Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and
N-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and
N-body Schrodinger operators and resonances by R. Froese
N-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark.
This comprehensive second volume mathematically formalizes the Orchestrated Objective Reduction (Orch OR) theory, advancing it from its conceptual foundations into a rigorous operational framework for biological learning and memory. By synthesizing concepts from open quantum systems, non-Hermitian dynamics, and quantum active inference, the report defines the total unified Hamiltonian operator (Ĥ_Total) that dictates the structure of learning. The core finding establishes that conscious, temporally deep active inference—the continuous optimization of internal generative models to minimize expected free energy—is mathematically indistinguishable from the quantum path integral. This equivalence leads to the derivation of the Master Learning Hamiltonian Mamun, SM (2026) ……………………………….1 Quantum Foundations of Cognition: A Hamiltonian Framework for Learning, Memory, and Active Inference within the Orchestrated Objective Reduction Paradigm (Vol-II) K S C (Ĥ_Learning), where the Schrödinger potential (V(ϕ)) physically represents the dynamic landscape of long-term memory and prior beliefs. The document further addresses classical decoherence challenges by modeling Microtubules as Qudit Hopfield Networks governed by a Lindbladian framework (exhibiting superradiant and subradiant states) and by scaling the theory to macroscopic cognition using Neural Spinfoam Networks (NSNs). Also available on Academia.edu: https://www.academia.edu/attachments/132658997/download_file?s=portfolio