A probabilistic evolution approach trilogy. III: Temporal variation of state variable expectation values from Liouville equation perspective

DOI10.1007/s10910-012-0081-zzbMath1365.82022OpenAlexW2018654823MaRDI QIDQ2377045

Metin Demiralp, Burcu Tunga

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/s10910-012-0081-z

zbMATH Keywords

evolution matrixphase space distributionprobabilistic evolutionelastic spring forcesexpected value dynamics

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Quantum stochastic calculus (81S25) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (10)

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 ⋮ New optimization techniques in engineering ⋮ 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

• MuPAD
• 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: 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
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