Dynamical Chaos and Decoherence(Quantum Mechanics and Chaos)

Jincheng Zhang

Quantum Information-Theoretic Chaos Theory explores the potential of quantum mechanics to fundamentally define and understand chaos, offering a novel approach to predicting and controlling its behavior. This paper proposes a formalization of chaos as a fundamental quantum phenomenon, leveraging quantum entanglement and decoherence to generate inherently chaotic patterns. We introduce a new set of rules governing these interactions, aiming to provide a mathematically rigorous framework for analyzing and manipulating chaotic systems. The core mechanism revolves around establishing a precise relationship between quantum states and chaotic dynamics, offering a potential pathway to enhanced predictive capabilities. This research addresses a long-standing challenge in quantum mechanics: the lack of a consistent mathematical description of chaos, presenting a bold new direction for theoretical investigation and practical application.

Marko Robnik

Nicolás Mirkin, Diego A. Wisniacki, Paula I. Villar +1 more

Abstract Quantum chaos is usually characterized through its statistical implications on the energy spectrum of a given system. In this work we propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that it produces in the long-time dynamics of a probe coupled to it under a dephasing interaction. By introducing the notion of an effective averaged decoherence factor, we show that the correction to the geometric phase acquired by the probe with respect to its unitary evolution can be exploited as a robust tool for sensing the integrable to chaos transition of the many-body quantum system to which it is coupled. This sensing mechanism is verified for several systems with different types of symmetries, disorder and even in the presence of long-range interactions, evidencing its universality.

Wojciech Hubert Zurek

Robert C. Bishop

B. Kaulakys

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to understand the classical chaos in terms of quantum mechanics. The first question has been partially solved by the Gutzwiller semiclassical trace formula for the eigenvalues of chaotic systems, while the classical chaos may be derived from quantum equations only introducing the decoherence process due to interaction with system's environment or intermediate frequent measurement. We may conclude that continuously observable quasiclassical system evolves essentially classically-like.