arXiv subjects

Yeong E. Kim

Publications and source records attributed to Yeong E. Kim.

17 recordsLinked to original sources

arXiv2005

Hydrodynamic Modes in a Trapped Strongly Interacting Fermi Gases of Atoms

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.

cond-mat.stat-mech↗

arXiv2005

Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap

The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the Hylleraas-Undheim method, we construct rigorous upper bounds to the collective frequencies for the radial and the axial breathing mode of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The bounds are compared to experimental data for trapped vapors of Li6 atoms.

cond-mat.other↗

arXiv2004

Strongly Interacting Fermi Gases of Atoms Confined in a Harmonic Trap

Dynamics of strongly interacting Fermi gases, consisting of a 50-50 mixture of two different fermionic species, is investigated. For the equation of state we consider a Padé [2/2] approximations, which gives the weak-coupling perturbative formula (up to 4th order) in the low density regime, the unitary-limit Monte Carlo result in the high density regime, and reproduces the 4-fermion prediction for dimer-dimer scattering length in the BEC region. We use a time-dependent LDA to derive various properties of the Fermi gas under a harmonic confinement and compare them with the data of very recent experiments of 6Li atoms across a Feshbach resonance.

cond-mat.other↗

arXiv2004

Dynamics of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap

Dynamics of strongly interacting trapped dilute Fermi gases is investigated at zero temperature. As an example of application we consider the expansion of the cloud of fermions initially confined in an anisotropic harmonic trap, and study the equation of state dependence of the radii of the trapped cloud and the collective oscillations in the vicinity of a Feshbach resonance.

cond-mat.soft↗

arXiv2004

Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms

The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime. It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.

cond-mat.soft↗

arXiv2003

Cold Bose Gases near Feshbach Resonances

The lowest order constrained variational method [Phys. Rev. Lett. 88, 210403 (2002)] has been generalized for a dilute (in the sense that the range of interatomic potential is small compared with inter-particle spacing) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na (F=1, m_F=1) atoms near the $B_0=907$G Feshbach resonance. It is shown that at high densities, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform con densate for the case of negative scattering length.

cond-mat.soft↗

arXiv2003

Three-Body Losses in Trapped Bose-Einstein Condensed Gases

A time-dependent Kohn-Sham (KS)-like equation for N bosons in a trap is generalized for the case of inelastic collisions. We derive adiabatic equations which are used to calculate the nonlinear dynamics of the Bose-Einstein condensate (BEC) and non-mean field corrections due to the three-body recombination. We find that the calculated corrections are about 13 times larger for 3D trapped dilute bose gases and about 7 times larger for 1D trapped weakly interacting bose gases when compared with the corresponding corrections for the ground state energy and for the collective frequencies.

cond-mat.soft↗

arXiv2002

Density Functional Theory of Bosons in a Trap

A time-dependent Kohn-Sham (KS) like theory is presented for N bosons in thre e and lower-dimensional traps. We derive coupled equations, which allow one to calculate the energies of elementary excitations. A rigorous proof is given to show that the KS like equation correctly describes properties of the one-dimensional condensate of impenetrable bosons in a general time-dependent harmonic trap in the larg N limit.

cond-mat.soft↗

arXiv2001

Interacting Electrons in Quantum Dots

The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with the results of exact diagonalization. Analytic results for the lower bounds to the ground-state energies of the quantum dots in a strong magnetic field (known as electron molecule) agree very well with numerically calculated lower bounds.

cond-mat↗

arXiv2001

Beyond the Thomas-Fermi Approximation for Nonlinear Dynamics of Trapped Bose-Condensed Gases

We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms $N$. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments.

cond-mat.stat-mech↗

arXiv2001

Ground-State of Charged Bosons Confined in a Harmonic Trap

We study a system composed of N identical charged bosons confined in a harmonic trap. Upper and lower energy bounds are given. It is shown in the large N limit that the ground-state energy is determined within an accuracy of $\pm 8%$ and that the mean field theory provides a reasonable result with relative error of less than 16% for the binding energy .

cond-mat.stat-mech↗

arXiv2000

Separable Structure of Many-Body Ground-State Wave Function

We have investigated a general structure of the ground-state wave function for the Schrödinger equation for $N$ identical interacting particles (bosons or fermions) confined in a harmonic anisotropic trap in the limit of large $N$. It is shown that the ground-state wave function can be written in a separable form. As an example of its applications, this form is used to obtain the ground-state wave function describing collective dynamics for $N$ trapped bosons interacting via contact forces.

cond-mat.soft↗

arXiv1999

Effective Linear Two-Body Method for Many-Body Problems

This paper reports a detailed description of the equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. To test the accuracy of the method it has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.

cond-mat↗

arXiv1999

Equivalent Linear Two-Body Equations for Many-Body Systems

A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in anisotropic harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.

cond-mat↗

arXiv1998

Stability of Solution of the Nonlinear Schrödinger Equation for the Bose-Einstein Condensation

We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment.

cond-mat↗

arXiv1997

A Unified Construction of Variational Methods for the Nonlinear Schroedinger Equation

Based on an approach introduced byGerjuoy, Rau, and Spruch, we constract variational principles in a systematic way for the nonlinear Schroedinger equation and obtain new variational principles for the case of Ginzburg-Pitaevskii-Gross equation (PGP) which is belived to describe accurately the Bose-Einstein condensation at zero temperature. As an application of these variational methods, a variational iteration method is proposed for calculating eigenvalue (chemical potential) and wave function for the GPG equation

cond-mat↗

arXiv1997

The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory

Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for improving the convergence are discussed when the R-function series is truncated for practical applications.

physics.atom-ph↗