Related papers: Propagating edge states for a magnetic Hamiltonian

We present a method to find asymptotics for the evolution of coherent states (or Gaussian wavepackets with standard deviation $\sqrt{h}$) under semiclassical Schr\"odinger's equation for a given Hamiltonian. These results extend the work of…

The discovery of the Quantum Spin Hall state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the Quantum Spin Hall state confirmed the presence of edge states, showed ballistic edge…

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows…

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate a charge redistribution between cyclotron-split edge states at high imbalance. We also modify…

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this…

Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…

We analyse the effects of Robin boundary conditions on quantum field theories of spin 0, 1 and 1/2. In particular, we show that these conditions always lead to the appearance of edge states that play a significant role in quantum Hall…

Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moore's law. Nevertheless, their dispersion has…

We present an approach to the fractional quantum Hall effect observed in grapheme (GFQHE), basing us on the model developed previously for the fractional quantum Hall effect in a two-dimensional electron system embedded in a quantum well…

We study the persistent edge current in the fractional quantum Hall effect. We give the grand partition functions for edge excitations of hierarchical states coupled to an Aharanov-Bohm flux and derive the exact formula of the persistent…

In this paper we study a particle under the influence of a Lennard-Jones potential moving in a simple quantum wire modelled by the positive half-line. Despite its physical significance, this potential is only rarely studied in the…

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…

We expand the off-resonant scattering theory for particle diffusion in magnetized current filaments that can be typically compared to astrophysical jets, including active galactic nucleus jets. In a high plasma beta region where the…

We review the fermionic Chern-Simons field theory for the Fractional Quantum Hall Effect (FQHE). We show that in this field theoretic approach to the problem of interacting electrons moving in a plane in the presence of an external magnetic…

Highly correlated states of electrons are thought to produce quasiparticles with very unusual properties. Here we consider how these properties are manifested in space-time propagation. Specifically, we discuss how spin-charge separation is…

The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…

We obtain the exact solution of the Klein-Gordon equation describing the propagation of a particle in two regions of different constant magnetic field, separated by an infinite plane wall. The continuity of the wave function and of its…

We demonstrate that perfect state transfer can be achieved in an optical waveguide lattice governed by a Hamiltonian with modulated nearest-neighbor couplings. In particular, we report the condition that the evolution Hamiltonian should…

We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific…

While usual edge states in the quantum Hall effect(QHE) reside between adjacent Landau levels, QHE in graphene has a peculiar edge mode at E=0 that reside right within the n=0 Landau level as protected by the chiral symmetry. We have…