scholarly journals CONSTRUCTION OF A DISPERSION RELATION FROM AN ARBITRARY DENSITY OF STATES

2002 ◽  
Vol 16 (23) ◽  
pp. 3491-3501 ◽  
Author(s):  
MARCUS KOLLAR
Keyword(s):  
Dispersion Relation ◽  
Density Of States ◽  
Three Dimensional ◽  
Dispersion Relations ◽  
Band Spectrum ◽  
Spherically Symmetric ◽  
Infinite Dimensions ◽  
Energy Bands ◽  
Band Structures ◽  
Finite Bandwidth

The dispersion relations of energy bands in solids are characterized by their density of states, but a given density of states may originate from various band structures. We show how a spherically symmetric dispersion can be constructed for any one-band density of states. This method is applied to one-, two- and three-dimensional systems. It also serves to establish that any one-band spectrum with finite bandwidth can be obtained from a properly scaled dispersion relation in the limit of infinite dimensions.

scholarly journals Dimensional effects on the density of states in systems with quasi-relativistic dispersion relations and potential wells

2016 ◽  
Vol 94 (8) ◽  
pp. 773-779 ◽  
Author(s):  
A. Pokraka ◽  
R. Dick
Keyword(s):  
Hybrid Systems ◽  
Density Of States ◽  
Three Dimensional ◽  
Dispersion Relations ◽  
Potential Wells ◽  
Dimensional Effects ◽  
Densities Of States ◽  
Relativistic Dispersion ◽  
Low Dimensional

Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we determine densities of states in materials with low dimensional substructures and relativistic dispersion relations. We find that these dimensionally hybrid systems yield quasi-relativistic densities of states that are a superposition of the corresponding two- and three-dimensional densities of states.

scholarly journals A Newly Developed Dispersive Interaction Approach, DFT-D3, To The Three-Dimensional Topological Host Material Sb2Te3

2021 ◽  
Author(s):  
Nishant Shukla ◽  
Pawan Chetri ◽  
Gazi A. Ahmed
Keyword(s):  
Density Of States ◽  
Lattice Structure ◽  
Three Dimensional ◽  
Surface States ◽  
Partial Density ◽  
Total Density ◽  
Energy Bands ◽  
Layered Semiconductor ◽  
Interaction Approach ◽  
Quantum Espresso

Abstract Antimony Telluride (Sb2Te3), a topological insulator is a layered semiconductor material with hexagonal unit cell similar to graphene. The characteristic presence of their conducting edges or surfaces with self-induced protection, promise for remarkable future applications. In this exertion based on the first principle approach, the structural and electronic properties of Sb2Te3 compound have been investigated for both without and with spin orbit coupling (SOC). Lattice structure, band structure, total density of states (TDOS), partial density of states (PDOS), energy bands of surface states are determined within Quantum Espresso simulation package. Furthermore, dispersive interactions, induced due to the presence of van-der-Waals forces have also been taken care of. The newly developed method of DFT-D3 has been incorporated for accurate predictions of band gap and lattice parameters. A proficient model, The Slab Model, has been used to observe the presence of single Dirac cone on the surface. To our knowledge, our theoretical investigations are valid and are found to be congruous with the observed data.

scholarly journals Evolution of a narrow-band spectrum of random surface gravity waves

2003 ◽  
Vol 478 ◽  
pp. 1-10 ◽  
Author(s):  
KRISTIAN B. DYSTHE ◽  
KARSTEN TRULSEN ◽  
HARALD E. KROGSTAD ◽  
HERVÉ SOCQUET-JUGLARD
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Band Spectrum ◽  
Nls Equation ◽  
Random Surface ◽  
Narrow Bandwidth ◽  
Quasi Stationary State ◽  
The Stability ◽  
Three Dimensional Simulations

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

Local Density of States of a Three-Dimensional Conductor in the Extreme Quantum Limit

2001 ◽  
Vol 86 (8) ◽  
pp. 1582-1585 ◽  
Author(s):  
D. Haude ◽  
M. Morgenstern ◽  
I. Meinel ◽  
R. Wiesendanger
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Three Dimensional ◽  
Quantum Limit ◽  
Local Density Of States

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

Dispersion relations of dust lattice waves in two-dimensional honeycomb configuration

2013 ◽  
Vol 79 (5) ◽  
pp. 629-633
Author(s):  
B. FAROKHI
Keyword(s):  
Dispersion Relation ◽  
Group Velocity ◽  
Hexagonal Lattice ◽  
Dispersion Relations ◽  
Two Dimensional ◽  
The Third ◽  
Lattice Waves ◽  
The Waves

AbstractThe linear dust lattice waves propagating in a two-dimensional honeycomb configuration is investigated. The interaction between particles is considered up to distance 2a, i.e. the third-neighbor interactions. Longitudinal and transverse (in-plane) dispersion relations are derived for waves in arbitrary directions. The study of dispersion relations with more neighbor interactions shows that in some cases the results change physically. Also, the dispersion relation in the different direction displays anisotropy of the group velocity in the lattice. The results are compared with dispersion relations of the waves in the hexagonal lattice.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

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