A class of commutative dynamics of open quantum systems

We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent generators. We consider both Markovian and non-Markovian cases.Comment: 22 page

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.Comment: 31 page

Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society

Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud \ud \ud KEYWORDS: Emergence of Life and Human Consciousness;\ud Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud \u

General form of quantum evolution

We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local generator which generalizes well known Lindblad representation for the Markovian dynamics. It shows that the structure of non-Markovian generators is highly intricate and the problem of their classification is still open. Simple examples illustrate our approach.Comment: 4 page

Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime

We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field theories for matter directly from the GFT action, in both 3 and 4 dimensions and in both Riemannian and Lorentzian signatures. As such they represent an important step, we argue, in bridging the gap between a quantum, discrete picture of a pre-geometric spacetime and the effective continuum geometric physics of gravity and matter, using ideas and tools from field theory and condensed matter analog gravity models, applied directly at the GFT level.Comment: 13 pages, no figures; uses JPConf style; contribution to the proceedings of the D.I.C.E. 2008 worksho