Related papers: Parallel Transport and Band Theory in Crystals
Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of…
Illustration of the geometric and topological properties of Berry phase is often in an obscure and abstract language of fiber bundles. In this article, we demonstrate these properties with a lucid and concrete system whose parameter space…
The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but…
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence…
In order to compute with $l$--adic sheaves or crystals on a line over $\mathbb{F} _q$ a low-technology alternative to the traditional computation with the Hecke operators on the automorphic side could be helpful. A program which has evolved…
Non-equilibrium property of turbulence modifies characteristics of turbulent transport. With the aid of response-function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the…
The theoretical identification of crystalline topological materials has enjoyed sustained success in simplified materials models, often by singling out discrete symmetry operations protecting the topological phase. When band structure…
Kendall shape spaces are a widely used framework for the statistical analysis of shape data arising from many domains, often requiring the parallel transport as a tool to normalise time series data or transport gradient in optimisation…
We derive the semiclassical Bloch dynamics with the second-order Berry phase correction in the presence of the slow-varying scalar potential as perturbation. Our mathematical derivation is based on a two-scale WKB asymptotic analysis. For a…
Applying the technique of characteristic functions developped for one-dimensional regular surfaces (curves) with compact support, we obtain the distribution of hitting probabilities for a wide class of finite membranes on square lattice.…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
Motivated by recent experiments demonstrating the creation of atomically sharp interfaces between hexagonal sapphire and cubic SrTiO$_3$ with finite twist, we here develop and study a general electronic band theory for this novel class of…
Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent…
We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in…
Bloch-Boltzmann transport theory fails to describe the carrier diffusion in current crystalline organic semiconductors, where the presence of large-amplitude thermal molecular motions causes substantial dynamical disorder. The charge…
The transport of many kinds of singular structures in a medium, such as vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic solids, or topological singularities in magnetism, can be expressed in terms of the…
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences…
The behavior of a Bloch particle in a complex crystal with PT symmetry subjected to a sinusoidal ac force is theoretically investigated. For unbroken PT symmetry and in the single-band approximation, it is shown that time reversal symmetry…
We investigate the anomalous effects due to the Berry correction and the considerable perturbations in the silicene-like hexagonal lattice system. The Berry curvature in periodic Bloch band system which related to the electromagnetic field…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…