For the interacting models, we compare our approximate results to those found via exact diagonalization.
Michael Vogl, Pontus Laurell, Aaron D. Barr, Gregory A. Fiete 2019, 'Flow Equation Approach to Periodically Driven Quantum Systems', Physical Review Xhttp://doi.org/10.1103/PhysRevX.9.021037. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Two sub-optimal precoding programs are also discussed: singular value decomposition and block diagonalization.
Haole Chen, Lin Xiao, Yinfeng Li, Dingcheng Yang, Xiaoxiao Zhou 2017, 'Precoding Design and Power Allocation in Two-User MU-MIMO Wireless Ad Hoc Networks',Symmetryhttps://www.mdpi.com/2073-8994/9/11/247. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In order to make the non-convex problem tractable, diagonalization-based alternating optimization algorithms are proposed.
Xiaoqing Liu, Zhigang Wen, Dan Liu, Junwei Zou, Shan Li 2019, 'Joint Source and Relay Beamforming Design in Wireless Multi-Hop Sensor Networks withSWIPT', Sensorshttp://www.mdpi.com/1424-8220/19/1/182. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Many-particle states are calculated numerically by the exact diagonalization method.
Okuyama Rin, Eto Mikio, Hyuga Hiroyuki 2011, 'Magnetoluminescence from trion and biexciton in type-II quantum dot', Nanoscale Research Lettershttp://www.nanoscalereslett.com/content/6/1/351. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The transformation to achieve the diagonalization was obtained from group theorectic considerations.
J. N. Boyd, P. N. Raychowdhury 1983, 'Two dimentional lattice vibrations from direct product representations of symmetrygroups', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/S0161171283000666. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
A simple matrix diagonalization provides a powerful way to deduce the resonant frequencies for finite size array.
C. Jouvaud, A. Ourir, J. de Rosny 2012, 'Electromagnetic coupling in a planar periodic configuration of resonators', Advanced Electromagneticshttp://www.aemjournal.org/index.php/AEM/article/view/97. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We show that this model satisfies the eigenstate thermalization hypothesis by solving the system in exact diagonalization.
Julian Sonner, Manuel Vielma 2017, 'Eigenstate thermalization in the Sachdev-Ye-Kitaev model', Journal of High Energy Physicshttp://link.springer.com/article/10.1007/JHEP11(2017)149. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)