Dynamical Lower Bounds for 1D Dirac Operators

TL;DR

This paper establishes quantum dynamical lower bounds for 1D Dirac operators using transfer matrices and applies these results to models like Bernoulli-Dirac, revealing critical energies especially in the continuous case with positive mass.

Contribution

It introduces new dynamical lower bounds for 1D Dirac operators and identifies critical energies in continuous models, extending prior work on quantum dynamics.

Findings

Lower bounds for quantum dynamics in 1D Dirac operators.

Application to Bernoulli-Dirac models.

Identification of critical energies in continuous Dirac systems.

Abstract

Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass.