor interaction energy as the critical temperature of the system $T_C$ is approached. We compare our results to what we should expect given that the correlation length diverges as the critical temperature is approached. We also determine the heat capacity using data from our simulation to benchmarking against Onsager's asymptotic solution near the critical temperature $T_C$. We explain how discrepancies between Onsager's results and ours can be reduced by increasing the lattice size used in our analysis. We also provide free energy plots at temperatures ranging from $T =0.9T_C$ to $T=0.999T_C$ and show that the barrier separating the two states of the $2d$ Ising model decreases as the temperature $T$ of the system is increased, in agreement with what should be observe. After presenting our results, we discuss further work that can be done when applying pRAVE to the $2d$ Ising model as well as more complex Hamiltonians. This then paves the way for the use of pRAVE to study mechanisms for crystal nucleation as mentioned in the Conclusion of this thesis.Item Kelvin Probe Microscopy Studies of Epitaxial Graphene on SiC(0001)(2011) Curtin, Alexandra E.; Fuhrer, Michael S; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Epitaxial graphene on SiC(0001) presents a promising platform for device applications and fundamental investigations. Graphene growth on SiC(0001) can produce consistent monolayer thickness on terraces and good electronic properties. In exfoliated graphene on SiO2, random charged impurities in the SiO2 surface are thought to be the dominant scatterers, explaining the observed transport properties as well as the spatial charge inhomogeneity seen in scanned-probe experiments. In contrast, the scattering mechanisms and charge distribution in epitaxial graphene remain relatively unexplored. Here I use Kelvin probe microscopy (KPM) in ambient and UHV conditions to directly measure the surface potential of epitaxial graphene on SiC(0001). Ambient-environment KPM on graphene/SiC(0001) shows surface potential variations of only 12 meV. Taken together with transport measurements, the data suggest that the graphene samples in ambient are in the low-doped regime, near the minimum conductivity of roughly 4e2/h. I am also able to use UHV KPM of graphene/ SiC(0001) to identify the discrete surface potentials of monolayer and bilayer graphene as well as the insulating interfacial carbon layer and bare SiC, correlated with scanning electron micrographs of the same location. The surface potential differences between monolayer and bilayer graphene and between IFL and monolayer graphene are both suggestive of low doping (≤1012 cm-2). The surface potentials of monolayer and bilayer graphene are relatively smooth, while the IFL and bare SiC, in contrast, showed larger variations in surface potential suggesting the presence of unscreened charged impurities present on the IFL that are later screened by the overgrown graphene. I model the potential variations for unscreened and graphene-screened charged impurities using the self-consistent theory of graphene developed by Adam et al. The results show that although surface potential variations are, as expected, larger in the IFL than in graphene, both surfaces display surface potential variations 10-40 times smaller than predicted by theory. While ambient electronic transport data and surface potential steps suggest our samples are only lightly doped (≤1012 cm-2), in a regime dominated by electron-hole puddles, we do not observe these puddles in UHV. The absence of puddles in UHV leaves the source of doping in these samples an open question.Item Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies(2011) Robertson, Andrew Benjamin; Galitski, Victor M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A toolbox of theoretical methods pertinent to the study of non-equilibrium many-body quantum mechanics is presented with an eye to specific applications in cold atoms systems and solids. We discuss the generalization from unitary quantum mechanics to the non-unitary framework of open quantum systems. Theoretical techniques include the Keldysh close-time-path integral and its associated correlation functions, the quantum kinetic equation, and numerical integration of equations of motion both unitary and non-unitary. We explore how the relaxation of the assumption of equilibrium yields a whole new array of sometimes counterintuitive effects. We treat such examples as the non-equilibrium enhancement of BCS superfluidity by driving, bistability and coherent population transfer in Feshbach coupled fermions, and the dynamic stimulation of quantum coherence in bosons confined to a lattice. These systems are considered with an eye to enhancing some useful quantum properties and making them available in wider parameter regimes.