Yongle Yu

Renormalization of the Hartree-Fock-Bogoliubov equations in the case of a zero range pairing interaction.

We introduce a natural and simple way to implement the regularization scheme of the Hartree-Fock-Bogoliubov equations with zero range pairing interaction. The renormalization scheme proves to be equivalent to a simple energy cutoff with a position dependent running coupling constant.

Energy density functional approach to superfluid nuclei

We show that, within the framework of a simple local nuclear energy density functional (EDF), one can describe accurately the one- and two-nucleon separation energies of semimagic nuclei. While for the normal part of the EDF we use previously suggested parametrizations, for the superfluid part of the EDF we use the simplest possible local form compatible with known nuclear symmetries.

Real-Time Dynamics of Quantized Vortices in a Unitary Fermi Superfluid

A generalized theoretical approach is developed to describe the dynamics and phase transitions of Fermi superfluids. We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.

Vortex state in a strongly coupled dilute atomic fermionic superfluid.

We show that in a dilute fermionic superfluid, when the fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in fermionic superfluids possible.

Spatial structure of a vortex in low density neutron matter.

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.

Cold fermionic atoms in two-dimensional traps: pairing versus Hund's rule.

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hunds rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

Electron-Hole Duality and Vortex Rings in Quantum Dots

In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for fermions in a rotating trap the vortices appear as holes in the Fermi sea. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunneling spectroscopy. We use the duality picture to show that these oscillations are caused by the localization of vortices in rings.

Vortex localization in rotating clouds of bosons and fermions

Finite quantal systems at high angular momenta may exhibit vortex formation and localization. These phenomena occur independent of the statistics of the repulsively interacting particles, which may be of bosonic or fermionic nature. We analyze the relation between vortex localization and formation of stable Wigner molecules at high angular momenta in the view of particle-hole duality. Trial wave functions for the vortex states and the corresponding fermion-boson relations are discussed.

Shell correction energy for bubble nuclei

The positioning of a bubble inside a many fermion system does not affect the volume, surface, or curvature terms in the liquid drop expansion of the total energy. Besides possible Coulomb effects, the only other contribution to the ground state energy of such a system arises from shell effects. We show that the potential energy surface is a rather shallow function of the displacement of the bubble from the center and in most cases the preferential position of a bubble is off-center. Systems with bubbles are expected to have bands of extremely low lying collective states, corresponding to various bubble displacements.

Rotating quantum liquids crystallize

Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles.