Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator

DOI10.1063/1.1948328zbMath1110.81079arXivmath-ph/0505046OpenAlexW3103496028MaRDI QIDQ3438501

César R. de Oliveira, Roberto A. Prado

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0505046

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear difference operators (47B39)

Related Items

Quantum Hamiltonians with quasi-ballistic dynamics and point spectrum ⋮ Dynamical localization for discrete Anderson Dirac operators ⋮ Exponential estimates of solutions of pseudodifferential equations on the lattice \((h \mathbb Z)^n\): applications to the lattice Schrödinger and Dirac operators ⋮ Localization for one-dimensional Anderson-Dirac models ⋮ One-dimensional discrete Dirac operators in a decaying random potential. I: Spectrum and dynamics ⋮ Sparse 1D discrete Dirac operators. I: Quantum transport ⋮ Almost periodic orbits and stability for quantum time-dependent Hamiltonians ⋮ Localization for gapped Dirac Hamiltonians with random perturbations: application to graphene antidot lattices ⋮ Density of states and Lifshitz tails for discrete 1D random Dirac operators ⋮ Dynamical lower bounds for 1D Dirac operators ⋮ Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators ⋮ Quantum energy expectation in periodic time-dependent Hamiltonians via Green functions ⋮ Location of eigenvalues of non-self-adjoint discrete Dirac operators ⋮ Sparse one-dimensional discrete Dirac operators II: Spectral properties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Power-law bounds on transfer matrices and quantum dynamics in one dimension. II
• A new proof of localization in the Anderson tight binding model
• Absence of ballistic motion
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Constructive proof of localization in the Anderson tight binding model
• Dynamical localization for discrete and continuous random Schrödinger operators
• Dynamical localization for the random dimer Schrödinger operator
• Anderson localization for Bernoulli and other singular potentials
• Delocalization in random polymer models
• Transfer matrices and transport for Schrödinger operators.
• Operators with singular continuous spectrum. IV: Hausdorff dimensions, rank one perturbations, and localization
• Schrödinger semigroups
• Dynamical upper bounds on wavepacket spreading
• Dynamical delocalization for the 1D Bernoulli discrete Dirac operator
• Supertransparent potentials for the Dirac equation
• Critical energies in random palindrome models

This page was built for publication: Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator