Matrix and Variant Transformations Simulate Statistical Canonical Ensembles from Fock to Poissonian States of Random Sequences

Jeffrey Zheng1, 2*, Yamin Luo1, 2, Xin Zhang1, 2, Chris Zheng3 

1Key Lab of Quantum Information, Yunnan University, Kunming Yunnan 650091, China

2Key Lab of Software Engineering, Yunnan University, Kunming Yunnan 650091, China

3Tahto, Sydney, Australia 

DOI: 10.5185/amlett.2019.9911

Publication Date (Web): Mar 02, 2019

E-mail: conjugatelogic@yahoo.com

Abstract

From a quantum statistical viewpoint, four typical quantum states are Fock, Sub-Poissonian, Poissonian and Super-Poissonian states. Quantum interactions are among Fock and Poissonian states. Using quantum statistics, model and simulation, this paper propose two models: matrix and variant transformations: 1. MT Matrix Transformation – eigenvalue states; 2. VT Variant Transformation – invariant states to analyze three random sequences: 1) random; 2) conditional random in a constant; 3) periodic pattern.  Four procedures are proposed. Fast Fourier Transformation FFT is applied as one of MT schemes and two invariant scheme of VT schemes are applied, three random sequences are used in M segments, and each segment has a length m to generate a measuring sequence. Shifting operations are applied on each random sequence to create m+1 spectrum distributions. Better than FFT, VT can identify Fock, Sub-Poissonian, Poissonian states in random analysis to distinguish three random sequences as three levels of statistical ensembles: Micro-canonical, Canonical, and Grand-Canonical ensembles. Applying two transformations, quantum statistics, model and simulation of modern quantum theory and applications can be explored. 

Keywords

Fock, sub-poissonian, poissonian, super-poissonian, matrix transformation, variant transformation, canonical ensembles.

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