相关论文: Multi-Resolution Analysis and Fractional Quantum H…

For a gaussian interaction V(x,y)=\lambda e^{-(x^2+y^2)/r^2} with long range r>>l_B, l_B the magnetic length, we rigorously prove that the eigenvalues of the finite volume Hamiltonian H_{N,LL}=P_{LL} H_N P_{LL}, H_N=\sum_{i=1}^N [-i\hbar…

The problem of a single electron in a magnetic field is revisited from first principles. It is shown that the standard quantization, used by Landau, is inconsistent for this problem, whence Landau's wave functions spontaneously break the…

We study two alternative definitions of localized states in the lowest Landau level (LLL) on a torus. One definition is to construct localized states, as projection of the coordinate delta function onto the LLL. Another definition, proposed…

I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors $\nu$, continuously as a function of magnetic field,…

To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…

Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At ``filling factor'' near…

We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of…

Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field…

We find a quantum group structure in two-dimensional motion of nonrelativistic electrons in a uniform magnetic field on a torus. The representation basis of the quantum algebra is composed of the quantum Hall wavefunctions proposed by…

In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge…

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the…

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…

Through the introduction of a class of appropriate translationally invariant trial wave functions, we show that the strong correlations in the lowest Landau level (LLL) reflect in finite systems the emergence of intrinsic point-group…

The Laughlin function of quantum Hall effect is shown to satisfy Hirota's bilinear difference equation with certain coefficients a little different from the KP hierarchy. Vertex operators which constitute blocks of solutions generate a…

We investigate the Hall effect in a quasi one-dimensional system made of weakly coupled Luttinger Liquids at half filling. Using a memory function approach, we compute the Hall coefficient as a function of temperature and frequency in the…

We develop the theory of multiresolutions in the context of Hausdorff measure of fractional dimension between 0 and 1. While our fractal wavelet theory has points of similarity that it shares with the standard case of Lebesgue measure on…

In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the…

Through the introduction of a class of trial wave functions portraying combined rotations and vibrations of molecules formed through particle localization in concentric polygonal rings, a correlated basis is constructed that spans the…

The Hamiltonian Theory of the fractional quantum Hall effect is an operator description that subsumes many properties of Composite Fermions, applies to gapped and gapless cases, and has been found to provide results in quantitative accord…

We construct an effective Hamiltonian for electrons in the fractional quantum Hall regime for GaAs and graphene that takes into account Landau level mixing (for both GaAs and graphene) and subband mixing (for GaAs, due to the nonzero width…