On the time evolution at a fluctuating exceptional point

Christian Wolff*, Christos Tserkezis, N. Asger Mortensen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We theoretically evaluate the impact of drift-free noise on the dynamics of PT -symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as promising templates for sensing applications, because of their intrinsically extremely sensitive response to external perturbations. However, this applies equally to the impact of fabrication imperfections and fluctuations in the system parameters. Here we focus on the influence of such fluctuations caused by inevitable (thermal) noise and show that the exceptional-point eigenstate is not stable in its presence. To this end, we derive an effective differential equation for the mean time evolution operator averaged over all realizations of the noise field, and via numerical analysis we find that the presence of noise leads to exponential divergence of any initial state after some characteristic period of time. We therefore show that it is rather demanding to design sensor systems based on continuous operation at an exceptional point.

Original languageEnglish
JournalNanophotonics
Volume8
Pages (from-to)1319-1326
ISSN2192-8606
DOIs
Publication statusPublished - 2019

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Noise
Thermal noise
Sensors
Mathematical operators
Numerical analysis
Differential equations
sensors
thermal noise
Fabrication
Defects
numerical analysis
divergence
eigenvectors
differential equations
templates
operators
perturbation
fabrication
defects

Keywords

  • exceptional point
  • P T -symmetric systems
  • thermal noise

Cite this

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title = "On the time evolution at a fluctuating exceptional point",
abstract = "We theoretically evaluate the impact of drift-free noise on the dynamics of PT -symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as promising templates for sensing applications, because of their intrinsically extremely sensitive response to external perturbations. However, this applies equally to the impact of fabrication imperfections and fluctuations in the system parameters. Here we focus on the influence of such fluctuations caused by inevitable (thermal) noise and show that the exceptional-point eigenstate is not stable in its presence. To this end, we derive an effective differential equation for the mean time evolution operator averaged over all realizations of the noise field, and via numerical analysis we find that the presence of noise leads to exponential divergence of any initial state after some characteristic period of time. We therefore show that it is rather demanding to design sensor systems based on continuous operation at an exceptional point.",
keywords = "exceptional point, P T -symmetric systems, thermal noise",
author = "Christian Wolff and Christos Tserkezis and Mortensen, {N. Asger}",
year = "2019",
doi = "10.1515/nanoph-2019-0036",
language = "English",
volume = "8",
pages = "1319--1326",
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}

On the time evolution at a fluctuating exceptional point. / Wolff, Christian; Tserkezis, Christos; Mortensen, N. Asger.

In: Nanophotonics, Vol. 8, 2019, p. 1319-1326.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - On the time evolution at a fluctuating exceptional point

AU - Wolff, Christian

AU - Tserkezis, Christos

AU - Mortensen, N. Asger

PY - 2019

Y1 - 2019

N2 - We theoretically evaluate the impact of drift-free noise on the dynamics of PT -symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as promising templates for sensing applications, because of their intrinsically extremely sensitive response to external perturbations. However, this applies equally to the impact of fabrication imperfections and fluctuations in the system parameters. Here we focus on the influence of such fluctuations caused by inevitable (thermal) noise and show that the exceptional-point eigenstate is not stable in its presence. To this end, we derive an effective differential equation for the mean time evolution operator averaged over all realizations of the noise field, and via numerical analysis we find that the presence of noise leads to exponential divergence of any initial state after some characteristic period of time. We therefore show that it is rather demanding to design sensor systems based on continuous operation at an exceptional point.

AB - We theoretically evaluate the impact of drift-free noise on the dynamics of PT -symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as promising templates for sensing applications, because of their intrinsically extremely sensitive response to external perturbations. However, this applies equally to the impact of fabrication imperfections and fluctuations in the system parameters. Here we focus on the influence of such fluctuations caused by inevitable (thermal) noise and show that the exceptional-point eigenstate is not stable in its presence. To this end, we derive an effective differential equation for the mean time evolution operator averaged over all realizations of the noise field, and via numerical analysis we find that the presence of noise leads to exponential divergence of any initial state after some characteristic period of time. We therefore show that it is rather demanding to design sensor systems based on continuous operation at an exceptional point.

KW - exceptional point

KW - P T -symmetric systems

KW - thermal noise

U2 - 10.1515/nanoph-2019-0036

DO - 10.1515/nanoph-2019-0036

M3 - Journal article

VL - 8

SP - 1319

EP - 1326

JO - Nanophotonics

JF - Nanophotonics

SN - 2192-8606

ER -