Chaos Generator 5.0: From Reference to Standard

2005

The relationship between chaos and quantum mechanics has been somewhat uneasy -even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes -such as chaos -that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments.

Phys Rev Lett, 2004

The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation -- as all experimental systems must be -- their dynamics is no longer linear and, in the appropriate limit(s), the evolution of expectation values, conditioned on the observations, closely approaches the behavior of classical trajectories. Here we show, by analyzing a specific example, that microscopic continuously observed quantum systems, even far from any classical limit, can have a positive Lyapunov exponent, and thus be truly chaotic.

PLoS ONE, 2014

We give a new explanation for why some biological systems can stay quantum coherent for long timeS at room temperatures, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time BY orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.

NeuroQuantology, 2007

The nature of subjective conscious experience, and its consequences in intentionality, remain the central unsolved problem in science and one of critical importance to humanity's future as sentient observers and autonomous participants in a world history we are coming to have ever more pivotal influence upon. Each of us who read this paper are subjective conscious observers, making an autonomous decision to carry out a volitional action. All our knowledge of the physical universe is gained through the immediate conduit of our subjective experience and our intentionality in turn has major impacts on the physical world around us. To understand how the subjective aspect arises requires both a radical investigation down to the foundations of physics and an understanding of how subjective awareness, as opposed to mere computational capacity, may have become elaborated by Darwinian natural selection. We thus have to find reasons why subjectivity itself, rather than computation alone, is of pivotal importance in organismic survival. The answer lies in its capacity to anticipate situations crucial to survival. For this to be possible, the foundations of physics must contain a principle of space-time anticipation not covered by any mechanism of computation alone, or subjectivity would become superfluous and would have never been selected for in evolution. This paper sets out to demonstrate how quantum transactions universal to all quantum phenomena my fulfil this pivotal role. The role of dynamical chaos 1 and bifurcation in neurodynamics has been the subject of an increasing volume of theoretical and experimental research in which transition from chaos to order may form a key process in perception and cognition. There has also been a continuing interest in the possible link between quantum non-locality and consciousness. This paper presents a two-part theory in which: (a) a fractal link between neurodynamical chaos and quantum non-locality; and (b) a complex system theory of the sub-quantum world; together provide a physical solution to the mind-brain paradoxes of subjective consciousness and free-will. The fractal link between dynamical chaos and quantum uncertainty is proposed to be made through overlapping non-linearities capable of chaos, running from the neurosystems level down through the neuron, synapse, to the ion channel. Chaotic systems possess sensitive dependence, and brain states also contain features of self-organized criticality. In a critically poised brain state representing uncertainty of outcome, it is proposed that sensitive dependence opens the brain to quantum processes. In the transactional interpretation of quantum mechanics, future states form part of the boundary condition of reduction of the wave packet 2. Transactional supercausality may allow a form of prediction in the excitable cell which bypasses and complements formal computation. The selective advantage of such a process would explain the emergence of consciousness in organismic evolution.

This thesis provides a comprehensive exploration of quantum chaos theory, a field dedicated to understanding the quantum mechanical behavior of systems that exhibit chaotic dynamics in their classical limit. Unlike classical chaos, characterized by exponential sensitivity to initial conditions and continuous energy spectra, quantum systems are governed by the linear Schrödinger equation and possess discrete energy spectra in bounded systems. This fundamental difference necessitates a distinct approach to defining and identifying quantum chaos, focusing on statistical signatures rather than direct trajectory-based measures. The report delves into the historical development of the field, from its classical roots to the pioneering quantum insights that shaped its trajectory. It meticulously examines the theoretical frameworks, including Random Matrix Theory and semiclassical approximations like the Gutzwiller Trace Formula, which serve as crucial bridges between classical and quantum descriptions. Key quantum signatures such as spectral statistics (Wigner-Dyson and Poisson distributions), quantum scarring, quantum ergodicity, and information scrambling (probed by Out-of-Time-Ordered Correlators) are discussed in detail, along with their experimental observations across diverse physical systems, from atomic and nuclear physics to condensed matter and quantum optics. The thesis also explores the profound applications of quantum chaos in emerging technologies like quantum computing and its deep connections to fundamental physics, including black hole dynamics and quantum gravity. Finally, it addresses the persistent challenges and outlines promising future directions, emphasizing the ongoing quest for a rigorous definition, the impact of noise in open quantum systems, and the burgeoning field of many-body quantum chaos, all of which continue to shape the frontiers of this fascinating interdisciplinary domain.