From a quantum statistical viewpoint, four typical quantum states are Fock, Sub-Poissonian, Poissonian and Super-Poissonian states. Quantum interactions are focus among Fock and Poissonian states. Using quantum statistics, modeland simulation, this paper proposes 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 invariantscheme of VT schemes are applied, three random sequences are in M segments and each segment has a length m togenerate a measuring sequence. Shifting operations are applied on each random sequence to create m+1 spectrumdistributions. For FFT, a pair of eigenvalues are selected as the output. Two types of 1D & 2D variant maps aregenerated to illustrate multiple parameter selections to generate a series of results. Since sequences 1) and 3) are relatedsimple, more cases are focus on sequences 2).Better than FFT, VT distinguishes various Fock, Sub-Poissonian, Poissonian states in random analysis to distinguishthree random sequences as three levels of statistical ensembles: Micro-canonical, Canonical, and Grand-Canonicalensembles. Applying two transformations, quantum statistics, model and simulation of modern quantum theory andapplications can be explored.
展开▼
