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



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. 


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

Current Issue

Smart Healthcare pulls up Clouds for Virtual Medicine

Selecting the correct electromagnetic inspection technology 

Influence of railway-track grinding on the track material condition and tribological behaviour

Micromechanical Fatigue Modelling of the Size Effect in Micro-Scale 316L Stainless Steel Specimens

Functionalization of Graphene and Reduced Graphene Oxide in Different Matrices

Effect of parasitic polytypes on ballistic electron transport in chemical vapor deposition grown 6H-SiC epitaxial layers

Photomemristive heterostructures based on two-dimensional crystals

Architecture - behaviour - properties relationship in Star-shaped MPA-PMMA and MPA-PS hyper-branched copolymers

Graphene and doped graphene: A comparative DFT study

Ag2CO3 / Magnetic reduced graphene oxide nanocomposite as advanced visible light photocatalytic hybrid materials for efficient degradation of azo dye

Optimization of acid hydrolysis process for the preparation cellulose nanofibrils

Alginate/k-carrageenan and alginate/gelatin composite hydrogel beads for controlled drug release of curcumin

Study of microstructure and mechanical properties of friction stir welded ferrite-martensite DP700 steel

Previous issues

9th Anniversary of Advanced Materials Letters: Progress and Opportunities

Coating - A potent method to enhance electrochemical performance of Li(NixMnyCoz)O2 cathodes for Li-ion batteries

Analysis of machined electron beam treated Ti6Al4V-ELI implant surfaces

Bottom-up design of hydrogels through click-chemistry modification of magnetic nanoparticles

Visualization of mechanical loads with semiconductor nanocrystals 

Room temperature growth of ultra porous hot-wire deposited tantalum pentoxide

Substrate integrated circular cavity resonator filled with nano-fibrillated cellulose for humidity detection

Oxygen vacancy filament-based resistive switching in Hf0.5Zr0.5O2 thin films for non-volatile memory

Innovative silicon compatible materials for light emitting devices  

Graphene micromesh for transparent conductive films application 

Applications of nano-scale Cirrus DopantTM to improve existing coatings

Chitin nanofibrils in renewable materials for packaging and personal care applications

Synthesis of AgNPs embedded double network nanocomposite hydrogels having high swelling and anti-bacterial characteristics

Upcoming Congress

Knowledge Experience at Sea TM