arXiv subjects
Publications and source records attributed to Sang-Hoon Kim.
We produce the discontinuity in the specific heat of a homogeneous, dilute, and weakly interacting Bose gas in a short-wavelength range with a simple statistical method. The magnitude of the discontinuity at the phase transition temperature is obtained as a function of the density and scattering length of the Bose particles.
We suggest a practical way to estimate the condensate fraction of an interacting dilute Bose gas confined by an external harmonic potential as a function of temperature and scattering length. It shows that an increase of the scattering length produces an exponential decrease of condensate fraction.
With the integral representation of Bose functions, the Bose-Einstein condensation of non-interacting bosons in a three-dimensional harmonic trap was studied. The relation between the particle number and its phase transition temperature was clarified. Some next-order terms in the thermodynamic expansions were obtained. We plotted the chemical potential, the mean energy, and the specific heat and found most of these properties obtained by using the integral representation were almost identical with those of the series representation of Bose functions.
We investigated an integral representation of a complex function which was obtained from the molecular beam magnetic resonance, and named it as `$g$- function' because it was connected with Gamma function as a special case. We introduced a physical example of the $g$-function from a dipole-dipole interaction of rigid polar molecules.
We suggested a method to estimate the quantum depletion of interacting Bose particles confined by a three dimensional harmonic trap.
The macroscopic quantum states of a condensed neutral Bose gas in one-dimensional power-law traps are obtained by solving the Gross-Pitaevskii equation numerically. A suitable candidate for a trial wave function for the variational calculation of ground state energy is suggested, and shown that the suggested function produces a lower ground state energy than the conventional Gaussian trial wave function.
The fractal structures of a green broccoli and a white cauliflower are investigated by box-counting method of their cross-sections. The capacity dimensions of the cross-sections are $1.78 \pm 0.02$ for a green broccoli and $1.88 \pm 0.02$ for a white cauliflower, and both are independent of their directions. From the results we predict that the capacity dimensions of the bulks are about 2.7 for a green broccoli and $2.8.$ for a white cauliflower. The vertical cross-sections of the two plants are modeled into self-similar sets of triangular and rectangular trees. We discuss the conditions of the fractal objects in the model trees.
The fractal structure of a white cauliflower is investigated by box-counting method of its cross-section. The capacity dimension of the cross-section is $1.88 \pm 0.02$ independent of directions. From the result, we predict that the capacity dimension of the cauliflower is about 2.8. The vertical cross-section of the cauliflower is modeled into a self-similar set of a rectangular tree. We discuss the condition of the fractal object in the tree, and show that the vertical cross-section has an angle of 67 degrees in our model.
A stack of disks with numerous holes composed of a non-interacting charged Bose gas is modeled as a low dimensional disk. The Bose condensation of the net-like disk system in a uniform magnetic field is studied. Calculation of the condensate fraction of the net-like disk system showed that there still exists a non-zero condensate fraction at low temperature and in weak field.
Condensate of a charged boson fluid at non-integer dimensions between 2 and 3 is studied. Interaction between particles is assumed to be Coulombic, and Bogoliubov approximation is applied for a weak coupling regime. The condensate and the superfluid fraction at finite temperatures and at non-integer dimensions are calculated. The theoretical results are compared with the superfluid densities of superconducting films, which show a universal splitting behavior. The qualitative similarity between the charged boson fluid and the superconducting films gives a strong clue for the origin of the universality.
The Bose condensation of a stack of low dimensional disks which is composed of a noninteracting charged Bose gas in a uniform magnetic field is studied. A statistical approach with density of states at noninteger dimensions are applied for the system. The condensate fraction of the disk system in a uniform magnetic field is calculated. The stack of low dimensional charged Bose disks is found not to share the condensate behavior of the traditional BCS superfluids.
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results of the 2D Bose condensation are also compared with those of the well-known 3D case.
Physical properties of ideal Bose gas with the fractal dimensionality between D=2 and D=3 are theoretically investigated. Calculation shows that the characteristic features of the specific heat and the superfluid density of ideal Bose gas in fractal dimensions are strikingly similar to those of superfluid Helium-4 in porous media. This result indicates that the geometrical factor is dominant over mutual interactions in determining physical properties of Helium-4 in porous media.
The trapped Bose system can be regarded as two-dimensional if the thermal fluctuation energy is less than the lowest energy in the perpendicular direction. Under this assumption, we derive an expression for the maximum thickness of an effective two-dimensional trapped Bose system.
We derive the Gross-Pitaevskii equation in two-dimension from the first principles of two-dimensional scattering theory. Numerical calculation of the condensate wave function shows that atoms in a two-dimensional harmonic trap can be condensed into its ground state. Moreover, the ground state energy and the wave function of two-dimensional vortex state are also obtained. Quantitative comparisons between 2D results and 3D ones are made in detail.
A dilute Bose gas system is studied using the functional Schrödinger picture theory. The ground state properties are obtained by solving the infinite dimensional Schrödinger equation variationally. It is shown that a shifted Gaussian trial wavefunctional enables us to calculate a higher order correction, which corresponds to the fluctuation contribution from the condensate. The obtained term is compared with the quantum correction arising from the low energy $3 \to 3$ scattering.