Study of scattering from aperiodic set-ups with the use of local parity

Doctoral Dissertation uoadl:1309743 557 Read counter

Unit:
Τομέας Πυρηνικής Φυσικής και Φυσικής Στοιχειωδών Σωματιδίων
Library of the School of Science
Deposit date:
2014-05-20
Year:
2014
Author:
Καλοζούμης Παναγιώτης
Dissertation committee:
Φώτιος Διάκονος Αναπλ. Καθηγητής ΕΚΠΑ (Επιβλέπων), Αλέξανδρος Καρανίκας Αναπλ. Καθηγητής ΕΚΠΑ, Prof. Dr. Peter Schmelcher Professor University of Hamburg
Original Title:
Study of scattering from aperiodic set-ups with the use of local parity
Languages:
English
Translated title:
Μελέτη σκέδασης από απεριοδικές διατάξεις με τη χρήση της τοπικής ομοτιμίας
Summary:
We study the breaking of global discrete symmetries -specifically inversion and
translation- in one-dimensional scattering set-ups. We focus on the case where
the broken global symmetry is retained locally, in arbitrary domains of finite
spatial extent and we find a class of space invariant, non-local currents,
which are remnants of the broken global symmetry. These currents provide a
mapping of the wave function from an arbitrary spatial domain, considered as
source, to a target domain. The two domains are linked through the
corresponding symmetry transform. The derived mapping constitutes a
generalization of the Bloch and parity theorems for arbitrary finite systems
which can be aperiodic or non-inversion symmetric. The obtained invariant
currents are identified as remnants of the respective global symmetry,
providing a systematic approach to the breaking of discrete global symmetries.
The proposed method addresses successfully any combination of translation and
inversion symmetry and can be applied to the study of wave propagation in
aperiodic and quasi-periodic media. The fact that it lies on very general
symmetry arguments, combined with the Helmholtz-Schrodinger isomorphism,
provide a unified framework which can be applied to the quantum optical and
acoustic systems, notwithstanding their essential differences. Focusing on the
parity transformation when applied to finite mirror symmetric domains, we
introduce the concept of local parity (LP) and the corresponding operator. We
consider non-symmetric, aperiodic scattering set-ups which can be completely
decomposed in space domains where the LP symmetry is satisfied and reveal its
impact on their transport properties and particularly on perfect transmission
resonances (PTRs). With emphasis on the PTR manifestation and by employing the
aforementioned invariant currents, we propose a classification of PTRs, based
on their geometric representation on the complex plane. This classification
lifts certain overlaps of alternative approaches in the existing literature and
provides an unambiguous distinction between resonances based on fundamental,
local symmetry principles. Finally we develop a construction principle which
utilizes the simultaneous existence of different LP symmetry scales in the same
set-up for the design of aperiodic wave mechanical devices with prescribed PTR
properties. The implementation of this construction principle on quantum,
photonic and acoustic systems, reveals its applicability in diverse systems.
Keywords:
Local symmetries, Parity, Generalized Bloch theorem, Scattering, Resonance
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
149
Number of pages:
VIII, 148
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