| This dissertation touches on a few semiclassical topics, all pertaining to many-body quantum systems.; An analysis of two-dimensional vortex dynamics in a dilute Bose superfluid is presented first. The appropriate field equation is the time-dependent nonlinear Schrödinger equation, which has static vortex solutions. The fluid's linear response to slow motions of the vortex core is derived through a normal mode analysis. The classical motion of the core under an arbitrary external force is studied and compared to the incompressible case.; Immersed molecules in three-dimensional superfluids are studied in the next section, with emphasis on the role of molecular shape and symmetry in determining the quantum spectrum. The fluid is assumed to be incompressible, which allows for complete quantization of the effective molecular Lagrangian. The resulting quantum Hamiltonian generalizes the usual rigid-rotor Hamiltonian, as it includes a coupling between linear and angular momenta which is impossible in a Galilean-invariant system. The spectrum has some interesting new features, such as a ground state with nonzero linear momentum, and it is argued that experimental verification of its main attributes should be possible.; The next chapter deals with the relation between classical and quantum ordering in spin lattices. The Schwinger-boson transformation is used to exactly map spin to bosonic degrees of freedom; the rotationally invariant mean-field theory suggested by the result is discussed. A detailed calculation demonstrates how Gaussian fluctuations around the semiclassical theory can be included for an arbitrary lattice. An application of the theory to a concrete spin model is given.; The final section addresses the semiclassical physics of anharmonic chains. Results on classical and quantum-mechanical intrinsic localized modes in nonlinear lattices are reviewed. A derivation of the Gutzwiller trace formula is given, based on the phase-space path integral, with attention to those extensions required for systems with symmetry. Generalized Bohr-Sommerfeld quantization conditions are used to study the semiclassical correspondence between classical and quantum localized modes. The results show that periodic-orbit quantization of a classical chain can be used to find bands of localized states in the corresponding quantum system. |
