Abstract
In the problem of classification of the parameter-controlled quantum phase transitions, attention is turned from the conventional manipulations with the energy-level mergers at exceptional points to the control of mergers of the exceptional points themselves. What is obtained is an exhaustive classification which characterizes every phase transition by the algebraic and geometric multiplicity of the underlying confluent exceptional point. Typical qualitative characteristics of non-equivalent phase transitions are illustrated via a few elementary toy models.
Highlights
Our present project is aimed at the search for new forms of manipulation and control of important qualitative features of quantum dynamics
Its variable parameters only lie on the main diagonal. This lowers the flexibility of dynamics leading, typically, just to the EP2 energy mergers
Let us add that there still exist multiple parallels between the present considerations and the Thom’s theory. In the latter case, a classification of classical catastrophes was achieved via the reduction of arbitrary V(x)s to its “canonical” form
Summary
We argued that in connection with the evolution of models (8) in H(physical) one can localize certain non-empty corridors of unitary access to the quantum phase transition extremes at EPs. A clear separation between the open- and closed-system theories must always be kept sufficiently well verbalized. In this local-interaction model the Hamiltonian contains just an N-plet of the dynamics-determining diagonal matrix elements vk = h2V (xk) yielding the spectrum of the re-scaled and shifted bound-state energies Fn = h2En − 2 with n = 0, 1, .
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call