A probabilistic evolution approach trilogy. II: Spectral issues for block triangular evolution matrix, singularities, space extension

DOI10.1007/s10910-012-0080-0zbMath1365.82021OpenAlexW2055803359MaRDI QIDQ2377048

N. A. Baykara, 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/s10910-012-0080-0

zbMATH Keywords

singular Hamiltoniansspace extensionquantum expected valuescoordinate transformsprobabilistic evolution equations

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Quantum stochastic calculus (81S25) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (7)

Using enchanted features of constancy adding space extension (CASE) to reduce the dimension of evolver dynamics: single monomial probabilistic evolution theory ⋮ 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. I: Integral representation of Kronecker power series and multivariate Hausdorff moment problems ⋮ 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
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• Numerical solution of ordinary differential equations by fluctuationlessness theorem
• VSVO multistep formulae adapted to perturbed second-order differential equations
• Lie algebraic factorization of multivariable evolution operators: Definition and the solution of the canonical problem
• Lie algebraic factorization of multivariable evolution operators: Convergence theorems for the canonical case
• 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
• A probabilistic evolution approach trilogy. I: Quantum expectation value evolutions, block triangularity and conicality, truncation approximants and their convergence
• Solving Ordinary Differential Equations I
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