A probabilistic evolution approach trilogy. I: Quantum expectation value evolutions, block triangularity and conicality, truncation approximants and their convergence

DOI10.1007/s10910-012-0079-6zbMath1365.82020OpenAlexW2081053784MaRDI QIDQ2377042

Metin Demiralp

Publication date: 27 June 2013

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-012-0079-6

zbMATH Keywords

expectation value dynamicsprobabilistic evolutionblock triangularityconicalityevolution matricesinitial conditions and fluctuations

Mathematics Subject Classification ID

Commutation relations and statistics as related to quantum mechanics (general) (81S05) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (10)

Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension ⋮ Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics ⋮ Somehow emancipating probabilistic evolution theory (PREVTH) from singularities via getting single monomial PREVTH ⋮ Using enchanted features of constancy adding space extension (CASE) to reduce the dimension of evolver dynamics: single monomial probabilistic evolution theory ⋮ A probabilistic evolution approach trilogy. II: Spectral issues for block triangular evolution matrix, singularities, space extension ⋮ Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. I: Arbitrariness and equipartition theorem in Kronecker power series ⋮ Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices ⋮ Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. II: The use of mathematical fluctuation theory ⋮ Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices ⋮ Truncation approximants to probabilistic evolution of ordinary differential equations under initial conditions via bidiagonal evolution matrices: simple case

Uses Software

• RODAS

Cites Work

• A probabilistic foundation for dynamical systems: theoretical background and mathematical formulation
• A probabilistic foundation for dynamical systems: phenomenological reasoning and principal characteristics of probabilistic evolution
• Numerical solution of ordinary differential equations by fluctuationlessness theorem
• VSVO multistep formulae adapted to perturbed second-order differential equations
• A contemporary linear representation theory for ordinary differential equations: multilinear algebra in folded arrays (folarrs) perspective and its use in multidimensional case
• A contemporary linear representation theory for ordinary differential equations: probabilistic evolutions and related approximants for unidimensional autonomous systems
• No fluctuation approximation in any desired precision for univariate function matrix representations
• Solving Ordinary Differential Equations I
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A probabilistic evolution approach trilogy. I: Quantum expectation value evolutions, block triangularity and conicality, truncation approximants and their convergence