전건상 교수

A microscopic confirmation of the fractional statistics of the quasiparticles in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at nu=1/3 and nu=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the sta

We study the Hubbard-Holstein model which includes both the electron-electron and electron-phonon interactions, characterized by $U$ and $g$, respectively. The model is solved with $U$ and $g$ on an equal footing in the infinite dimensions by employing the dynamical mean-field theory in combination with Wilson's numerical renormalization group. A zero temperature phase diagram of symmetry unbroken states at half filling is mapped out which exhibits the interplay between the two kinds of interact

We study the symmetric Anderson-Holstein (AH) model at zero temperature with Wilson's numerical renormalization-group (NRG) technique to investigate the interplay between the electron-electron and electron-phonon interactions. An improved method for calculating the phonon propagator using the NRG technique is presented. It is more accurate and reliable than the previous methods in that it is written in the form of the Dyson equation which calculates the phonon renormalization explicitly, and sat

Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that

The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, nontrivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kj\o{}

We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau levels. In particular, the composite-fermion wave function for a single quasiparticle has 15% lower energy than the trial wave function suggested by Laughlin, and for two quasiparticles, the composite fermion theory also gives new qualitative structures.

We investigate autonomous stochastic resonance in fully frustrated Josephson-junction ladders, which are driven by uniform constant currents. At zero temperature large currents induce oscillations between the two ground states, while for small currents the lattice potential forces the system to remain in one of the two states. At finite temperatures, on the other hand, oscillations between the two states develop even below the critical current; the signal-to-noise ratio is found to display array

We construct a simple model which describes the lattice dynamics of a single-wall boron nitride nanotube. The model includes short-range interactions between nearest and second-nearest neighbors as well as long-range Coulomb interactions between polar atoms. It is clearly shown that flexure modes exist in boron nitride nanotubes consisting of polar atoms. We also find that the frequency of the radial breathing mode is inversely proportional to the tube radius $R$ and that the lowest optical mode

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in fini

We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instab

We investigate the phonon dispersion of graphite within a generalized bond-charge model with emphasis on the microscopic origin of the infrared active mode. The resulting dispersion is in good agreement with experiments, particularly with the full optical spectra obtained by the recent x-ray scattering experiment. The computed strengths of the infrared peak are found to be comparable to the experimental values. We show that the dipole moment responsible for the infrared activity is induced by th

The phonons of single-wall carbon nanotubes are investigated within a generalized bond-charge model. The computed phonon dispersions generally agree with earlier results: two acoustic phonons (longitudinal and rotating), flexure modes at low frequencies, and radius-dependent radial breathing modes. Computation of the strength of the infrared active phonons reveals that only three modes have the first-order infrared activity in achiral tubes. We compare the observed modes with both experimental a

We study the properties of some known trial wave functions in bilayer quantum Hall systems at the total filling factor ${\ensuremath{\nu}}_{T}=1$. In particular, we find that the properties of a meron wave function and a natural ``quasihole'' wave function are dramatically different due to the broken symmetry and the associated Goldstone mode in the bulk. Although the (smallest) meron has localized charge $1∕2$ and logarithmically divergent energy, the charge of the quasihole excitation extends

The fully frustrated XY model is studied via the position-space renormalization group approach. The model is mapped into two coupled XY models, for which the scaling equations are derived. By integrating directly the scaling equations, we observe that there exists a narrow temperature range in which both the vortex and coupling charge fugacities grow large, suggesting double transitions in the system. While the transition at lower temperature is identified to be of the Kosterlitz-Thouless type,