One dimensional periodic Dirac Hamiltonians: Semiclassical and high‐energy asymptotics for gaps

1996 ◽  
Vol 37 (7) ◽  
pp. 3153-3167 ◽  
Author(s):  
Gheorghe Nenciu ◽  
Radu Purice
Keyword(s):  
Author(s):  
M. S. P. Eastham ◽  
K. M. Schmidt

It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.


2017 ◽  
Vol 9 (4) ◽  
pp. 4024-4033 ◽  
Author(s):  
Zhongbin Pan ◽  
Lingmin Yao ◽  
Jiwei Zhai ◽  
Dezhou Fu ◽  
Bo Shen ◽  
...  

2020 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
N. G. Antoniou

Incorporating fractal geometry in the Regge-Mueller approach to strong interaction dynamics one may formulate a model for the one-dimensional critical sector of the hadronic 5-matrix in a high energy collision. A non conventional component of the correlation functions in rapidity space is obtained, the phenomenological implications of which are related with the intermittency effects in quark-gluon plasma physics.


Nanoscale ◽  
2021 ◽  
Author(s):  
Zhichang Xiao ◽  
Junwei Han ◽  
Haiyong He ◽  
Xinghao Zhang ◽  
Jing Xiao ◽  
...  

Lithium-ion capacitors (LICs) have attracted much attention considering their efficient combination of high energy density and high-power density. However, to meet the increasing requirements of energy storage devices and the...


2019 ◽  
Vol 33 (02) ◽  
pp. 1950006
Author(s):  
Huaisong Zhao ◽  
Jiasheng Qian ◽  
Sheng Xu ◽  
Feng Yuan

Based on the t-J model and slave-boson theory, we have studied the electronic structure in one-dimensional SrCuO2 by calculating the electron spectrum. Our results show that the electron spectra are mainly composed of three parts in one-dimensional SrCuO2, a sharp low-energy peak, a broad intermediate-energy peak and a high-energy peak. The sharp low-energy peak corresponds to the main band (MB) while the broad intermediate-energy peak and high-energy peak are associated with the shadow band (SB) and high-energy band (HB), respectively. From low-energy to intermediate-energy region, a clear two-peak structure (MB and SB) around the momentum [Formula: see text] appears, and the distance between two peaks decreases along the momentum direction from [Formula: see text] to [Formula: see text], then disappears at the critical momentum point [Formula: see text], leaving a single peak above [Formula: see text]. The electron spectral function in one-dimensional SrCuO2 is also the doping and temperature dependent. In particular, in the very low doping concentration, the HB merges into the MB. However, with the increases of the doping concentration, the HB separates from the MB and moves quickly to the high-binding energy region. The HB and MB are the direct results of the spin-charge separation while SB is the result of strong interaction between charge and spin parts. Therefore, our theoretical result predicts that the HB is more likely to be found at the low doping concentration, and it will be drowned in the background when the doping concentration is larger. Then with the temperature increases, the magnitude of the SB decreases, and it disappears at high temperature.


Author(s):  
M. S. P. Eastham ◽  
K. M. Schmidt

It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.


Author(s):  
Sul-Ah Park ◽  
Young-Woo Son ◽  
Kang-Hun Ahn

We reveal new stripe states in deformed hexagonal array of photonic wave guides when the array is terminated to have a ribbon-shaped geometry. Unlike the well-known zero energy edge modes of honeycomb ribbon, the new one-dimensional states are shown to originate from high-energy saddle-shaped photonic bands of the ribbon's two-dimensional counterpart. We find that the strain field deforming the ribbon generates pseudo-electric fields in contrast to pseudo-magnetic fields in other hexagonal crystals. Thus, the stripe states experience Bloch oscillation without any actual electric field so that the spatial distributions of stripes have a singular dependence on the strength of the field. The resulting stripe states are located inside the bulk and their positions depend on their energies.


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