Quantum phase transitions in nonhermitian harmonic oscillator

DOI10.1038/S41598-020-75468-WarXiv2008.04012WikidataQ101051222 ScholiaQ101051222MaRDI QIDQ6346787

Miloslav Znojil

Publication date: 10 August 2020

Abstract: The Stone theorem requires that in a physical Hilbert space $calH$ the time-evolution of a stable quantum system is unitary if and only if the corresponding Hamiltonian $H$ is self-adjoint. Sometimes, a simpler picture of the evolution may be constructed in a manifestly unphysical Hilbert space $calK$ in which $H$ is nonhermitian but $calPT-$symmetric. In applications, unfortunately, one only rarely succeeds in circumventing the key technical obstacle which lies in the necessary reconstruction of the physical Hilbert space $calH$. For a $calPT-$symmetric version of the spiked harmonic oscillator we show that in the dynamical regime of the unavoided level crossings such a reconstruction of $calH$ becomes feasible and, moreover, obtainable by non-numerical means. The general form of such a reconstruction of $calH$ enables one to render every exceptional unavoided-crossing point tractable as a genuine, phenomenologically most appealing quantum-phase-transition instant.

This page was built for publication: Quantum phase transitions in nonhermitian harmonic oscillator

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6346787)