Work

Dispersive Decay Estimates for Dirac Equations with a Domain Wall

Year: 2024

Type: article

Abstract: . Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at [Formula: see text] and [Formula: see text]. This family of Hamiltonians arises in the theory of topologically protected states of one-dimensional quantum materials. For certain values of the phase-shift parameter, [Formula: see text], the Dirac Hamiltonian has a threshold resonance at the endpoint of its essential spectrum. Such resonances are known to influence the time-decay rate. Our main result explicitly displays the transition in time-decay rate as [Formula: see text] varies between resonant and nonresonant values. Our results appear to be the first dispersive time-decay estimates for Dirac Hamiltonians which are not a relatively compact perturbation of a free Dirac operator.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/23m1625378

Authors: Joseph Kraisler, Amir Sagiv, Michael I. Weinstein

Institutions: Amherst College, Technion – Israel Institute of Technology, Columbia University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation, United States-Israel Binational Science Foundation

Awards: Waves, Novel Two-Dimensional Materials, and Applications, G5307667492, G5959191678, G6807147672