相关论文: The Edge Currents in IQHE
We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at…
Application of the generalized continuity equation reveals that the drift current in conductors is equivalent to a negative diffusion current. A phenomenological model of conductivity is developed using the generalized continuity equations.…
Impulse formulations of Hall magnetohydrodynamic (MHD) equations are developed. The Lagrange invariance of a generalized ion magnetic helicity is established for Hall MHD. The physical implications of this Lagrange invariant are discussed.…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
We present a general theory for the equilibrium current distribution in an interacting two-dimensional electron gas subjected to a perpendicular magnetic field, and confined by a potential that varies slowly on the scale of the magnetic…
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically…
In the integer quantum Hall (IQH) regime, an antidot provides a finite, controllable `edge' of quantum Hall fluid that is an ideal laboratory for investigating the collective dynamics of large numbers of interacting electrons. Transport…
The canonical quantization of flux is performed. It is shown that according to the canonical flux quantization there must be a new uncertainty relation: $e \Delta A_m . \Delta x_m \geq \hbar$ where $A_m$ and $\Delta x_m \geq l_B$ are the…
We discuss a model where the relation between Hall potential $A_H$ = and gate potential $A_G$, which is manifested by the stepped QHE = curve, is described by an uncertainty relation $\Delta A_H . = \Delta A_G =3D B(\hbar/e)$.
The disappearance of integer quantum Hall effect (IQHE) at strong disorder and weak magnetic field is studied in a lattice model. A generic sequence by which the IQHE plateaus disappear is revealed: higher IQHE plateaus always vanish…
By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall…
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) regime is carried out. The problem of precision of quantization is analyzed for samples of finite size. It is demonstrated that the precision of…
A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be…
We study the global existence of classical solutions for two-dimensional incompressible MHD system with only magnetic diffusion. By using the time-weighted lower-order energy and uniformly bounded higher-order energy estimates, we prove the…
The static Coulomb potential of Quantum Electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level (LLL) approximation using two different methods. First, the vacuum expectation value of the…
Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum. The current may be produced either in an unbounded curved spacetime or in a…