Unified Quantum Dynamics Framework: Finite-Time Evolution, Decoherence, and Entanglement Dynamics

Sanchez, Rogelio Lucero

Y. Li

We present a first-principles derivation of a master equation that unifies quantum dynamics, thermal effects, and Riemannian geometry within a holomorphic framework. By extending the temporal parameter into the complex domain $\theta = t + i\frac{\hbar}{2k_B T}$, we demonstrate that the KMS condition in thermal field theory necessitates a specific form of evolution. We correct previous dimensional inconsistencies and derive the unique coupling constant $\alpha = \lambda \sqrt{\hbar G / c}$, which links the Laplace-Beltrami operator to complex time evolution. The resulting Complex Time Quantum Thermal Geometric (CTQTG) equation predicts gravity-induced decoherence and a fundamental ultraviolet regularization of momentum states at finite temperatures.

V. M. Akulin

Mouhcine Yachi, Brahim Amghar, Jamal Elfakir +4 more

Understanding how intrinsic decoherence affects the interplay between geometry, dynamics, and entanglement in quantum systems is a central challenge in quantum information science. In this work, we develop a unified framework that explores this interplay for a pair of interacting spins governed by an XXZ-type Heisenberg model under an external magnetic field and intrinsic decoherence. We quantify entanglement using the concurrence measure and examine its evolution under decoherence, revealing that intrinsic noise rapidly suppresses entanglement as it increases. We then analyze the Hilbert-Schmidt and Bures distances between quantum states and show how both the degree of entanglement and the noise rate modulate these distances and their associated quantum speeds. Importantly, we demonstrate that the Hilbert-Schmidt speed is more responsive to entanglement and coherence loss than the Bures speed, making it a powerful tool for probing the geometry of quantum dynamics. Moreover, we solve the quantum brachistochrone problem in the presence of intrinsic decoherence, identifying the minimal evolution time and the corresponding optimal entangled states. Finally, we explore the geometric phase accumulated during the system's evolution. Our results show that decoherence hinders geometric phase accumulation, while entanglement counteracts this effect, enhancing phase stability.

Trinity Lab

This paper introduces Unified Relational Projection Dynamics (URPD), an information-theoretic framework that derives quantum probabilities, temporal evolution, classical motion, and relativistic causality from a single relational principle. By modeling physical states as points on a projective Hilbert manifold and defining an information-based measure of relational displacement between consecutive frames, the framework replaces the Born rule, Schrödinger dynamics, and geodesic motion with a unified update rule. The theory also explains how classical spacetime structure emerges from decoherence and how quantum entanglement remains compatible with causal constraints. URPD serves as a minimal and coherent foundation that integrates quantum theory and relativity into one informational structure.