Related papers: Quantum Hall effect from soliton equation
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We present here a classical hydrodynamic model of a two-dimensional fluid which has many properties of Fractional Quantum Hall effect. This model incorporates the FQHE relation between the vorticity and density of the fluid and exhibits the…
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 systematically derive the quantum kinetic equation in full phase space for any quadratic hamiltonian of bosonic fields, including in the absence of translational invariance. This enables the treatment of boundaries, inhomogeneous systems…
The exactness and universality observed in the quantum Hall effect suggests the existence of a symmetry principle underlying Laughlin's theory. We review the role played by the infinite $W_{\infty }$ and conformal algebras as dynamical…
The quantum Hall effect is a fascinating electrical transport phenomenon signified by precise quantization of Hall conductivity $\sigma_\mathrm{xy}$ and vanishing longitudinal conductivity $\sigma_\mathrm{xx}$. Laughlin proposed an elegant…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…
We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of {\it{bilayer}} QH system and our model can simulate it, in…
The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the first observed signature is a Hall resistance quantized to…
We derive an effective hamiltonian in the Lowest Landau Level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy. We then…
The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven phenomenon bearing…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component…
Bilayer quantum Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level…
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
We uncover a new origin of the planar Hall effect - as an intrinsic property of layer coherent electrons - that exists even in bilayer and trilayer atomically thin limit. It reforms the existing theories requiring three-dimensional orbital…
Breakdown of the Quantum Hall Effect at high values of injected current is explained as a consequence of an abrupt formation of a metallic ``river'' percolating from one edge of the sample to the other. Such river is formed when lakes of…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
A quaternionic analog of the Aharonov-Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics (QQM). A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new…