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The uncertainty principle and quantum chaos

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Chirikov, Boris V.

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

Konkov, L. E.

Simulations of Probabilities for Quantum Computing

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Turing machines

Dynamical Simulation of Probabilities

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices(such as random number generators). Self-orgainizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed. Special attention was focused upon coupled stochastic processes, defined in terms of conditional probabilities, for which joint probability does not exist. Simulations of quantum probabilities are also discussed.

number generators quantum probabilities

CH3O(A-X) fluorescence from photodissociation of dimethyl ether

The paper reports the quantitative photoabsorption and fluorescence cross sections of dimethyl ether (DME) measured with synchrotron radiation. Determinations were also made of the absolute fluorescence cross sections, the fluorescence quantum yield, and the radiative lifetime.

Suto, Masako

Quantum phase uncertainties in the classical limit

Several sources of phase noise, including spontaneous emission noise and the loss of coherence due to which-path information, are examined in the classical limit of high field intensities. Although the origin of these effects may appear to be quantum-mechanical in nature, it is found that classical analogies for these effects exist in the form of chaos.

Franson, James D.

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail

Multiple-Event, Single-Photon Counting Imaging Sensor

The single-photon counting imaging sensor is typically an array of silicon Geiger-mode avalanche photodiodes that are monolithically integrated with CMOS (complementary metal oxide semiconductor) readout, signal processing, and addressing circuits located in each pixel and the peripheral area of the chip. The major problem is its single-event method for photon count number registration. A single-event single-photon counting imaging array only allows registration of up to one photon count in each of its pixels during a frame time, i.e., the interval between two successive pixel reset operations. Since the frame time can t be too short, this will lead to very low dynamic range and make the sensor merely useful for very low flux environments. The second problem of the prior technique is a limited fill factor resulting from consumption of chip area by the monolithically integrated CMOS readout in pixels. The resulting low photon collection efficiency will substantially ruin any benefit gained from the very sensitive single-photon counting detection. The single-photon counting imaging sensor developed in this work has a novel multiple-event architecture, which allows each of its pixels to register as more than one million (or more) photon-counting events during a frame time. Because of a consequently boosted dynamic range, the imaging array of the invention is capable of performing single-photon counting under ultra-low light through high-flux environments. On the other hand, since the multiple-event architecture is implemented in a hybrid structure, back-illumination and close-to-unity fill factor can be realized, and maximized quantum efficiency can also be achieved in the detector array.

Zheng, Xinyu

Evanescent radiation, quantum mechanics and the Casimir effect

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Schatten, Kenneth H.

Probability Simulations by Non-Lipschitz Chaos

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

classical dynamics classical probabilities probabi

Non-scalar uncertainty: Uncertainty in dynamic systems

The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.

Martinez, Salvador Gutierrez

Information-Theoretic Aspects of Scrambling and Chaos

The goal of this overview talk on information-theoretic aspects of scrambling and chaos is to connect "out-of-time-ordered correlators" (OTOC) with as many "information-theoretic" quantities as we can, in hopes of better understanding what the OTOC actually measures. Recently published papers on this topic will include but not be limited to Styliaris, et al., PRL 126, 030601 (2021); Zanardi and Anand, PRA 103, 06224 (2021); and Anand and Zanardi, Quantum 6, 746 (2022).

quantum information scrambling

Corals from Space

The goal of this research is to monitor the health and vigor of coral reef ecosystems, and their sensitivity to natural and anthropogenic climate changes. To achieve these lofty goals, this research is investigating the feasibility of using spaceborne high-resolution spectrometers (on the US Landsat, French Systeme Probatoire pour l'Observation de la Terre [SPOT] and/or the Indian Resources Satellite [IRS 1C & 1D] spacecraft) to first map the aerial extent of coral reef systems, and second separate the amount of particular corals. If this is successful, we could potentially provide a quantum leap in our understanding of coral reef systems, as well as provide much needed baseline data to measure future changes in global coral reef ecosystems. In collaboration with Tomas Tomascik, Yann Morel, and other colleagues, a series of experiments were planned to coordinate in situ coral observations, high-resolution spaceborne imagery (from Landsat, SPOT, and, possibly, IRS IC spacecraft), and NASA Space Shuttle photographs and digital images. Our eventual goal is to develop "coral health algorithms" that can be used to assess time series of imagery collected from satellite sensors (Landsat since 1972, SPOT since 1986) in concert with in situ observations. The bad news from last year was that from 1997 to mid- 1998, the extreme cloudiness over southeast Asia due to prolonged smoke from El Nino-related fires and the economic chaos in this region frustrated both our space and reef-based data collection activities. When this volatile situation stabilizes, we will restart these activities. The good news was that in collaboration with Al Strong at the National Oceanic and Atmospheric Administration (NOAA) we had an exciting year operationally using the NOAA's Advanced Very High Resolution Radiometer sensor derived sea surface temperature products to warn of coral "bleaching" at many locations throughout the tropics. Data from NOAA's satellites showed that during the El Nino of 1997 and the first half of 1998, more ocean area in the tropics experienced exceptionally high sea surface temperatures, or "hot spots," than have been observed in any fall year since the El Nino of 1982. From January to July, the coral bleaching events were concentrated in the Southern Hemisphere (during its warm season). Since July 1998, the reports of extensive coral bleaching have again spread into regions of the Northern Hemisphere following abnormally high sea surface temperatures, especially around the Philippines and throughout the Caribbean Basin, Bahamas, Bermuda and Florida Keys. These El Nino induced events clearly demonstrated that corals are the "canaries of the marine ecosystem," highly sensitive to short-term natural climate events (El Nino), and should be monitored as measures of longer-term environmental and climate change. Additional information is contained in the original.

Patzert, William C.

SOI CMOS Imager with Suppression of Cross-Talk

A monolithic silicon-on-insulator (SOI) complementary metal oxide/semiconductor (CMOS) image-detecting integrated circuit of the active-pixel-sensor type, now undergoing development, is designed to operate at visible and near-infrared wavelengths and to offer a combination of high quantum efficiency and low diffusion and capacitive cross-talk among pixels. The imager is designed to be especially suitable for astronomical and astrophysical applications. The imager design could also readily be adapted to general scientific, biological, medical, and spectroscopic applications. One of the conditions needed to ensure both high quantum efficiency and low diffusion cross-talk is a relatively high reverse bias potential (between about 20 and about 50 V) on the photodiode in each pixel. Heretofore, a major obstacle to realization of this condition in a monolithic integrated circuit has been posed by the fact that the required high reverse bias on the photodiode is incompatible with metal oxide/semiconductor field-effect transistors (MOSFETs) in the CMOS pixel readout circuitry. In the imager now being developed, the SOI structure is utilized to overcome this obstacle: The handle wafer is retained and the photodiode is formed in the handle wafer. The MOSFETs are formed on the SOI layer, which is separated from the handle wafer by a buried oxide layer. The electrical isolation provided by the buried oxide layer makes it possible to bias the MOSFETs at CMOS-compatible potentials (between 0 and 3 V), while biasing the photodiode at the required higher potential, and enables independent optimization of the sensory and readout portions of the imager.

Pain, Bedabrata

Cosmic Complexity

What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainty did not invent) ls that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for me explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemll"!gly Improbable events are actually happening a!1 the time? Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physlc!sts have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features. Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capadty" in which extracting energy from a gravitating system makes it hotter -- clearly the 2nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations. And because or that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceasess experimentation would not be able to produce life elsewhere -- but we don't know for sure. And life went on to cause new Instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles. with predators for every kInd of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves. One of the instabilities Is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are In 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verllnde has argued that gravitation, the one force that has so far resisted our efforts at a Quantum description, is not even a fundamental force, but is itself it a statistical force, like osmosis. What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

Mather, John C.