Dancing with Entropy: Max-Ent Restricted Dynamics in Quantum Systems

Dancing with Entropy: Max-Ent Restricted Dynamics in Quantum Systems

Seminar author:Tomás Pérez

Event date and time:03/07/2024 04:00:pm

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The problem of simulation of quantum many-body systems has garnered considerable attention in recent years, due to its profound applications to fields such as quantum information and quantum computing as well as their numerical/analytical complexity. The main difficulty lies in efficiently proposing approximate simulation schemes, capable of dealing with non-integrable and non-Gaussian correlations. It is crucial, then, to acknowledge that (Time-Dependent) Mean-Field Theory and Gaussian approaches are confined to Max-Ent manifolds of states $\sigma$ [1, 2]. Within these manifolds, the system’s state, guided by an orthogonally-projected Schrödinger (or Lindblad) 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. \n 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 system, via appropriate mappings, arises. Our approach, accomplished through a systematic expansion of the basis of operators, facilitates non-perturbative approximations to exact dynamics. \n [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 (https://arxiv.org/abs/2307.08683, 2024).