Abstract:
Past theoretical studies have considered excitations of a given flavor of composite fermions across composite-fermion quasi-Landau levels. We show that in general there exists a ladder of flavor changing excitations in which composite fermions shed none, some, or all of their vortices. The lowest energy excitations are obtained when the composite fermions do not change their flavor, whereas in the highest energy excitations they are stripped of all of their vortices, emerging as electrons in the final state. The results are relevant to the intriguing experimental discovery of Hirjibehedin {\em et al.} (cond-mat/0306152) of coexisting excitation modes of composite fermions of different flavor in the filling factor range $1/3>\nu\geq 1/5$.

Abstract:
Using a Luttinger liquid description, the correlation function exponents of various response functions are calculated. Their striking sensitivity to the non perturbative Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons, the equivalent of a phase diagram is established. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity is rapidly approached. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.

Abstract:
The charge of quasiparticles in Pfaffian states of composite fermion excitations (the presence of which is indicated by recent experiments) is found. At the filling fraction of the Pfaffian state $\nu=p/q$ (of the lowest Landau level) the charge is $\pm e/(2q)$. As in the case of the Pfaffian state of electrons the statistics of $N_{qh}$ quasiholes in the Pfaffian state corresponds to the spinor representation of $U(1)\times SO(2N_{qh})$ (the continuous extension of the braid group). Here U(1) is given by the phase factor $e^{i({1/8}+\frac{1}{4m})\pi}$ with $m=1+\alpha$, $\alpha$ -- the exclusion statistics parameter of Jain quasiparticles. The possiblity of Read-Rezayi states of Jain quasiparticles is also discussed.

Abstract:
Excitation modes in the range $2/5 \geq \nu \geq 1/3$ of the fractional quantum Hall regime are observed by resonant inelastic light scattering. Spectra of spin reversed excitations suggest a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Spin-flip energies determined from spectra reveal significant composite fermion interactions. The filling factor dependence of mode energies display an abrupt change in the middle of the range when there is partial population of a composite fermion level.

Abstract:
We have investigated low energy excitations of a disk of electrons in half-filled Landau level using trail wave function and small-size exact diagonalization approaches. We have constructed a set of many-body basis states that describe correctly the low energy excitations. In this theory a droplet consists of two types of composite fermion liquids, and suggests that a droplet can support an edge magnetoplasmon and low energy droplet excitations. A possibility of measuring these excitations in a quantum dot is discussed.

Abstract:
Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range $2/5 \geq \nu \geq 1/3$. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor $\nu \gtrsim 1/3$ and at $\nu \lesssim 2/5$ identify a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At $\nu = 1/3$ energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.

Abstract:
Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.

Abstract:
We propose a fermion Chern-Simons field theory describing two- dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest Landau level constraint is enforced through a delta-functional described by an auxiliary field lambda. Unlike the field theory constructed directly with the states in the lowest Landau level, this theory allows one utilizing the physical picture of "composite fermion" to study the fractional quantum Hall states by mapping them onto certain integer quantum Hall states; but unlike it in the unconstrained theory, such a mapping is sensible only when interactions between electrons are present. An "effective mass", which characterizes the scale of low energy excitations in the fractional quantum Hall systems, emerges naturally from our theory. We study a Gaussian effective theory and interpret physically the dressed stationary point equation for lambda as an equation for the "mass renormalization" of composite fermions.

Abstract:
We derive a microscopic theory of the composite fermion type quasiparticles describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu=1/m$. Using the composite fermion transformation, one finds that the edge states of the system in a disc sample are described by the Calogero-Sutherland-like model (CSLM) in the one-dimensional limit. This result presents the consistency between one-dimensional and two-dimensional statistics. It is shows that the low-lying excitations, indeed, have the chiral Luttinger liquid behaviors because there is a gap between the right- and left-moving excitations of the CSLM.

Abstract:
We investigate the response of a two-dimensional electron gas, in the fractional quantum Hall regime, to the sudden appearance of a localised charged probe using the Chern-Simons theory of composite fermions. The dynamic structure factor of the electron gas is found to have a major influence on the spectral function of the probe. In particular, there is an orthogonality catastrophe when the filling factor is an even-denominator filling fraction due to the compressibility of the state, but there is no catastrophe at odd-denominator filling factors because these states have a gap to excitations. The catastrophe is found to be more severe for composite fermions in zero effective magnetic field than it is for electrons in zero real magnetic field. Oscillations in the spectral function, arising when the composite fermions are at integer filling, have a period equal to the composite fermion cyclotron energy. We propose a tunneling experiment which directly measures the spectral function from which one could determine the composite fermion effective mass.