Stellar Black Hole Binaries in the Gravitational Universe - Part 2
By Monica Colpi
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (4/4)
By Albert Schwarz
Appears in collection : 2024 - T1 - Quantum many-body systems out-of-equilibrium
To address challenges in dealing with approximate effective dynamics and non-Gaussian correlations, it is crucial to acknowledge that both exact dynamics and Mean Field Theoretic (MFT) approaches are confined to Max-Ent manifolds $\mathcal{M}_\text{Max-Ent}$ of states $σ$ [1, 2]. Within these manifolds, the system’s state, guided by an orthogonally-projected Schrödinger equation of motion, maximizes the von Neumann entropy while sharing expectation values of a set of independent observables, giving rise to a self-consistency condition.
This seminar introduces a variation of the formalism that relaxes the self-consistency condition and employs a simpler form of orthogonal projection, reducing the numerical complexity associated with solving these equations of motion [3]. Consequently, a system of non-linear differential equations governing the dynamics of the logarithm of the density operator emerges, independent of the chosen observables. Our approach, accomplished through a systematic expansion of the basis of operators, facilitates non-perturbative approximations to exact dynamics.
[1] Jaynes, E. T. (1957), Physical Review. Series II. 106 (4): 620–630.
[2] R. Balian, Y. Alhassid, and H. Reinhardt, Physics Reports 131, 1–146 (1986).
[3] FTB. Pérez and JM. Matera, ArXiv 2307.08683 (Preprint, 2024).