scholarly journals Exponential Asymptotics for Solitons in PT-Symmetric Periodic Potentials

2014 ◽  
Vol 133 (4) ◽  
pp. 373-397 ◽  
Author(s):  
Sean D. Nixon ◽  
Jianke Yang
Keyword(s):  
Periodic Potentials ◽  
Exponential Asymptotics

scholarly journals Exponential Asymptotics for Line Solitons in Two-Dimensional Periodic Potentials

2013 ◽  
Vol 131 (2) ◽  
pp. 149-178 ◽  
Author(s):  
Sean D. Nixon ◽  
T. R. Akylas ◽  
Jianke Yang
Keyword(s):  
Two Dimensional ◽  
Periodic Potentials ◽  
Exponential Asymptotics

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

Landau–Zener tunneling in spin–orbit-coupled Bose–Einstein condensates in PT periodic potentials

Optik ◽  
2021 ◽  
Vol 231 ◽  
pp. 166350
Author(s):  
T.F. Xu ◽  
B.Y. Shen ◽  
C.Y. Zhou ◽  
Y.H. Liu
Keyword(s):  
Spin Orbit ◽  
Periodic Potentials ◽  
Zener Tunneling ◽  
Bose Einstein

scholarly journals Asymmetric Loop Spectra and Unbroken Phase Protection due to Nonlinearities in PT -Symmetric Periodic Potentials

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Yongping Zhang ◽  
Zhu Chen ◽  
Biao Wu ◽  
Thomas Busch ◽  
Vladimir V. Konotop
Keyword(s):  
Periodic Potentials

The spectra of periodic potentials in finite boxes

1995 ◽  
Vol 16 (3) ◽  
pp. 119-123 ◽  
Author(s):  
T M Kalotas ◽  
A R Lee
Keyword(s):  
Periodic Potentials

scholarly journals Matter-wave solitons in radially periodic potentials

2006 ◽  
Vol 74 (6) ◽  
Author(s):  
Bakhtiyor B. Baizakov ◽  
Boris A. Malomed ◽  
Mario Salerno
Keyword(s):  
Matter Wave ◽  
Periodic Potentials
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