### Conveners

#### PT symmetric Hamiltonians

- Carl Bender (Washington University in St Louis)

#### PT symmetric Hamiltonians

- Carl Bender (Washington University in St Louis)

We describe recent progress in understanding the symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We start by revisiting the derivation of Noether’s theorem, showing that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. The associated symmetry transformations instead yield families of equivalent...

In this talk I will describe a surprising link between discrete structures found in two different contexts: the Stokes phenomenon as arises in problems in PT symmetric quantum mechanics, and the functional equations that encode the properties of certain integrable quantum field theories. One spin-off from this connection has been a proof of spectral reality in a set of PT-symmetric problems...

Parity-time (PT) symmetric quantum mechanics has attracted ever-increasing attention over recent years because it offers a class of complex Hamiltonians which, in spite of their non-Hermiticity, can possess discrete real eigenvalue spectra. Moreover, these Hamiltonians feature the property of exceptional points, i.e., points in parameter space where both energy values and eigenfunctions...

Demetrios Christodoulides

CREOL-The College of Optics & Photonics, University of Central Florida

Title: Parity-Time and other Symmetries in Optics and Photonics

Abstract: The prospect of judiciously utilizing both optical gain and loss has been recently suggested as a means to control the flow of light. This proposition makes use of some newly developed concepts based on non-Hermiticity and...

The cerebrated Riemann Hypothesis asserts that the nontrivial zeros of the Riemann zeta function lie on a critical line parallel to the imaginary axis, whose real part is 1/2. If it holds true, then the values of the nontrivial zeros minus 1/2 would constitute a discrete set of purely imaginary numbers, giving rise to the speculation that they may correspond to the eigenvalues of a...

In my talk I will present results from two recent projects centered around non-Hermitian physics and PT-symmetry. In the first project we managed to show that the line-width of a phonon laser broadens significantly when approaching a so-called "exceptional point" [1]. In the second project we implemented our theoretical prediction on scattering states in disordered media with constant...

Interest in discrete symmetries in particle physics is concentrated primarily in determining the degree to which they may or may not be obeyed by nature. However, with the advent of the non-Hermitian, antilinear PT-symmetry program of Bender and collaborators it has become apparent that quantum theory is richer than the standard Dirac Hermitian approach, to thereby increase the number of...

In the framework of PT-symmetric physics and more generally that of non-Hermitian photonics, we will examine the extreme power dynamics close to higher order exceptional points. The relation between the transient amplification of light and the enhanced sensitivity is going to be examined based on the pseudospectrum of the associated PT-symmetric Hamiltonians.

The $\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the real line, $x\in\mathbb{R}$, is IR truncated and considered as Sturm-Liouville problem over a finite interval $x\in\left[-L,L\right]\subset\mathbb{R}$. Structures hidden in the Airy function setup of the $V=-ix$ model are combined with WKB techniques developed by Bender and Jones in 2012 for the derivation of the real part...

In this talk, I will discuss the role of emergent symmetries for energy

transport through microscopic networks with active gain and loss sites.

Despite its simplicity, such a network exhibits a range of anomalous

transport phenomena, which arise from the competition between coherent

and incoherent processes in combination with non-linear saturation

effects. Specifically, I will show that...