Results for “Coherent instabilities” — Page 10

NASA NTRS2010

Hidden Statistics Approach to Quantum Simulations

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

Zak, Michail↗

NASA NTRS2012

Survey of Coherent Approximately 1 Hz Waves in Mercury's Inner Magnetosphere from MESSENGER Observations

We summarize observations by the MESSENGER spacecraft of highly coherent waves at frequencies between 0.4 and 5 Hz in Mercury's inner magnetosphere. This survey covers the time period from 24 March to 25 September 2011, or 2.1 Mercury years. These waves typically exhibit banded harmonic structure that drifts in frequency as the spacecraft traverses the magnetic equator. The waves are seen at all magnetic local times, but their observed rate of occurrence is much less on the dayside, at least in part the result of MESSENGER's orbit. On the nightside, on average, wave power is maximum near the equator and decreases with increasing magnetic latitude, consistent with an equatorial source. When the spacecraft traverses the plasma sheet during its equatorial crossings, wave power is a factor of 2 larger than for equatorial crossings that do not cross the plasma sheet. The waves are highly transverse at large magnetic latitudes but are more compressional near the equator. However, at the equator the transverse component of these waves increases relative to the compressional component as the degree of polarization decreases. Also, there is a substantial minority of events that are transverse at all magnetic latitudes, including the equator. A few of these latter events could be interpreted as ion cyclotron waves. In general, the waves tend to be strongly linear and characterized by values of the ellipticity less than 0.3 and wave-normal angles peaked near 90 deg. Their maxima in wave power at the equator coupled with their narrow-band character suggests that these waves might be generated locally in loss cone plasma characterized by high values of the ratio beta of plasma pressure to magnetic pressure. Presumably both electromagnetic ion cyclotron waves and electromagnetic ion Bernstein waves can be generated by ion loss cone distributions. If proton beta decreases with increasing magnetic latitude along a field line, then electromagnetic ion Bernstein waves are predicted to transition from compressional to transverse, a pattern consistent with our observations. We hypothesize that these local instabilities can lead to enhanced ion precipitation and directly feed field-line resonances.

ultra-low-frequency↗