Continuum analogues of excited-state quantum phase transitions

TL;DR

This paper extends the concept of excited-state quantum phase transitions to continuum systems by analyzing complex level densities and time shifts, revealing singularities linked to tunneling phenomena and verified through numerical methods.

Contribution

It introduces a continuum analogue of excited-state quantum phase transitions using complex level densities and time shifts, expanding the understanding of tunneling in unbound systems.

Findings

Singularities in level density and time shift relate to tunneling potential stationary points.

Complex scaling method confirms the predicted effects in various tunneling potentials.

Dual extension of excited-state quantum phase transitions from bound to continuum systems.

Abstract

Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended continuum level density of unbound systems and show its relation to a complex time shift of the transmitted wave. While the real part of the level density and time shift describes the passage of the particle through classically allowed coordinate regions, the imaginary part is connected with an instanton-like picture of the tunneling through forbidden regions. We describe singularities in the real and imaginary parts of the level density and time shift caused by stationary points of the tunneling potential, and show that they represent a dual extension of excited-state quantum phase transitions from bound to continuum systems. Using the complex scaling method, we numerically verify the predicted effects in several tunneling potentials.