Chi-Yong Lin

Doorway states and the Bose-Hubbard model

We apply the doorway method to solve the problem of N bosons in an optical lattice. This method allows for the inclusion of many-body correlations in a dynamically motivated hierarchical way, yielding useful approximations even within subspaces of the full Hilbert space of greatly reduced dimensionality. We calculate some important experimental observables. Excellent qualitative agreement with exact numerical calculations and recent experimental observations is obtained.

Equilibrium and stability properties of a coupled two-component Bose–Einstein condensate

The equilibrium and stability properties of a coupled two-component BEC is studied using a variational method and the one-dimensional model of Williams and collaborators. The variational parameters are the population fraction, translation and scaling transformation of the condensate densities, assumed to have a Gaussian shape. We study the equilibrium and stability properties as a function of the strength of the laser field and the traps displacement. We find many branches of equilibrium configurations, with a host of critical points. In all the cases, the signature of the onset of criticality is the collapse of a normal mode which is a linear combination of the out-of-phase translation and an in-phase breathing oscillation of the condensate densities. Our calculations also indicate that we have symmetry breaking effects when the traps are not displaced.

Fermion pairing dynamics in the relativistic scalar plasma

Using many-body techniques we obtain the time-dependent Gaussian approximation for interacting fermion-scalar field models. This method is applied to an uniform system of relativistic spin-1/2 fermion field coupled, through a Yukawa term, to a scalar field in 3+1 dimensions, the so-called quantum scalar plasma model. The renormalization for the resulting Gaussian mean-field equations, both static and dynamical, are examined and initial conditions discussed. We also investigate solutions for the gap equation and show that the energy density has a single minimum.

Elementary Excitations of a Higgs-Yukawa System

This work investigates the physics of elementary excitations for the so-called relativistic quantum scalar plasma system, also known as the Higgs–Yukawa system. Following the Nemes–Piza–Kerman–Lin many-body procedure, the random-phase approximation (RPA) equations were obtained for this model by linearizing the time-dependent Hartree–Fock–Bogoliubov equations of motion around equilibrium. The resulting equations have a closed solution, from which the spectrum of excitation modes are studied. We show that the RPA oscillatory modes give the one-boson and two-fermion states of the theory. The results indicate the existence of bound states in certain regions in the phase diagram. Applying these results to recent Large Hadron Collider observations concerning the mass of the Higgs boson, we determine limits for the intensity of the coupling constant g of the Higgs–Yukawa model, in the RPA mean-field approximation, for three decay channels of the Higgs boson. Finally, we verify that, within our approximations, only Higgs bosons with masses larger than 190 GeV/

Molecular signatures in hybrid atomic-molecular Bose-Einstein condensates

c^2

Initial value problem in quantum field theory: An Application to the relativistic scalar plasma

can decay into top quarks.

Bogoliubov theory for mutually coherent hybrid atomic molecular condensates: Quasiparticles and superchemistry

As it was proposed and recently verified experimentally, the mechanism of Feshbach resonance in a condensate can create a second condensate component of molecules that coexists with the atomic condensate. In this work we investigate signatures of the presence of the molecular condensate through the equilibrium properties and collective excitations of the hybrid system of atoms and molecules, subjected to a trap, employing a time-dependent variational ansatz. We show that the shape of the condensate changes significantly by the presence of the molecules and that modes unique to this hybrid system appear at observable frequencies.