Numerical simulations of coupled map lattices with various degree of nonlocality have been performed. Quantitative characteristics of recently introduced for local coupling have been applied in the nonlocal case. It has been attempted to draw qualitative conclusions about nonlocality from the emerging pictures.
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When D is a density matrix and A1, A2 are self-adjoint operators, then the standard variance is a 2 × 2 matrix: VarD(A1, A2)i,j := TrDAiAj − (TrDAi)(TrDAj) (1 ≤ i, j ≤ 2). The main result in this work is that there are projections Pk such that D = Σk λk Pk with 0 < λk and Σk λk = 1 and VarD (A1, A2) = Σk λk VarPk (A1, A2). In a previous paper only the A1 = A2 case was included and the relevance is motivated by the paper [8].
The work discusses mathematical models using paradigms developed for quantum phenomena, including the vector-matrix Hilbert space and quantum gates for linear transformations of states to build a day-ahead market model (DAM). The article presents the most popular directions in the development of models using tools used in the description of quantum phenomena to present the methodology of conducting this type of calculation. Mathematical structures such as Hilbert space and operations on this space were used to build a quantum-inspired Artificial Neural Network. The work presents the proposition of implementation of DAM system to build a Neural Network Model with usage quantum phenomena based on Hilbert space. The concept of quantum processing based on quantum circuits was also noticed due to its large use and the development of implementing tools as a supplement to the entire area of development of building models based on quantum computing.
W artykule omówiono metody modelowania obszaru aktywnego struktury kwantowego lasera kaskadowego. Na przykładzie struktury lasera, emitującego w zakresie średniej podczerwieni, wskazano analogie i różnice między obrazem transportu elektronowego wynikające z analizy z użyciem m.in. najprostszego modelu równań kinetycznych, metody macierzy gęstości oraz najbardziej zaawansowanym modelem bazującym na formalizmie nierównowagowych funkcji Greena. Uzupełnieniem ww. metod jest metoda Monte Carlo, w której możliwe jest m.in. uwzględnienie rozproszeń elektron-elektron oraz rozproszeń międzydolinowych.
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In the paper, the modeling methods of active region of quantum cascade laser (QCL) structure are reviewed. For QCL structure, emitting in the mid-infrared range, the similarities and the differences between electron transport image resulting from (i) the simplest rate equations model, (ii) the density matrix method, and (iii) the most advanced model based on nonequilibrium Green’s formalism are discussed. The Monte Carlo method, which benefits from including electron-electron, electron-photon, and intervalleys scatterings, is also considered.
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