相关论文: Interactions and non-commutativity in quantum Hall…

We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective…

As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…

It is shown that the non-commutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of non-commutative geometries labeled by the self-adjoint extension parameters. We…

We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find…

Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…

When coordinates are noncommutative, the Hall effect is reinvestigated. The Hall conductivity is expressed with noncommutative parameters, so that in the commutative limit it tends to the conventional result.

We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special…

We introduce s.n where n is the unit vector in the direction of the radius vector and s is the spin, which along with the velocity forms a spin-orbit interaction of the order of v/c whereas the usual spin-orbit interaction is of the order…

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…

Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $\nu=n/(2pn\pm…

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which…

We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle…

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…

I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…

A new model for calculating the structure of bound states of interacting particles is considered. The model takes into account the noncommutativity of the space and impulse operators plus the correlation equations for the indeterminacy of…

We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating…

We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…