scholarly journals A model of the circulation on the outer Scotian Shelf with open boundary conditions inferred by data assimilation

1998 ◽  
Vol 103 (C13) ◽  
pp. 30641-30660 ◽  
Author(s):  
Keith R. Thompson ◽  
David A. Griffin
Keyword(s):  
Data Assimilation ◽  
Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Scotian Shelf

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

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