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SUMMARY:Symmetry properties of non-Hermitian\, PT-symmetric quantum field
theories
DTSTART;VALUE=DATE-TIME:20181129T130000Z
DTEND;VALUE=DATE-TIME:20181129T132500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165240@indico.cern.ch
DESCRIPTION:Speakers: Peter Millington (University of Nottingham)\nWe desc
ribe recent progress in understanding the symmetry properties of non-Hermi
tian\, PT-symmetric quantum field theories. We start by revisiting the der
ivation of Noether’s theorem\, showing that the conserved currents of no
n-Hermitian theories correspond to transformations that do not leave the L
agrangian invariant. The associated symmetry transformations instead yield
families of equivalent PT-symmetric theories. These results are illustrat
ed by means of two concrete examples: a theory of one complex scalar and o
ne complex pseudo-scalar\, and a non-Hermitian extension of quantum electr
odynamics. After describing the construction of the path integral for non-
Hermitian but PT-symmetric Lagrangians\, we finish by considering the spon
taneous breakdown of both global and local symmetries\, and describe how t
he Goldstone theorem and Englert-Brout-Higgs mechanism are borne out.\n\nh
ttps://indico.cern.ch/event/732911/contributions/3165240/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165240/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lasing and Disorder Scattering Inspired by PT-Symmetry
DTSTART;VALUE=DATE-TIME:20181129T153000Z
DTEND;VALUE=DATE-TIME:20181129T155500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165245@indico.cern.ch
DESCRIPTION:Speakers: Stefan Rotter (Vienna University of Technology)\nIn
my talk I will present results from two recent projects centered around no
n-Hermitian physics and PT-symmetry. In the first project we managed to sh
ow that the line-width of a phonon laser broadens significantly when appro
aching a so-called "exceptional point" [1]. In the second project we imple
mented our theoretical prediction on scattering states in disordered media
with constant intensity and perfect transmission [2] in an acoustic setup
. Using several loudspeakers with gain and loss allows us to steer an inco
ming sound wave across a strongly disordered waveguide without any reflect
ion or variation in its pressure [3]. \n[1] Zhang\, Peng\, Özdemir\, Pich
ler\, Krimer\, Zhao\, Nori\, Liu\, Rotter\, Yang\, Nature Photonics\, 12\,
479 (2018).\n[2] Makris\, Brandstötter\, Ambichl\, Musslimani\, Rotter\,
Light Sci. Appl. 6\, e17035 (2017). \n[3] Rivet\, Brandstötter\, Makris\
, Lissek\, Rotter\, Fleury\, arXiv:1804.02363 (Nature Physics\, in print).
\n\nhttps://indico.cern.ch/event/732911/contributions/3165245/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165245/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Energy transport and symmetry breaking in a microscopic power grid
DTSTART;VALUE=DATE-TIME:20181129T171000Z
DTEND;VALUE=DATE-TIME:20181129T173500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165246@indico.cern.ch
DESCRIPTION:Speakers: Julian Huber (TU Wien)\nIn this talk\, I will discus
s the role of emergent symmetries for energy \ntransport through microscop
ic networks with active gain and loss sites. \nDespite its simplicity\, su
ch a network exhibits a range of anomalous \ntransport phenomena\, which a
rise from the competition between coherent \nand incoherent processes in c
ombination with non-linear saturation \neffects. Specifically\, I will sho
w that such networks exhibit a \nnon-equilibrium phase transition between
a noise-dominated and a \ncoherent transport regime. This transition is cl
osely related to the \nphenomenon of PT-symmetry breaking in balanced gain
-loss systems\,\nbut occurs more generally\, even in systems where this sy
mmetry is not \nreflected in the underlying equations of motion. Therefore
\, this \nmechanism has practical consequences for the distribution of ene
rgy over \nmicrowave\, optical or phononic channels\, in particular close
to or at \nthe quantum limit.\n\nhttps://indico.cern.ch/event/732911/contr
ibutions/3165246/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165246/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parity-Time symmetry and exceptional points in Bose-Einstein conde
nsates
DTSTART;VALUE=DATE-TIME:20181129T135000Z
DTEND;VALUE=DATE-TIME:20181129T141500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165251@indico.cern.ch
DESCRIPTION:Speakers: Guenter Wunner (University of Stuttgart)\nParity-tim
e (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 eigenvalu
e spectra. Moreover\, these Hamiltonians feature the property of exception
al points\, i.e.\, points in parameter space where both energy values and
eigenfunctions coincide\, a phenomenon impossible in Hermitian quantum mec
hanics (but known to appear for resonances in the continuum).\nBecause of
the formal equivalence of the Schrödinger equation and the Helmholtz equa
tion of electrodynamics\, the properties of such operators have meanwhile
been observed in a multitude of classical laboratory experiments – e.g.
optical waveguides\, microwave resonators and metamaterials. A bona fide
quantum mechanical realisation of PT-symmetric systems is still lacking. A
strong candidate is a Bose-Einstein condensate in a multi-well potential\
, or in a tilted optical lattice. The idea ist to outcouple atoms from one
well and incouple them coherently into the other. By numerically solving
the underlying nonlinear Gross-Pitaevskii equation\, but also by going bey
ond the mean-field description using Lindblad superoperators\, I will demo
nstrate that PT-symmetric Bose-Einstein condensates with balanced gain and
loss are indeed good candidates for the first observation of PT symmetry
in a real quantum system.\n\nhttps://indico.cern.ch/event/732911/contribut
ions/3165251/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165251/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extreme dynamics and sensitivity close to exceptional points
DTSTART;VALUE=DATE-TIME:20181129T162000Z
DTEND;VALUE=DATE-TIME:20181129T164500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165252@indico.cern.ch
DESCRIPTION:Speakers: KONSTANTINOS MAKRIS (University of Crete)\nIn the fr
amework of PT-symmetric physics and more generally that of non-Hermitian p
hotonics\, we will examine the extreme power dynamics close to higher orde
r exceptional points. The relation between the transient amplification of
light and the enhanced sensitivity is going to be examined based on the ps
eudospectrum of the associated PT-symmetric Hamiltonians.\n\nhttps://indic
o.cern.ch/event/732911/contributions/3165252/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165252/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Mechanics and Riemann Hypothesis
DTSTART;VALUE=DATE-TIME:20181129T144000Z
DTEND;VALUE=DATE-TIME:20181129T150500Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165248@indico.cern.ch
DESCRIPTION:Speakers: Dorje Brody (University of Surrey)\nThe cerebrated R
iemann Hypothesis asserts that the nontrivial zeros of the Riemann zeta fu
nction 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 mi
nus 1/2 would constitute a discrete set of purely imaginary numbers\, givi
ng rise to the speculation that they may correspond to the eigenvalues of
a self-adjoint (Hermitian) operator multiplied by the imaginary number. Fi
nding such an operator as a way of proving the Riemann Hypothesis is the e
ssence of the Hilbert-Pólya programme. In this talk I will illustrate an
example in which techniques of PT-symmetric quantum mechanics can be appli
ed to examine this problem. In particular\, I will identify the operator w
hich “does the trick” for the Hilbert-Pólya programme\, i.e. an opera
tor whose eigenvalues correspond exactly to the nontrivial zeros\, and sho
w\, perhaps surprisingly\, that the reality of the eigenvalues in itself i
s insufficient to establish the Riemann Hypothesis. (Based on joint work w
ith Carl Bender & Markus Müller.)\n\nhttps://indico.cern.ch/event/732911/
contributions/3165248/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165248/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The ODE-IM correspondence and PT symmetry
DTSTART;VALUE=DATE-TIME:20181129T132500Z
DTEND;VALUE=DATE-TIME:20181129T135000Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3209519@indico.cern.ch
DESCRIPTION:Speakers: Patrick Dorey (Durham University)\nIn this talk I wi
ll describe a surprising link between discrete structures found in two dif
ferent contexts: the Stokes phenomenon as arises in problems in PT symmetr
ic quantum mechanics\, and the functional equations that encode the proper
ties 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 p
roblems introduced by Bender and Boettcher\, and this will also be (briefl
y) described.\n\nhttps://indico.cern.ch/event/732911/contributions/3209519
/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3209519/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parity-Time and other Symmetries in Optics and Photonics
DTSTART;VALUE=DATE-TIME:20181129T141500Z
DTEND;VALUE=DATE-TIME:20181129T144000Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3214567@indico.cern.ch
DESCRIPTION:Speakers: Demetrios Christodoulides (University of Central Flo
rida)\nDemetrios Christodoulides\nCREOL-The College of Optics & Photonics\
, University of Central Florida\nTitle: Parity-Time and other Symmetries i
n Optics and Photonics\nAbstract: The prospect of judiciously utilizing bo
th 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 con
cepts based on non-Hermiticity and parity-time (PT) symmetry-ideas first c
onceived within quantum field theories. By harnessing such notions\, recen
t works indicate that novel synthetic structures and devices with counter-
intuitive properties can be realized\, potentially enabling new possibilit
ies in the field of optics and integrated photonics. Non-Hermitian degener
acies\, also known as exceptional points (EPs)\, have also emerged as a ne
w paradigm for engineering the response of optical systems. In this talk\,
we provide an overview of recent developments in this newly emerging fiel
d. The use of other type symmetries in photonics will be also discussed.\n
\nhttps://indico.cern.ch/event/732911/contributions/3214567/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3214567/
END:VEVENT
BEGIN:VEVENT
SUMMARY:PT and CPT Symmetry as a Dynamics
DTSTART;VALUE=DATE-TIME:20181129T155500Z
DTEND;VALUE=DATE-TIME:20181129T162000Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165242@indico.cern.ch
DESCRIPTION:Speakers: Philip Mannheim (University of Connecticut)\nInteres
t in discrete symmetries in particle physics is concentrated primarily in
determining the degree to which they may or may not be obeyed by nature. H
owever\, with the advent of the non-Hermitian\, antilinear PT-symmetry pro
gram of Bender and collaborators it has become apparent that quantum theor
y is richer than the standard Dirac Hermitian approach\, to thereby increa
se the number of options available to quantum theory. Moreover\, antilinea
r symmetry can be used as a dynamics that constrains what is allowed in ph
ysics. While interest has focused on PT itself\, here we show that the fun
damental antilinear symmetry is CPT. Specifically we show that if one impo
ses only two requirements\, namely the time independence of inner product
s and invariance under the complex Lorentz group\, it follows that the Ham
iltonian must be CPT invariant. Since no Hermiticity requirement is impose
d the CPT theorem is thus extended to non-Hermitian theories. We present s
ome examples of theories that are not Hermitian but are CPT invariant. Sin
ce charge conjugation plays no role in non-relativistic physics where one
is below the threshold for particle production\, CPT then defaults to PT\,
to thus put the PT-symmetry program on a quite secure theoretical foundat
ion.\nReferences: P. D. Mannheim\, Extension of the CPT Theorem to non-He
rmitian Hamiltonians and unstable states\, Phys. Lett. B 753\, 288 (2016)
. (arXiv:1512.03736 [quant-ph]).\nP. D. Mannheim\, Antilinearity rather th
an Hermiticity as a guiding principle for quantum theory\, J. Phys. A 51\
, 315302 (2018). (arXiv:1512.04915 [hep-th]).\n\nhttps://indico.cern.ch/ev
ent/732911/contributions/3165242/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165242/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The IR-truncated $\\mathcal{PT}-$symmetric $V=ix^3$ model and its
asymptotic spectral scaling graph
DTSTART;VALUE=DATE-TIME:20181129T164500Z
DTEND;VALUE=DATE-TIME:20181129T171000Z
DTSTAMP;VALUE=DATE-TIME:20210124T055154Z
UID:indico-contribution-284051-3165250@indico.cern.ch
DESCRIPTION:Speakers: Uwe Guenther (Helmholtz-Center Dresden-Rossendorf)\n
The $\\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the r
eal line\, $x\\in\\mathbb{R}$\, is IR truncated and considered as Sturm-Li
ouville problem over a finite interval $x\\in\\left[-L\,L\\right]\\subset\
\mathbb{R}$. Structures hidden in the Airy function setup of the $V=-ix$ m
odel are combined with WKB techniques developed by Bender and Jones in 201
2 for the derivation of the real part of the spectrum of the $(ix^3\,x\\in
[-1\,1])$ model. Via WKB and Stokes graph analysis\, the location of the c
omplex spectral branches of the $V=ix^3$ model as well as those of more ge
neral $V=-(ix)^{2n+1}$ models over $x\\in\\left[-L\,L\\right]\\subset\\mat
hbb{R}$ are obtained. Splitting the related action functions into purely r
eal scale factors and scale invariant integrals allows to extract underlyi
ng asymptotic spectral scaling graphs $\\mathcal{R}\\subset\\mathbb{C}$. T
hese (structurally very simple) scaling graphs are geometrically invariant
and cutoff-independent so that the IR limit $L\\to \\infty$ can be formal
ly taken. Moreover an increasing $L$ can be associated with an $\\mathcal{
R}-$constrained spectral UV$\\to$IR renormalization group flow on $\\mathc
al{R}$. It is shown that the eigenvalues of the IR-complete $(V=ix^3\,x\\i
n\\mathbb{R})$ model can be bijectively mapped onto a finite segment of $\
\mathcal{R}$ asymptotically approaching a (scale invariant) $\\mathcal{PT}
$ phase transition region. In this way\, a simple heuristic picture and co
mplementary explanation for the unboundedness of projector norms and $\\ma
thcal{C}-$operator for the $V=ix^3$ model are provided and the lack of qua
si-Hermiticity of the $ix^3$ Hamiltonian over $\\mathbb{R}$ appears physic
ally plausible. Possible directions of further research are briefly sketch
ed.\n\nhttps://indico.cern.ch/event/732911/contributions/3165250/
LOCATION:Johannessaal
URL:https://indico.cern.ch/event/732911/contributions/3165250/
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