Dynamical properties of vortices in superfluid systems.

摘要

The dynamical properties of vortices in superfluid systems are investigated theoretically and numerically. A novel nonlocal nonlinear Schrodinger Lagrangian for the superfluid system is derived from the microscopic many body Feynman wave function. The limiting cases are analyzed and relationship to ordinary nonlinear Schrodinger Lagrangian is established.;The same Feynman wave function is used to construct a Hamiltonian to study the interaction of vortices with collective excitations. A general formula for the scattering cross-section is found in the Born approximation in terms of the Feynman excitation spectrum. The transverse force on the vortex is shown to vanish due to the symmetry of the cross-section. The classical limit of the dynamical equations are also derived.;The linearized dynamical theory of the vortex is developed based on the local nonlinear Schrodinger Lagrangian. The dynamical equations that govern the motion of the vortex and the collective excitations are obtained. The natural motion of the vortex is found to be of cyclotron type. Clear definitions of vortex mass and viscousity are given in analogy to the cyclotron motion of a charged particle.;The compressibility of the system limits the applicability of the adiabatic assumption within a phonon wavelength at to the cyclotron frequency and the vortex mass does not diverge logarithmically with the system size. The vortex motion is heavily damped due to radiation of phonons. Loading the vortex core with external particles reduces damping. An analytical formula is obtained for the effective vortex mass for a heavy external particle. The dynamical equations of a loaded vortex under the influence of a time dependent force are numerically solved and the Green's function of the vortex is found for a general motion. The analytical results for heavy external particle are confirmed and the vortex core mass is calculated.