Related papers: The Canonical Flux Quantization and IQHE(revised)
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…
Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
Universal conductance fluctuations in disordered systems are one of the most known quantum mesoscopic effects. For ballistic cavity with smooth confining potential however, one should observe a much larger classical sample-to-sample…
Motivated by recent experiments, we study the coupling of quantum Hall (QH) hydrodynamics to quantum electrodynamics (QED) within a resonance cavity. In agreement with experimental observations, we find that the Hall conductivity remains…
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
In recent breakthrough experiments, twisted moir\'e layers of transition metal dichalcogenides are found to manifest both integer (IQAHE) and fractional (FQAHE) quantum anomalous Hall effects in zero applied magnetic field because of the…
The quantum anomalous Hall effect (QAHE) in magnetic topological insulators offers great potential to revolutionize quantum electrical metrology by establishing primary resistance standards operating at zero external magnetic field and…
In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the ``length of time" $q$ as the evolution direction of the system. In our novel…
We propose a new calculation of the DC conductance of a 1-dimensional electron system described by the Luttinger model. Our approach is based on the ideas of Landauer and B\"{u}ttiker and on the methods of current algebra. We analyse in…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making…
An asymmetric break-down of the integer quantized Hall effect is investigated. This rectification effect is observed as a function of the current value and its direction in conjunction with an asymmetric lateral confinement potential…
In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015)], it is claimed that the conductivity at low frequency $\omega$ and small wavevector $q$ along the edge of a quantum Hall (QH) system (that…
Laughlin's thought experiment of quantized charge pumping is central to understanding the integer quantum Hall effect (IQHE) and the topological origin of its conductance quantization. Its direct experimental observation, however, has been…
The quantum Hall effect (QHE) is theoretically understood as a superfluid condensate of composite bosons (CBs) -- bound states of electrons and magnetic flux quanta. While dissipationless transport is consistent with this picture, other…
This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free…
Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $\nu_c$ with respect to the bulk filling fraction…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…