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

Following recent work of Halperin, Lee, and Read, and Kalmeyer and Zhang, a double-layer electron system with total Landau-level filling factor $\nu=1/2$ is mapped onto an equivalent system of fermions in zero average magnetic field…

In the presence of a periodic potential Landau levels (LLs) are broadened, forming a barrier for accurate simulation of fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of…

We build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system. We show that the constraint can be transmitted from one hierarchical state to the…

A recent experimental study [Pan et al., arXiv: 1902.10262] has shown that fractional quantum Hall effect gaps are essentially consistent with particle-hole symmetry in the lowest Landau level. Motivated by this result, we consider a clean…

The structure of fractional fillings of higher Landau levels including spin subbands is systematically derived for the first time. Using topology-type commensurability arguments for 2D charged system in the presence of strong quantizing…

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis…

A fractional quantized Hall state with filling fraction $\nu = p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these…

New proofs of theorems on the multifractal formalism are given. They yield results even at points q for which Olsen's functions b(q) and B(q) differ. Indeed, we provide an example of measure for which functions b and B differ and for which…

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution…

At total Landau level filling factor $\nu_{tot}=1$ a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the…

Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $\nu=2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown…

On a class of asymptotically conical manifolds, we prove two types of low frequency estimates for the resolvent of the Laplace-Beltrami operator. The first result is a uniform $ L^2 \rightarrow L^2 $ bound for $ \langle r \rangle^{-1} (-…

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry (PHS) of the FQHE states about half-filling in the lowest Landau level. The…

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the…

We derive heuristically an integro-differential equation, as well as a shell model, governing the dynamics of the Lowest Landau Level equation in a high frequency regime.

Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states in higher Landau levels and those in the lowest Landau level,…

In the Fractional Quantum Hall Effect (FQHE), in the noninteracting limit, only a fraction $\nu $ of the Lowest Landau Level (LLL) is occupied, producing a huge degeneracy. Interactions lift this degeneracy and mix in higher LL's. In the…

We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and…

A new class of analytic and parameter-free, strongly correlated wave functions of simple functional form is derived for few electrons in two-dimensional quantum dots under high magnetic fields. These wave functions are constructed through…

We show that all lowest Landau level projected and unprojected chiral parton type fractional quantum Hall ground and edge state trial wave functions, which take the form of products of integer quantum Hall wave functions, can be expressed…