Quantum states and spectra of small cylindrical and toroidal lattices

IF 1.5 4区 物理与天体物理 Q3 OPTICS Journal of Physics B: Atomic, Molecular and Optical Physics Pub Date : 2024-09-15 DOI:10.1088/1361-6455/ad7552
Caelan Brooks and Kunal K Das
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Abstract

We examine the spectrum and quantum states of small lattices with cylindrical and toroidal topology subject to a scalar gauge potential that introduces a position dependent phase in the inter-site coupling. Equivalency of gauges assumed in infinite lattices is generally lost due to the periodic boundary conditions, and conditions that restore it are identified. We trace the impact of various system parameters including gauge choice, boundary conditions and inter-site coupling strengths, and an additional axial field. We find gauge dependent appearance of avoided crossings and persistent degeneracies, and we show their impact on the associated eigenstates. Smaller lattices develop prominent gaps in spectral lines associated with edge states, which are suppressed in the thermodynamic limit. Toroidal lattices have counterparts of most of the features observed in cylindrical lattices, but notably they display a transition from localization to delocalization determined by the relation between the field parameter and the number of lattice sites.
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小圆柱形和环形晶格的量子态和光谱
我们研究了具有圆柱形和环形拓扑结构的小晶格的频谱和量子态,这些小晶格受到标量规势的影响,在晶格间耦合中引入了与位置相关的相位。由于周期性边界条件的存在,无限晶格中假设的量规等效性通常会丧失,而恢复等效性的条件是确定的。我们追踪了各种系统参数的影响,包括量规选择、边界条件和位间耦合强度,以及额外的轴向场。我们发现避免交叉和持续退化的出现与量规有关,并显示了它们对相关特征状态的影响。较小的晶格会在与边缘态相关的谱线中出现明显的间隙,这些间隙在热力学极限中会被抑制。环形晶格具有在圆柱形晶格中观察到的大多数对应特征,但值得注意的是,它们显示了从局域化到脱局域化的转变,这种转变由场参数和晶格位点数量之间的关系决定。
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来源期刊
CiteScore
3.60
自引率
6.20%
发文量
182
审稿时长
2.8 months
期刊介绍: Published twice-monthly (24 issues per year), Journal of Physics B: Atomic, Molecular and Optical Physics covers the study of atoms, ions, molecules and clusters, and their structure and interactions with particles, photons or fields. The journal also publishes articles dealing with those aspects of spectroscopy, quantum optics and non-linear optics, laser physics, astrophysics, plasma physics, chemical physics, optical cooling and trapping and other investigations where the objects of study are the elementary atomic, ionic or molecular properties of processes.
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X-ray circular dichroism measured by cross-polarization x-ray transient grating Toward a Mølmer Sørensen gate with .9999 fidelity Quantum states and spectra of small cylindrical and toroidal lattices Addendum: Multichannel quantum defect theory of strontium bound Rydberg states (2014 J. Phys. B: At. Mol. Opt. Phys. 47 155001) Absolute nuclear charge radius by Na-like spectral line separation in high-Z elements
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