Neutrino masses have been extensively studied in the context of discrete symmetries. A family permutation symmetry easily explains all neutrino oscillations and their mixing angles. However it is not obvious the embedding of such symmetry in a grand unified theory where all fermions live in the same representation. We show that it is possible to embed such a horizontal discrete symmetry in a gr...

Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for electrons, can be applied to interacting bosons. Numerical evidence supporting the formation of composite fermions, each being the bound state of a boson and ...

We demonstrate the formation of composite fermions in two-dimensional quantum dots under high magnetic fields. The composite fermion interpretation provides a simple way to understand several qualitative and quantitative features of the numerical results obtained earlier in exact diagonalization studies. In particular, the ground states are recognized as compactly filled quasi-Landau levels of ...

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 d...

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions n51/3, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite-fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interaction...

Variational Monte Carlo calculations of the quasielectron and quasihole ex-citation energies in the fractional quantum Hall effect have been carried out at filling fractions ν = 1/3, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interact...

To test the validity of replacing a composite fermion by an elementary fermion,we calculate the transition rate from a statemade of one free electron and one trion to a similar electron–trion pair, through the time evolution of such a pair induced by Coulomb interaction between elementary fermions. It is convenient to describe trion as one electron interacting with one exciton. This allows us t...

The Fermi hypernetted-chain theory is applied to study the half-filled state of the fractional quantum Hall effect in the thermodynamic limit. We study in detail the radial distribution function, the correlation energy, and the quasiparticle-quasihole excitation spectrum of an unprojected Fermi wave function of the form cn51/2 5P j,k N (z j2zk) 2 Det$fkW(r W)%, a possible candidate to describe ...

We report on an effective vector-field theory of the fractional quantum Hall effect that takes into account projection to Landau levels. The effective theory refers to neither the compositeboson nor composite-fermion picture, but properly reproduces the results consistent with them, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states. In particular,...