Bootstrapping non-Hermitian Quantum System
High Energy Physics - Theory
2024-09-12 v1 Quantum Physics
Abstract
Recently, the ``Bootstrap" technique was applied in Quantum Mechanics to solve the eigenspectra of Hermitian Hamiltonians and extended to non-Hermitian PT-symmetric systems. However, its application has been limited to real spectra. In this work, we establish bootstrap conditions for the non-Hermitian system and generate eigenspectra for a generic complex polynomial potential, which includes PT-symmetric Hamiltonians as a special case. Additionally, we demonstrate the method's ability to obtain eigenspectra under various boundary conditions imposed on the eigenfunction, including the notable application of capturing the PT-symmetric phase transition.
Cite
@article{arxiv.2409.06784,
title = {Bootstrapping non-Hermitian Quantum System},
author = {Sakil Khan and Harsh Rathod},
journal= {arXiv preprint arXiv:2409.06784},
year = {2024}
}