相关论文: Parallel Transport and Band Theory in Crystals
The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with translational group. Based on a group theory analysis we present generalization of the Bloch theorem that incorporates all…
This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus…
We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators…
We use the Van Vleck-Primas perturbation theory to study the problem of parallel transport of the eigenvectors of a parameter-dependent Hamiltonian. The perturbative approach allows us to define a non-Abelian connection $\mathcal{A}$ that…
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…
Bloch oscillations (BOs), i.e. the oscillatory motion of a quantum particle in a periodic potential, are one of the most striking effects of coherent quantum transport in the matter. In the semiclassical picture, it is well known that BOs…
The Berry curvature of a Bloch band can be interpreted as a local magnetic field in reciprocal space. This analogy can be extended by defining an electric field analog in reciprocal space which arises from the time-dependent Berry…
We study the macroscopic transport properties of the quantum Lorentz gas in a crystal with short-range potentials, and show that in the Boltzmann-Grad limit the quantum dynamics converges to a random flight process which is not compatible…
The band structure of a crystal may have points where two or more bands are degenerate in energy and where the geometry of the Bloch state manifold is singular, with consequences for material and transport properties. Ultracold atoms in…
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated from the rest of the band structure of…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport…
The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally-induced Berry curvature. In striking contrast to the related situation in graphene, we find…
Non-Hermitian materials can not only exhibit exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons.…
We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor…
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the…
We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem…
Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge…
We study the nonlinear responses of relativistic chiral matter to the external fields, such as the electric field ${\bf E}$, gradients of temperature and chemical potential, ${\bf \nabla} T$ and ${\bf \nabla} \mu$. Using the kinetic theory…