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It is commonly believed that the current response of an electron fluid to a mechanical force (such as an electric field) or to a ``statistical force (e.g., a gradient of chemical potential) are governed by a single linear transport coefficient - the electric conductivity. We argue that this is not the case in anomalous Hall materials. In particular, we find that transverse (Hall) currents manifest two distinct Hall responses governed by an unconventional {it transverse} Einstein relation that captures an anomalous relation between the Hall conductivity and the Hall diffusion constant. We give examples of when the Hall diffusion anomaly is prominent, resulting in situations where the transverse diffusion process overwhelms the Hall conductivity and vice versa.
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phon
We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and i
In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a
We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown
The response of solids to temperature gradients is often described in terms of a gravitational analogue: the effect of a space-dependent temperature is modeled using a space dependent metric. We investigate the validity of this approach in describing