SUSY Quantum Mechanics, (non)-Analyticity and $\ldots$ Phase Transitions
Abstract
It is shown by analyzing the Schr\"odinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies {\it versus} the coupling constant, are of three types only: (i) discontinuous energies (similar to 1st order phase transitions), (ii) discontinuous first derivative in the energy while the energy is continuous (similar to 2nd order phase transitions), (iii) the energy and all its derivatives are continuous but the functions are different below and above the point of discontinuity (similar to infinite order phase transitions). Supersymmetric (SUSY) Quantum Mechanics provides a convenient framework to study this phenomenon.
Cite
@article{arxiv.2409.03081,
title = {SUSY Quantum Mechanics, (non)-Analyticity and $\ldots$ Phase Transitions},
author = {Alexander V Turbiner},
journal= {arXiv preprint arXiv:2409.03081},
year = {2025}
}
Comments
16 pages, 13 figures, typos and omissions fixed, submitted to J Phys Conference Series