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Controlled Quantum Packets

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

DeMartino, Salvatore↗

Irreversibility

The principles of thermodynamics in relation to the irreversibility of real processes in nature are examined, taking into account an analogy used by Gibbs to present a picture concerning the time evolution of a complicated dynamical system. The significance of quantum-mechanics relations with respect to irreversibility considerations is explored. It is shown that quantum mechanical uncertainties are not necessarily required to obtain irreversibility.

Lamb, W. E., Jr.↗

Quantum-mechanical transport equation for atomic systems.

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.↗

Floquet operator as integral of motion

Nonstationary quantum systems have no energy levels. However, for time-dependent periodical quantum systems, the notion of quasi-energy levels has been introduced. The main point of the quasi-energy concept is to relate quasi-energies to eigenvalues of the Floquet operator or monodromy operators which is equal to the evolution operator of a quantum system taken at the moment coinciding with the period of the system. The purpose of this article is to relate the Floquet operator to integrals of the motion and to introduce a new operator which is the integral of motion and has the same quasi-energy spectrum that the Floquet operator has. We wish to discuss an explicit formula for this new integral of motion.

Manko, V. I.↗

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗

Physical Invariants of Intelligence

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Zak, Michail↗

NASA Tech Briefs, March 2013

Topics covered include: Remote Data Access with IDL Data Compression Algorithm Architecture for Large Depth-of-Field Particle Image Velocimeters Vectorized Rebinning Algorithm for Fast Data Down-Sampling Display Provides Pilots with Real-Time Sonic-Boom Information Onboard Algorithms for Data Prioritization and Summarization of Aerial Imagery Monitoring and Acquisition Real-time System (MARS) Analog Signal Correlating Using an Analog-Based Signal Conditioning Front End Micro-Textured Black Silicon Wick for Silicon Heat Pipe Array Robust Multivariable Optimization and Performance Simulation for ASIC Design; Castable Amorphous Metal Mirrors and Mirror Assemblies; Sandwich Core Heat-Pipe Radiator for Power and Propulsion Systems; Apparatus for Pumping a Fluid; Cobra Fiber-Optic Positioner Upgrade; Improved Wide Operating Temperature Range of Li-Ion Cells; Non-Toxic, Non-Flammable, -80 C Phase Change Materials; Soft-Bake Purification of SWCNTs Produced by Pulsed Laser Vaporization; Improved Cell Culture Method for Growing Contracting Skeletal Muscle Models; Hand-Based Biometric Analysis; The Next Generation of Cold Immersion Dry Suit Design Evolution for Hypothermia Prevention; Integrated Lunar Information Architecture for Decision Support Version 3.0 (ILIADS 3.0); Relay Forward-Link File Management Services (MaROS Phase 2); Two Mechanisms to Avoid Control Conflicts Resulting from Uncoordinated Intent; XTCE GOVSAT Tool Suite 1.0; Determining Temperature Differential to Prevent Hardware Cross-Contamination in a Vacuum Chamber; SequenceL: Automated Parallel Algorithms Derived from CSP-NT Computational Laws; Remote Data Exploration with the Interactive Data Language (IDL); Mixture-Tuned, Clutter Matched Filter for Remote Detection of Subpixel Spectral Signals; Partitioned-Interval Quantum Optical Communications Receiver; and Practical UAV Optical Sensor Bench with Minimal Adjustability.

Source record↗

Reverse Energy Cascade in Turbulent Weakly Ionized Plasmas

For systems far from equilibrium, the neglect of a role for viscous effects in turbulence may be generally inappropriate when the relaxation time for the molecular process approaches the local flow time (Orou et al. (1996)). Furthermore, for stationary collisional plasmas, the conventional Reynolds number is irrelevant under circumstances where the standard features of turbulence in ordinary gases are observed in the plasma (Johnson et al. (1987)). The current theoretical understanding of these turbulent phenomenon is particularly inadequate for turbulence associated with ionizing shock waves; generally speaking, thermodynamic, acoustic and pressure fluctuations are all seen as amplified across the shock wave followed by a dramatic decay (relaminarization) usually attributed to a lack of importance of viscosity in the turbulent regions. This decay would be accelerated when the flow speed is also reduced due to the importance usually given to the conventional Reynolds number (which is directly proportional to velocity) as a quality of turbulence index. However, evidence supporting this consensus is lacking. By contrast, recent evidence of vanishing triple correlations form De Silva et al. (1996) provides strong support for early theoretical speculation of inherently molecular effects in macroscopic turbulence in Tsuge (1974). This specifically suggests that the role of compressive effects ordinarily associated with the shock wave could be significantly muted by the existence of a strongly turbulent local environment. There is also more recent theoretical speculation (Frisch et al. (1984)) of an inherently and previously unsuspected non-dissipative nature to turbulence, with energy conservation being nurtured by reverse energy cascades in the turbulent fluctuation spectra. Furthermore, the role which might be played by fluctuations on quantum mechanical phenomena and variations in molecular parameters is completely unknown, especially of the sort which might be found in optical spectra. A determination of the role which changing turbulent parameters might play on optical signatures behind a reflected shock wave should therefore provide a useful tool for the evolution of theoretical models for turbulence.

Williams, Kyron↗

Lunar Polar Exploration with Beamed Powered Rovers

Use of a laser to transmit power to a photovoltaic array has been proposed many times, including significant work done at NASA Glenn during the 1990s, but until recently the technology has lagged behind the ambitious requirements. The current NASA objective of lunar polar exploration provides the need, and evolution of higher-power and more efficient lasers provides the opportunity. Exploration of the ice-bearing craters near the lunar poles, where complete absence of sunlight precludes solar power, have been identified as a significant technology challenge for NASA’s future exploration. An approach to solve this is to use a laser to send power from the illuminated crater rim to a photovoltaic receiver on a rover inside the permanently dark region. A conceptual design was done of a prototype laser power system to be included on a proposed flight demonstration of the Kilopower space reactor. For the design, the laser transmitter is mounted on a small rover capable of moving to a location in line of sight of the receiving rover, e.g., on a crater rim with a view into the permanently dark region to be explored. A 250-watt laser diode bar transmits power at 808 nm, using a 10.5 cm optical beam director. The beam is received by a GaAs solar array mounted on the exploring rover, where it is converted into electrical power at ~50% optical to electrical efficiency. For the flight demonstration, 50 meters of laser transmission was required. The design showed a total laser mass of 7.8 kg is capable of producing the beam needed, not including the thermal control system. The demonstration design demonstrates 50-m transmission, but it would be valuable to have longer point-to-point beaming on the moon. Long beam paths require higher coherence than the diode laser bars of the demonstration system. The development of high-efficiency diode-pumped fiber lasers meets this technology need: and diode-pumped fiber lasers using the Er/Yb system can be purchased commercially with overall conversion efficiency of greater than 50% at wavelength 1.06 micrometers. Two technologies for a photovoltaic converter for this wavelength are the InGaAs photovoltaic cell, using technology developed for multi-junction space solar cells, or newly-developed high-quantum efficiency silicon cells. The next step to mature the technology would be a lunar flight demonstration. In the future, this has the potential to enhance and enable future human exploration of the moon, harvesting and utilizing the ice resources of these permanently-shadowed craters.

Geoffrey A Landis↗

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.↗