scholarly journals Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian

2011 ◽  
Vol 326 (6) ◽  
pp. 1425-1440 ◽  
Author(s):  
Dhagash Mehta ◽  
Michael Kastner
Keyword(s):  
Stationary Point ◽  
Random Phase ◽  
Landau Gauge ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Point Analysis ◽  
Gauge Fixing ◽  
The One

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022038
Author(s):  
T V Yakunina ◽  
V N Udodov
Keyword(s):  
Critical Exponent ◽  
Percolation Threshold ◽  
Correlation Length ◽  
Adjacency Matrix ◽  
Nearest Neighbors ◽  
Percolation Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One

Abstract A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

scholarly journals A Universal Low-Complexity Demapping Algorithm for Non-Uniform Constellations

2020 ◽  
Vol 10 (23) ◽  
pp. 8572
Author(s):  
Hao Wang ◽  
Mingqi Li ◽  
Chao Wang
Keyword(s):  
Euclidean Distance ◽  
Low Complexity ◽  
Coded Modulation ◽  
One Dimensional ◽  
Performance Loss ◽  
Point Analysis ◽  
Simulation Results ◽  
The One ◽  
Bit Interleaved Coded Modulation ◽  
Log Map

A non-uniform constellation (NUC) can effectively reduce the gap between bit-interleaved coded modulation (BICM) capacity and Shannon capacity, which has been utilized in recent wireless broadcasting systems. However, the soft demapping algorithm needs a lot of Euclidean distance (ED) calculations and comparisons, which brings great demapping complexity to NUC. A universal low-complexity NUC demapping algorithm is proposed in this paper, which creates subsets based on the quadrant of the two-dimensional NUC (2D-NUC) received symbol or the sign of the in-phase (I)/quadrature (Q) component of the one-dimensional NUC (1D-NUC) received symbol. ED calculations and comparisons are only carried out on the constellation points contained in subsets. To further reduce the number of constellation points contained in subsets, the proposed algorithm takes advantage of the condensation property of NUC and regards a constellation cluster containing several constellation points as a virtual point. Analysis and simulation results show that, compared with the Max-Log-MAP algorithm, the proposed algorithm can greatly reduce the demapping complexity of NUC with negligible performance loss.

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