A clean geometric construction is presented for the recent generalization of the Quantum Hall Effect to higher dimensional spaces. A very explicit formula is derived for the Hamiltonian in the generalized Quantum Hall Effect. This explicit formula suggests that the quantum Hall effect in even dimensions larger than two turns out to be simply copies of the two-dimensional effect.

1 Preface The present notes cover a series of three lectures on the quantum Hall effect given at the Singapore session " Ultracold Gases and Quantum Information " at Les Houches Summer School 2009. Almost 30 years after the discovery of the quantum Hall effect, the research subject of quantum Hall physics has certainly acquired a certain degree of maturity that is reflected by a certain number ...

a Department of Engineering and Public Policy, Carnegie Mellon University, Baker Hall 129, 5000 Forbes Avenue, Pittsburgh, PA 15213, United States b Climate and Energy Decision Making Center, Carnegie Mellon University, Baker Hall 129, 5000 Forbes Avenue, Pittsburgh, PA 15213, United States c H. John Heinz III College, Carnegie Mellon University, Hamburg Hall 3042, 5000 Forbes Avenue, Pittsburg...

It is shown that statistics on the wreath product groups, Ck �Sn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck � Sn. Finally, some new statistics on Ck � Sn are introduced, inspired by lecture hall theory, and their distributions are derived.

It is shown that statistics on the wreath product groups, Ck oSn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck oSn. Finally, some new statistics on Ck oSn are introduced, inspired by lecture hall theory, and their distributions are derived.

The Hall resistivity and magnetization have been investigated in the ferromagnetic state of the bilayered manganite La2−2xSr1+2xMn2O7 (x=0.36). The Hall resistivity shows an increase in both the ordinary and anomalous Hall coefficients at low temperatures below 50K, a region in which experimental evidence for the spin glass state has been found in a low magnetic field of 1mT. The origin of the ...

This lecture aims to present an overview of the properties of Hall effect devices. Descriptions of the Hall phenomenon, a review of the Hall effect device characteristics and of the various types of probes are presented. Particular attention is paid to the recent development of three-axis sensors and the related techniques to cancel the offsets and the planar Hall effect. The lecture introduces...