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Title: Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries

Abstract

Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates. - Highlights: • We extend the framework of non-local currents to discrete planar systems. • Structural information about the eigenstates is gained. • Conditions for the constancy of non-local currents are derived. • We use the framework to design two types of example systems featuring locally symmetric eigenstates.

Authors:
 [1];  [1];  [2];  [1];  [3]
  1. Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
  2. Department of Physics, University of Athens, GR-15771 Athens (Greece)
  3. (Germany)
Publication Date:
OSTI Identifier:
22617502
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENSTATES; ONE-DIMENSIONAL CALCULATIONS; SYMMETRY

Citation Formats

Röntgen, M., E-mail: mroentge@physnet.uni-hamburg.de, Morfonios, C.V., E-mail: christian.morfonios@physnet.uni-hamburg.de, Diakonos, F.K., E-mail: fdiakono@phys.uoa.gr, Schmelcher, P., E-mail: pschmelc@physnet.uni-hamburg.de, and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg. Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.03.011.
Röntgen, M., E-mail: mroentge@physnet.uni-hamburg.de, Morfonios, C.V., E-mail: christian.morfonios@physnet.uni-hamburg.de, Diakonos, F.K., E-mail: fdiakono@phys.uoa.gr, Schmelcher, P., E-mail: pschmelc@physnet.uni-hamburg.de, & The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg. Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries. United States. doi:10.1016/J.AOP.2017.03.011.
Röntgen, M., E-mail: mroentge@physnet.uni-hamburg.de, Morfonios, C.V., E-mail: christian.morfonios@physnet.uni-hamburg.de, Diakonos, F.K., E-mail: fdiakono@phys.uoa.gr, Schmelcher, P., E-mail: pschmelc@physnet.uni-hamburg.de, and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg. Mon . "Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries". United States. doi:10.1016/J.AOP.2017.03.011.
@article{osti_22617502,
title = {Non-local currents and the structure of eigenstates in planar discrete systems with local symmetries},
author = {Röntgen, M., E-mail: mroentge@physnet.uni-hamburg.de and Morfonios, C.V., E-mail: christian.morfonios@physnet.uni-hamburg.de and Diakonos, F.K., E-mail: fdiakono@phys.uoa.gr and Schmelcher, P., E-mail: pschmelc@physnet.uni-hamburg.de and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg},
abstractNote = {Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates. - Highlights: • We extend the framework of non-local currents to discrete planar systems. • Structural information about the eigenstates is gained. • Conditions for the constancy of non-local currents are derived. • We use the framework to design two types of example systems featuring locally symmetric eigenstates.},
doi = {10.1016/J.AOP.2017.03.011},
journal = {Annals of Physics},
number = ,
volume = 380,
place = {United States},
year = {Mon May 15 00:00:00 EDT 2017},
month = {Mon May 15 00:00:00 EDT 2017}
}