Related papers: The Hydrodynamical Limit of Quantum Hall system
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
We consider the behaviour of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low energy, large system limit. Using the close links between quantum Hall wavefunctions and conformal field theories we construct…
We study how the stability of the fractional quantum Hall effect (FQHE) is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit…
We consider a channel of an incompressible fractional-quantum-Hall-effect (FQHE) liquid containing an island of another FQHE liquid. It is predicted that the resistance of this channel will be periodic in the flux through the island, with…
This Letter presents a magnetohydrodynamic model that describes the small-amplitude fluctuations with wavelengths comparable to ion inertial length in the presence of a relativistically strong mean magnetic field. The set of derived…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…
Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
In this work we investigate collective excitations at the boundary of a recently constructed 4D quantum Hall state. Local bosonic operators for creating these collective excitations can be constructed explicitly. Massless relativistic wave…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
Fractional quantum Hall (FQH) systems are strongly interacting electron systems with topological order. These systems are characterized by novel ground states, fractionally charged and neutral excitations. The neutral excitations are…
In the strong magnetic field fractional quantum Hall regime, electrons in a two-dimensional electron system are confined to their lowest Landau level. Because of the macroscopic Landau level degeneracy nearly all physical properties at low…
We study the effects of Landau level mixing in the limit of weak electron interaction. We use a numerical method to obtain the two- and three-body corrections to quantum Hall pseudopotentials, which are exact to lowest order in the Landau…
I present a brief survey of important recent developments in the quantum Hall effect. The review covers both fractional and integer regimes, from an experimentalist's perspective. The topics include direct measurement of fractional charge,…
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…
We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems which are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to…
We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously beyond the reach…
We derive the formulae of fluctuating hydrodynamics appropiate to a relativistically consistent divergence type theory, obtaining Landau - Lifshitz fluctuating hydrodynamics as a limiting case.
A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $\nu < 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE…
The integer quantum Hall effect (QHE) belongs to the most fundamental phenomena of solid state physics and has an important application as resistance standard. It serves as a basis to understand the fractional, anomalous or spin QHEs,…