Found 112 Documents (Results 1–100)
Robustness of flat bands on the perturbed Kagome and the perturbed super-Kagome lattice. (English) Zbl 07893521
Improved uniform error estimates for the two-dimensional nonlinear space fractional Dirac equation with small potentials over long-time dynamics. (English) Zbl 07832807
Numerical methods for the nonlinear Dirac equation in the massless nonrelativistic regime. (English) Zbl 1530.65084
Explicit and structure-preserving exponential wave integrator Fourier pseudo-spectral methods for the Dirac equation in the simultaneously massless and nonrelativistic regime. (English) Zbl 1536.65118
Reviewer: Ljiljana Teofanov (Novi Sad)
Quantitative equidistribution of eigenfunctions for toral Schrödinger operators. (English) Zbl 1529.35167
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown. (English) Zbl 1531.35191
On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform. (English) Zbl 07771114
Mathematical aspects of the Kubo formula for electrical conductivity with dissipation. (English) Zbl 1538.78005
The Dirac bag model in strong magnetic fields. (English) Zbl 1528.35143
Reviewer: Eric Stachura (Marietta)
Unified approach to Floquet lattices, topological insulators, and their nonlinear dynamics. (English) Zbl 07726697
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials. (English) Zbl 1509.65106
Nonlinear dynamics of modulated waves on graphene like quantum graphs. (English) Zbl 1529.35466
Reviewer: Vincent Lescarret (Gif-sur-Yvette)
A local test for global extrema in the dispersion relation of a periodic graph. (English) Zbl 1505.35312
Reviewer: Thierry Jecko (Cergy-Pontoise)
Nonlinear optical waveguide lattices: asymptotic analysis, solitons, and topological insulators. (English) Zbl 1498.78031
Threefold Weyl points for the Schrödinger operator with periodic potentials. (English) Zbl 1497.35403
Reviewer: Dimitar A. Kolev (Sofia)
Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials. (English) Zbl 1524.81041
On the continuum limit for a model of binary waveguide arrays. (English) Zbl 1512.35501
Reviewer: Abderrazek Benhassine (Monastir)
Uniformly accurate nested Picard iterative integrators for the nonlinear Dirac equation in the nonrelativistic regime. (English) Zbl 1482.35190
Effective gaps in continuous Floquet Hamiltonians. (English) Zbl 1486.35357
Reviewer: Eric Stachura (Marietta)
A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials. (English) Zbl 07506534
The bulk-edge correspondence for continuous dislocated systems. (Correspondance bulk-edge pour des dislocations continues.) (English. French summary) Zbl 1492.81054
Three discontinuous Galerkin methods for one- and two-dimensional nonlinear Dirac equations with a scalar self-interaction. (English) Zbl 1473.65206
A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities. (English) Zbl 1472.81090
Reviewer: Michael Perelmuter (Kyïv)
Reducible Fermi surface for multi-layer quantum graphs including stacked graphene. (English) Zbl 1468.81052
Edge states for the magnetic Laplacian in domains with smooth boundary. (English) Zbl 1481.35350
Reviewer: Markus Holzmann (Graz)
Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential. (English) Zbl 1470.35299
Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential. (English) Zbl 1462.35318
Ubiquity of conical points in topological insulators. (Omniprésence des points de Dirac dans les isolants topologiques.) (English. French summary) Zbl 1516.57046
Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model. (English) Zbl 1519.82141
Nonlinear geometric optics based multiscale stochastic Galerkin methods for highly oscillatory transport equations with random inputs. (English) Zbl 1471.65137
Reviewer: Alain Brillard (Riedisheim)
Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers. (English) Zbl 1524.78043
Discrete Bethe-Sommerfeld conjecture for triangular, square, and hexagonal lattices. (English) Zbl 07308598
Continuum Schrödinger operators for sharply terminated graphene-like structures. (English) Zbl 1454.82053
Topologically protected edge modes in one-dimensional chains of subwavelength resonators. (English. French summary) Zbl 1454.35056
A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals. (English) Zbl 1466.74035
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. (English) Zbl 1440.35286
Numerical quadrature in the Brillouin zone for periodic Schrödinger operators. (English) Zbl 07178535
Dispersion relations of periodic quantum graphs associated with Archimedean tilings. II. (English) Zbl 1509.81598
Dispersion relations of periodic quantum graphs associated with Archimedean tilings. I. (English) Zbl 1509.81597
Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene. (English) Zbl 07581579
Error bounds of the finite difference time domain methods for the Dirac equation in the semiclassical regime. (English) Zbl 1453.65228
Reviewer: Bülent Karasözen (Ankara)
Cantor spectrum of graphene in magnetic fields. (English) Zbl 1447.82041
Reviewer: Yulianna Perepelkina (Moskva)
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation. (English) Zbl 1433.65234
Infinite mass boundary conditions for Dirac operators. (English) Zbl 1419.81014
Reviewer: Michael Perelmuter (Kyïv)
Nonlinear Dirac equation on graphs with localized nonlinearities: bound states and nonrelativistic limit. (English) Zbl 1411.35263
Elliptic operators with honeycomb symmetry: Dirac points, edge states and applications to photonic graphene. (English) Zbl 1410.78024
A hybrid method for computing the Schrödinger equations with periodic potential with band-crossings in the momentum space. (English) Zbl 1475.65143
Spectral band degeneracies of \(\frac{\pi}{2}\)-rotationally invariant periodic Schrödinger operators. (English) Zbl 1412.35283
Multiscale Model. Simul. 16, No. 4, 1684-1731 (2018); erratum ibid. 18, No. 3, 1371-1373 (2020).
Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing. (English) Zbl 1400.81103
Honeycomb Schrödinger operators in the strong binding regime. (English) Zbl 1414.35061
Reviewer: Jake Fillman (Blacksburg)
MSC:
35J10
Multiple solutions for a self-consistent Dirac equation in two dimensions. (English) Zbl 1393.81013
Reviewer: Piotr Garbaczewski (Opole)
Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures. (English) Zbl 1380.35142
Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity. (English) Zbl 1378.35257
Reviewer: Eric Stachura (Haverford)
Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. (English) Zbl 1370.81053
Topologically protected states in one-dimensional systems. (English) Zbl 1379.35076
Mem. Am. Math. Soc. 1173, viii, 118 p. (2017).
Reviewer: Patrick Winkert (Berlin)
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature. (English) Zbl 1357.81085
Edge diffraction on triangular and hexagonal lattices: existence, uniqueness, and finite section. (English) Zbl 1467.35307
Edge states in honeycomb structures. (English) Zbl 1404.35128
Reviewer: Jürgen Appell (Würzburg)
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime. (English) Zbl 1365.65208
Reviewer: Vit Dolejsi (Praha)
A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime. (English) Zbl 1346.35171
Reviewer: Alain Brillard (Riedisheim)
Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation. (English) Zbl 1339.37072
An overview of periodic elliptic operators. (English) Zbl 1346.35170
Reviewer: Boris A. Malomed (Tel Aviv)
Dirac cones for point scatterers on a honeycomb lattice. (English) Zbl 1342.35283
Reviewer: Thomas Ernst (Uppsala)
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