Decoherence and the Arrow of Time in Non-Markovian Quantum Dots — E8 Intelligence Research

FINDING: Decoherence is the mechanism by which quantum superpositions irreversibly leak into the environment, effectively collapsing the wavefunction and generating the classical arrow of time; recent work focuses on exact master equations for non-Markovian decoherence in quantum dot systems. | MATH: The core mathematical object is the reduced density matrix \(\rho_S(t) = \mathrm{Tr}_E[U(t)\rho_{SE}(0)U^\dagger(t)]\), with the Feynman–Vernon influence functional \(F[J] = \exp\left(-\frac{1}{\hbar}\int_0^t\int_0^t J(t') \tilde{D}(t'-t'') J(t'') dt' dt''\right)\). The exact master equation (from the arXiv paper) takes the form \(\dot{\rho}_S = -\frac{i}{\hbar}[H_S,\rho_S] - \frac{i}{\hbar}\Delta(t)[x^2,\rho_S] - \gamma(t)[x,\{p,\rho_S\}] - D(t)[x,[x,\rho_S]] - \bar{D}(t)[x,\{p,\rho_S\}]\), where \(\gamma(t)\) is the time-dependent damping, \(D(t)\) the normal diffusion, and \(\bar{D}(t)\) the anomalous diffusion coefficient. Decoherence time scales as \(\tau_d \sim \hbar^2 / (m k_B T \De Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com