Abstract matrix band theory for one‐dimensional lattices: Canonical representations and functions: A wave vector addition theorem

1983 ◽  
Vol 51 (1) ◽  
pp. 60-67 ◽  
Author(s):  
M. W. P. Strandberg
Keyword(s):  
Wave Vector ◽  
Addition Theorem ◽  
Band Theory ◽  
One Dimensional ◽  
Vector Addition ◽  
Canonical Representations ◽  
Matrix Band

scholarly journals MULTIBREATHER AND VORTEX BREATHER STABILITY IN KLEIN–GORDON LATTICES: EQUIVALENCE BETWEEN TWO DIFFERENT APPROACHES

2011 ◽  
Vol 21 (08) ◽  
pp. 2161-2177 ◽  
Author(s):  
J. CUEVAS ◽  
V. KOUKOULOYANNIS ◽  
P. G. KEVREKIDIS ◽  
J. F. R. ARCHILLA
Keyword(s):  
Coupled Oscillators ◽  
Hamiltonian Method ◽  
Band Theory ◽  
Floquet Multipliers ◽  
One Dimensional ◽  
Case Examples ◽  
Discrete Breathers ◽  
Klein Gordon ◽  
Band Method ◽  
Time Periodic

In this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stability analysis around such exponentially localized in space, time-periodic orbits, based on the Aubry band method and the MacKay effective Hamiltonian method, and prove that by making the suitable assumptions about the form of the bands in the Aubry band theory, their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods through a series of case examples including one-dimensional multi-breathers, and two-dimensional vortex breathers in the case of a lattice of linearly coupled oscillators with the Morse potential and in that of the discrete ϕ4 model.

QUANTUM WAVEGUIDE THEORY FOR TRIPLY CONNECTED AHARONOV–BOHM RINGS

1996 ◽  
Vol 10 (06) ◽  
pp. 701-712 ◽  
Author(s):  
CHANG-MO RYU ◽  
SAM YOUNG CHO ◽  
MINCHEOL SHIN ◽  
KYOUNG WAN PARK ◽  
SEONGJAE LEE ◽  
...  
Keyword(s):  
Magnetic Flux ◽  
Wave Vector ◽  
Quantum Interference ◽  
Transmission Probability ◽  
Interference Effects ◽  
Quantum Waveguide ◽  
One Dimensional ◽  
Waveguide Theory ◽  
Aharonov Bohm ◽  
Transmission And Reflection

Quantum interference effects for a mesoscopic loop with three leads are investigated by using a one-dimensional quantum waveguide theory. The transmission and reflection probabilities are analytically obtained in terms of the magnetic flux, arm length, and wave vector. Oscillation of the magnetoconductance is explicitly demonstrated. Magnetoconductance is found to be sharply peaked for certain localized values of flux and kl. In addition, it is noticed that the periodicity of the transmission probability with respect to kl depends more sensitively on the lead position, compared to the case of the two-lead loop.

scholarly journals Observation of higher-order non-Hermitian skin effect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiujuan Zhang ◽  
Yuan Tian ◽  
Jian-Hua Jiang ◽  
Ming-Hui Lu ◽  
Yan-Feng Chen
Keyword(s):  
Topological Insulators ◽  
Skin Effect ◽  
Higher Dimensions ◽  
Higher Order ◽  
Dependent Manner ◽  
Two Dimensional ◽  
Band Theory ◽  
One Dimensional ◽  
Finite Systems ◽  
Spin Polarized

AbstractBeyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics.

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