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

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 2; p. 308
• Main Authors: Prykarpatski, Anatolij K, Pukach, Petro Y, Vovk, Myroslava I
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 07-02-2023; MDPI
• Subjects: Algorithms; Conservation laws; Control theory; dark type flow; Dynamical systems; Glass substrates; Growth models; Optimal control; parametric evolution flow; Polymers; Process controls; Random variables; Spin glasses; Statistical physics; symplectic analysis; the Kardar–Parisi–Zhang-type equation; thermodynamic stability; Thermodynamics; symplectic structure; optimal control problem; asymptotic solution; parametric evolution flow; Lax–Noether condition; dynamical systems; the Kardar–Parisi–Zhang-type equation; dark type flow; conservation law; thermodynamic stability; Poisson structure; complete integrability; symplectic analysis
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25020308

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.