Effective dynamics for Bloch electrons: Peierls substitution and beyond
From MaRDI portal
Publication:1423653
DOI10.1007/s00220-003-0950-1zbMath1058.81020arXivmath-ph/0212041OpenAlexW3102117030MaRDI QIDQ1423653
Gianluca Panati, Herbert Spohn, Stefan Teufel
Publication date: 7 March 2004
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0212041
Electromagnetic interaction; quantum electrodynamics (81V10) Statistical mechanics of solids (82D20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)
Related Items
On adiabatic theory for extended fermionic lattice systems ⋮ A calculus for magnetic pseudodifferential super operators ⋮ Bistritzer–MacDonald dynamics in twisted bilayer graphene ⋮ Gaussian beam construction for adiabatic perturbations ⋮ Berry phase effects on electronic properties ⋮ Homogenization of the Cauchy Problem for the Wave Equation with Rapidly Varying Coefficients and Initial Conditions ⋮ A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential ⋮ Semiclassical approximations for Hamiltonians with operator-valued symbols ⋮ On the role of symmetries in the theory of photonic crystals ⋮ On a Schrödinger--Landau--Lifshitz System: Variational Structure and Numerical Methods ⋮ Tight-binding reduction and topological equivalence in strong magnetic fields ⋮ Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations ⋮ Bloch dynamics with second order Berry phase correction ⋮ Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups ⋮ Operator separation of variables for adiabatic problems in quantum and wave mechanics ⋮ Effective mass theorems with Bloch modes crossings ⋮ Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions ⋮ The adiabatic theorem and linear response theory for extended quantum systems ⋮ Ubiquity of conical points in topological insulators ⋮ A new approach to transport coefficients in the quantum spin Hall effect ⋮ Generalized Foldy-Wouthuysen transformation and pseudodifferential operators ⋮ Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase ⋮ Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices ⋮ Mathematical aspects of the Kubo formula for electrical conductivity with dissipation ⋮ Waves in Slowly Varying Band-Gap Media ⋮ Electronic Properties of Strained Double‐Weyl Systems ⋮ On the stationary non-equilibrium measures for the ``field-crystal system ⋮ Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials ⋮ Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein-Gordon field ⋮ A Spectral Algorithm for the Time-Dependent Kohn--Sham Equations: Accurately Treating External Potentials Based on Frozen Gaussian Approximations ⋮ Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature ⋮ Topology of time-reversal invariant energy bands with adiabatic structure ⋮ Wigner measures and effective mass theorems ⋮ Peierls substitution and the Maslov operator method ⋮ Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. II: Closed three-dimensional waveguide in a magnetic field ⋮ Effective light dynamics in perturbed photonic crystals ⋮ Peierls’ substitution via minimal coupling and magnetic pseudo-differential calculus ⋮ Adiabatic currents for interacting fermions on a lattice ⋮ Classification of ``real Bloch-bundles: topological quantum systems of type AI ⋮ Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential ⋮ APPLICATIONS OF MAGNETIC ΨDO TECHNIQUES TO SAPT ⋮ Integrable models of the longitudinal motion of electrons in curved \(3D\) nanotubes ⋮ The cohomological nature of the Fu-Kane-Mele invariant ⋮ On the linear stability of crystals in the Schrödinger-Poisson model ⋮ Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results ⋮ On the dispersion decay for crystals in the linearized Schrödinger-Poisson model ⋮ Optimal decay of Wannier functions in Chern and quantum Hall insulators ⋮ A Hybrid Method for Computing the Schrödinger Equations with Periodic Potential with Band-Crossings in the Momentum Space ⋮ Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schrödinger Operators ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Low lying spectral gaps induced by slowly varying magnetic fields ⋮ Derivation of ray optics equations in photonic crystals via a semiclassical limit ⋮ The geometry of the double gyroid wire network: quantum and classical ⋮ Homogenization limit for a multiband effective mass model in heterostructures ⋮ Microlocal analysis of the bulk-edge correspondence ⋮ Quantum transport in a low-density periodic potential: homogenisation via homogeneous flows ⋮ On the construction of composite Wannier functions ⋮ Topological invariants of eigenvalue intersections and decrease of Wannier functions in graphene ⋮ Construction of real-valued localized composite Wannier functions for insulators ⋮ Non-equilibrium almost-stationary states and linear response for gapped quantum systems ⋮ Coherent electronic transport in periodic crystals ⋮ Quantum transport in a crystal with short-range interactions: the Boltzmann-Grad limit ⋮ Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field ⋮ A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations ⋮ Geometric currents in piezoelectricity ⋮ Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles ⋮ Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations ⋮ Wave Packets in the Fractional Nonlinear Schrödinger Equation with a Honeycomb Potential ⋮ Spin-orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals ⋮ Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid ⋮ Exponentially localized Wannier functions in periodic zero flux magnetic fields ⋮ Homogenization of the Schrödinger equation and effective mass theorems ⋮ Two-parameter asymptotics in magnetic Weyl calculus ⋮ Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry ⋮ Differential equations of quantum mechanics