Related papers: Quadratic pseudospectrum for identifying localized states

Quadratic pseudospectrum for identifying localized states

URL: http://arxiv.org/abs/2204.10450v1
Date: Fri, 22 Apr 2022 00:57:09 GMT
Title: Quadratic pseudospectrum for identifying localized states
Authors: Alexander Cerjan, Terry A. Loring, Fredy Vides
Abstract summary: quadratic pseudospectrum is a method for approaching systems with incompatible observables. We derive an important estimate relating the Clifford and quadratic pseudospectra. We prove that the quadratic pseudospectrum is local, and derive bounds on the errors that are incurred by truncating the system in the vicinity of where the pseudospectrum is being calculated.
Score: 68.8204255655161
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We examine the utility of the quadratic pseudospectrum in photonics and condensed matter. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables, as it both minimizes the "eigen-error" in the joint approximate spectrum of the incompatible observables and does not increase the system's computational complexity. Moreover, we derive an important estimate relating the Clifford and quadratic pseudospectra. Finally, we prove that the quadratic pseudospectrum is local, and derive the bounds on the errors that are incurred by truncating the system in the vicinity of where the pseudospectrum is being calculated.

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