III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

1. Quantum Organics in the 21st Century

Sone, Akira and Sebastian Deffner. Quantum and Classical Ergotropy from Relative Entropies. Entropy. 23/9, 2021. We enter this paper by Center for Nonlinear Studies, LANL and University of Maryland physicists to note the latest theoretical exercises with regard to this open habitable frontier which is now known to be graced by these malleable qualities and much more. See also Quantum Coherence and Ergotropy by Gianluca Francica, et al at arXov:2006.05424.

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem. (Abstract)

My research interests focus on quantum information theory, spanning from quantum control theory to quantum thermodynamics, inspired by classical control and optimization, and their applications quantum computation, quantum simulation, quantum communication and quantum metrology. By working at industry, research universities or liberal arts colleges, I hope to contribute to developing the state-of-the-art quantum technology as a theoretical physicist. (Akira Sone)

Song, Chaoming. Zero Curvature Condition for Quantum Criticality. arXiv:2303.09591.. A University of Miami physicist (search) enters still another way to perceive and quantify this so pervasive natural tendency to seek and exhibit the best state.

Quantum criticality typically lies outside the bounds of the conventional Landau paradigm and there is no generic way to replace it for quantum phase transitions. In this paper, we present a new theory of quantum criticality based on a novel geometric approach which centers on the competition of commuting operators. We find that the quantum phase transition occurs precisely at the zero-curvature point on this boundary, which implies operators are at the critical point. (Excerpt)

Spitz, Damiel, et al. Finding Universal Structures in Quantum Many-Body Dynamics via Persistent Homology. arXiv:2001.02616. We cite this entry by Heidelberg University physicists including Jurgen Berges (search) and Anna Wienhard for its report that this widely used mathematical method can be availed even in this deepest domain. Akin to its broad application to neural networks, galactic clusters and more, quantum phenomena are found to be quite amenable. Thus our Organics title and consequent universality is well supported.

Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of quantum field theories. As a test case, we consider a two-dimensional Bose gas far from equilibrium with a spectrum of dynamical scaling exponents. We find that the persistent homology exponents are inherently linked to the geometry of the system. The approach opens new ways to study quantum many-body dynamics in terms of robust topological structures. (Abstract)

Tan, Ryan, et al. Towards Quantifying Complexity with Quantum Mechanics. arXiv:1404.6255. As many current papers report, a century after the quantum revolution began, via our human to humankind transition, a radical revision is underway through realizations that this subatomic domain is actually graced by the same nonlinear dynamics as everywhere else. Here researchers from China, Singapore, Australia, and the United Kingdom, including Vlatko Vedral and Jayne Thompson, open one more window, through certain terminologies, upon the vital reunion of micro quantum and macro classical nature.

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model - the model that requires the least past information for optimal future prediction. Here we review how such models, known as ϵ-machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum epsilon-machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave. (Abstract)

Are there any universal laws governing the evolution of complexity? While the second law of thermodynamics indicates ever increasing entropy, complexity seems to behave differently. The hot, smooth plasma near the Universe's birth and the final state of thermal equilibrium predicted by its heat death both appeal to our intuition of simplicity. Yet between these extremes, where there are stars, galaxies and life, the universe is complex; and because of that it is interesting. To answer this question, one must first quantify complexity. (1)

Epsilon-machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense, as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization, though, an alternative generator definition was given: unifilar, edge-emitting hidden Markov models with probabilistically distinct states. The key difference is that history epsilon-machines are defined by a process, whereas generator epsilon-machines define a process. We show here that these two definitions are equivalent in the finite-state case. (arXiv:1111.4500, Equivalence of History and Generator Epilson Machines)

Tian, Yu, et al. Tian, Yu, et al. Quantum Networks: from Multipartite Entanglement to Hypergraph Immersion.. arXiv:2406.13452.. We record this entry by Stockholm University, KTH Royal Institute of Technology and Northwestern University researchers to show how readily this once arcane domain has become amenable and assimilated with nature’s nonlinear transitional ascent. See also Topologically Robust Quantum Network Nonlocality by Sadra Boreiri, et al at arXiv:2406.09510 for a version that includes Bell nonlocality.

Multipartite entanglement, a higher-order interaction unique to quantum information, offers advantages in quantum network (QN) applications. Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing. Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs. This generalized solution introduces a partial order between QN topologies, permitting transformations which offer insights into the design and manipulation of higher-order network topologies. (Abstract)

Torlai, Giacomo, et al. Neural Network Quantum State Tomography. Mature Physics. May, 2018. We cite this paper by Perimeter Institute, D-Wave Systems, and ETH Zurich physicists as an example in the late 2010s of a novel view of “quantum” phenomena. In regard, this deep realm is presently being treated in several ways as brain-like, computational/informative, while other entries may view it in a genomic sense. A further attribute, similar to everywhere else, seems to be a tendency to settle into and exhibit critically poised states.

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods to validate and fully exploit quantum resources. Quantum state tomography (QST) aims to reconstruct the full quantum state from simple measurements. Here we show how machine learning techniques can be used to perform QST of highly entangled states with more than a hundred qubits, to a high degree of accuracy. This approach can benefit existing and future generations of devices ranging from quantum computers to ultracold-atom quantum simulators. (Abstract excerpt)

Tran, Minh, et al. Locality and Digital Quantum Simulation of Power-Law Interactions. Physical Review X. 9/031006, 2019. This entry by an eight person team based at the University of Maryland Joint Center for Quantum Information including Alexey Gorshkov is one more instance of how quantum nature, long seen as strangely off-putting, has lately been brought into a common systems fold.

Valentini, Antony. Beyond the Quantum. Physics World. November, 2009. A British physicist now at the Perimeter Institute has been in pursuit for some years of a novel “non-equilibrium” version. As a reference is cited the famous 1927 Solvay Conference on quantum mechanics, attended by Einstein, Bohr, and every player at the time. Although certain presentations, such as by Louis De Broglie, made note of dynamical “wavefunction” or “pilot wave” aspects (in the 1950s “hidden variables” by David Bohm), the meeting tended to a “particle” bias or paradigm still in place to this day. If one might then gloss this history and paper, of its arcane terms in translation, Valentini strives to revive a once and future “relational” nature, where such holistic, “non-local,” connections are equal and complementary to discrete units alone.

Today we realize that De Broglie’s original theory contains within it a new and much wider physics, of which ordinary quantum theory is merely a special case – a radically new physics that might perhaps be within our grasp. (33) Pilot-wave theory…is then not merely an alternative formulation of quantum theory. Instead, the theory itself tells us that quantum physics is a special “equilibrium” case of a much wider “non-equilibrium” physics. (35)

Walleczek, Jan, et al, eds. Special Issue: Emergent Quantum Mechanics – David Bohm Centennial Perspectives. Entropy. 21/2, 2019. In a special issue with this title, senior physicists JW, Germany, Gerhard Grossing, Austria, Paavo Pylkkanen, Finland and Basil Hiley, UK (a lifetime collaborator with Bohm) introduce 32 papers from the Emergent Quantum Mechanics 2017 (www.emqm17.org) conference Towards Ontology of Quantum Mechanics and the Conscious Agent, held at the University of London in October. His sage insights about the fundamental nature and affinity of universe and human, cosmos and consciousness, seem to become more relevant as years pass. I have heard David (1917-1992, search) speak on several occasions in the 1970s and 1980s. Some entries are The Philosophical and Scientific Metaphysics of David Bohm by William Seager (search), What Constitutes Emergent Quantum Reality? By Arno Keppens, A Lenient Causal Arrow of Time? by Nathan Argaman, and Why Bohmian Mechanics? by Nicolas Gisin.

This Special Issue explores the possibility of an ontology for quantum mechanics. The focus is the search for a "deeper level" theory for quantum mechanics that interconnects three fields of knowledge: emergence, the quantum, and information. Contributions will be featured that present current advances in realist approaches to quantum mechanics, including new experiments, work in quantum foundations, and the physics of the quantum observer and the conscious experimenter agent. Some (edited) topics are: Quantum Contextuality, Information Measures in Quantum Theory, Quantum Observation, Nonlinear Methods, and Self-organization and Quantum Emergence.

Wei, Bo-Bo, et al. Phase Transitions in the Complex Plane of Physical Parameters. Nature Scientific Reports. 4/5202, 2014. As a good example among a growing number, Chinese University of Hong Kong, Centre for Quantum Coherence, (see quote) physicists proceed to treat subatomic phenomena as a similar thermodynamic, evolutionary system.

At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Here we show that the quantum evolution of a system, initially in thermal equilibrium and driven by a designed interaction, is equivalent to the partition function of a complex parameter. Therefore, we can access the complex singularity points of thermodynamic functions and observe phase transitions even at high temperature. We further show that such phase transitions in the complex plane are related to topological properties of the renormalization group flows of the complex parameters. (Abstract)

Quantum coherence is the origin of novel physics in quantum matters such as cold atoms/molecules, topological insulators, and superconductors, and is the basis for future technologies such as quantum communication, quantum computing, and quantum metrology. The research on quantum coherence is an exploding frontier of modern physics and calls for innovative efforts from both theorists and experimentalists. The centre has a mission to provide a platform for enhancing academic exchange and collaborations, both internally and externally. The Center aims to tackle some grand challenges in understanding and exploiting quantum coherence with a synergy of theoretical and experimental expertise from diverse backgrounds including quantum optics, atomic, molecular and optical physics, condensed matter physics, and materials science. (Center for Quantum Coherence, Chinese University of Hong Kong)

Wei, Zong-Wen, et al. Renormalization and Small-World Model of Fractal Quantum Repeater Networks. Nature Scientific Reports. 3/1222, 2013. As the title conveys, University of Science and Technology of China, and Hangzhou Normal University, physicists are able to find in this previously arcane realm the same complexity phenomena as everywhere else in classical nature.

Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. (Abstract)

Wetterich, Christof. Quantum Scale Symmetry. arXiv:1901.04741. In a theoretical 100 page paper a University of Heidelberg physicist describes a natural cosmic repetition which emerges in kind from this fundamental realm. An array of topics run from Classical scale invariant standard model, Particle scale symmetry, and Flow in field space to Naturalness of the Fermi scale, Crossover in quantum gravity, and Cosmon inflation (see 1303.4700). And as we log in such technical entries, within this resource website it ought to be recorded that the Grail goal of complex network systems science from the 1960s and 1980s into the late 2010s to discern, quantify and realize an exemplary recurrence everywhere has at last been achieved.

Quantum scale symmetry is the realization of scale invariance in a quantum field theory. No parameters with dimension of length or mass are present in the quantum effective action. Quantum scale symmetry is generated by fluctuations via the presence of fixed points for running couplings. We review consequences of scale symmetry for particle physics, quantum gravity and cosmology. For particle physics, scale symmetry is closely linked to the tiny ratio between the Fermi scale of weak interactions and the Planck scale for gravity. For quantum gravity, it is associated to the ultraviolet fixed point which allows for a non-perturbatively renormalizable quantum field theory. In cosmology, approximate scale symmetry explains the almost scale-invariant primordial fluctuation spectrum which is at the origin of all structures in the universe. (Abstract excerpt)

For scale invariant inflation no intrinsic mass scale plays a role during the inflationary epoch. Quantum scale invariance can be considered as an exact symmetry. If a single scalar field has a non-vanishing cosmological value, it is a Goldstone boson. Its evolution settles early to a constant value. Inflation, if realized, does not end for a scale invariant model with a single scalar field. One therefore needs at least two physical scalar degrees of freedom. An example is “scale invariant Starobinski inflation”. The constant Plank mass for Starobinski inflation is replaced by a scalar field X. (71)

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