One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-co...

In this paper, we study the effects of Hall and ion-slip currents on the steady magneto-micropolar of a viscous incompressible and electrically conducting fluid over a horizontal plate by taking in to account the viscous dissipation effects. By means of similarity solutions, deviation of fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using qu...

[1] To understand the role of the Hall effect during fast magnetic reconnection, hybrid simulations with and without the Hall term in the generalized Ohm’s Law are compared, as done originally by Karimabadi et al. (2004). It is found that reconnection with the Hall term is fast, but reconnection in the so-called Hall-less hybrid simulations is Sweet-Parker like (slow) when the resistivity is co...

Noncoplanar magnetic orders in magnetic metals give rise to an anomalous Hall effect of unconventional origin, which, by the spin Berry phase effect, is known as the topological Hall effect. This effect is pronounced in the low-temperature limit, where the fluctuation of spins is suppressed. In contrast, we here discuss that the fluctuating but locally correlated spins close to the phase bounda...

Based upon spin-lattice interaction, we propose a theoretical model for the phonon Hall effect in paramagnetic dielectrics. The thermal Hall conductivity is calculated by using the Kubo formula. Our theory reproduces the essential experimental features of the phonon Hall effect discovered recently in ionic dielectric Tb3Ga5O12, including the sign, magnitude and linear magnetic field dependence ...

We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to 2e/h and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low energy physics. In the absence of disorder, a point-contact generically lead...

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We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the...