Modulation instability in two-dimensional nonlinear Schrödinger lattice models with dispersion and long-range interactions

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Ljupčo Hadžievski ◽  
Milutin Stepić ◽  
Miloš M. Škorić
Keyword(s):  
Long Range ◽  
Modulation Instability ◽  
Lattice Models ◽  
Two Dimensional ◽  
Nonlinear Schrödinger ◽  
Long Range Interactions

scholarly journals Tunable super- and subradiant boundary states in one-dimensional atomic arrays

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Anwei Zhang ◽  
Luojia Wang ◽  
Xianfeng Chen ◽  
Vladislav V. Yakovlev ◽  
Luqi Yuan
Keyword(s):  
Long Range ◽  
Quantum States ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Metrology ◽  
One Dimensional ◽  
Topological Quantum ◽  
Long Range Interactions ◽  
Boundary States ◽  
Quantum Optical

AbstractEfficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.

Computer Simulation Study of a Disordered Two-Dimensional Nematogenic Lattice Model with Long-Range Interactions Isotropic in Spin Space

1997 ◽  
Vol 11 (07) ◽  
pp. 919-928
Author(s):  
S. Romano
Keyword(s):  
Computer Simulation ◽  
Long Range ◽  
Temperature Phase ◽  
Two Dimensional ◽  
Spin Space ◽  
Pair Potentials ◽  
Long Range Interactions ◽  
Invariant Pair ◽  
Ordering Transition ◽  
Low Temperature Phase

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k∈ Z2}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form [Formula: see text] Here ∊ is a positive constant setting energy and temperature scales (i.e. T*=k B T /∊), P2 denotes the second Legendre polynomial, and xj are dimensionless coordinates of the lattice sites. Available theorems entail the existence of an ordering transition at finite temperature when 0 < σ < 2, and its absence when σ ≥ 2. We have studied the border case σ=2, by means of computer simulation. Similarly to the nearest-neighbour counterpart of the present model, and to other long-range models, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinski[Formula: see text]–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ=1.112 ± 0.005.

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