Symplectic Geometry Aspects of the Parametrically-Dependent Kardar-Parisi-Zhang Equation of Spin Glasses Theory, Its Integrability and Related Thermodynamic Stability.

Anatolij K Prykarpatski Petro Y Pukach Myroslava I Vovk

Published in: Entropy (Basel, Switzerland) (2023)

A thermodynamically unstable spin glass growth model described by means of the parametrically-dependent Kardar-Parisi-Zhang equation is analyzed within the symplectic geometry-based gradient-holonomic and optimal control motivated algorithms. The finitely-parametric functional extensions of the model are studied, and the existence of conservation laws and the related Hamiltonian structure is stated. A relationship of the Kardar-Parisi-Zhang equation to a so called dark type class of integrable dynamical systems, on functional manifolds with hidden symmetries, is stated.

Keyphrases

density functional theory
room temperature
machine learning
single molecule
deep learning
molecular dynamics
transition metal