Quantum Chaos & Quantum Computers

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.Comment: Lecture at Nobel symposium on "Quantum chaos", June 2000, Sweden; revtex, 10 pages, 9 figure

Coronal hole boundaries evolution at small scales: I. EIT 195 A and TRACE 171 A view

We aim at studying the small-scale evolution at the boundaries of an equatorial coronal hole connected with a channel of open magnetic flux with the polar region and an `isolated' one in the extreme-ultraviolet spectral range. We intend to determine the spatial and temporal scale of these changes. Imager data from TRACE in the Fe IX/X 171 A passband and EIT on-board Solar and Heliospheric Observatory in the Fe XII 195 A passband were analysed. We found that small-scale loops known as bright points play an essential role in coronal holes boundaries evolution at small scales. Their emergence and disappearance continuously expand or contract coronal holes. The changes appear to be random on a time scale comparable with the lifetime of the loops seen at these temperatures. No signature was found for a major energy release during the evolution of the loops. Although coronal holes seem to maintain their general shape during a few solar rotations, a closer look at their day-by-day and even hour-by-hour evolution demonstrates a significant dynamics. The small-scale loops (10" - 40" and smaller) which are abundant along coronal hole boundaries have a contribution to the small-scale evolution of coronal holes. Continuous magnetic reconnection of the open magnetic field lines of the coronal hole and the closed field lines of the loops in the quiet Sun is more likely to take place.Comment: 7 pages, 6 figures. in press in A&

Emergence of the second law out of reversible dynamics

Abstract If one demystifies entropy the second law of thermodynamics comes out as an emergent property entirely based on the simple dynamic mechanical laws that govern the motion and energies of system parts on a micro-scale. The emergence of the second law is illustrated in this paper through the development of a new, very simple and highly efficient technique to compare time-averaged energies in isolated conservative linear large scale dynamical systems. Entropy is replaced by a notion that is much more transparent and more or less dual called ectropy. Ectropy has been introduced before but we further modify the notion of ectropy such that the unit in which it is expressed becomes the unit of energy. The second law of thermodynamics in terms of ectropy states that ectropy decreases with time on a large enough time-scale and has an absolute minimum equal to zero. Zero ectropy corresponds to energy equipartition. Basically we show that by enlarging the dimension of an isolated conservative linear dynamical system and the dimension of the system parts over which we consider time-averaged energy partition, the tendency towards equipartition increases while equipartition is achieved in the limit. This illustrates that the second law is an emergent property of these systems. Finally from our large scale linear dynamic model we clarify Loschmidt’s paradox concerning the irreversible behavior of ectropy obtained from the reversible dynamic laws that govern motion and energy at the micro-scal

On Quantum Mechanical Aspects of Microtubules

We discuss possible quantum mechanical aspects of MicroTubules (MT), based on recent developments in quantum physics.We focus on potential mechanisms for `energy-loss-free' transport along the microtubules, which could be considered as realizations of Fr\"ohlich's ideas on the r\^ole of solitons for superconductivity and/or biological matter. By representing the MT arrangements as cavities,we present a novel scenario on the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. We suggest specific experiments to test the above-conjectured quantum nature of the microtubular arrangements inside the cell. These experiments are similar in nature to those in atomic physics, used in the detection of the Rabi-Vacuum coupling between coherent cavity modes and atoms. Our conjecture is that a similar Rabi-Vacuum-splitting phenomenon occurs in the MT case.Comment: 26 pages LATEX (minor typos corrected no effect on conclusions

The properties of horizontal magnetic elements in quiet solar intranetwork

Using the data observed by the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode satellite, the horizontal and vertical fields are derived from the wavelength-integrated measures of Zeeman-induced linear and circular polarizations. The quiet intranetwork regions are pervaded by horizontal magnetic elements. We categorize the horizontal intranetwork magnetic elements into two types: one is the non-isolated element which is accompanied by the vertical magnetic elements during its evolution; another is the isolated element which is not accompanied by the vertical magnetic elements. We identify 446 horizontal intranetwork magnetic elements, among them 87 elements are isolated and 359 are non-isolated. Quantitative measurements reveal that the isolated elements have relatively weaker horizontal magnetic fields, almost equal size, and shorter lifetime comparing with the non-isolated elements. Most non-isolated horizontal intranetwork magnetic elements are identified to associate with the emergence of Omega-shaped flux loops. A few non-isolated elements seem to indicate scenarios of submergence of Omega loops or emergence of U-like loops. There is a positive correlation between the lifetime and the size for both the isolated and non-isolated HIFs. It is also found that there is also positive correlation between the lifetime and the magnetic flux density for non-isolated HIFs, but no correlation for isolated HIFs. Even though the horizontal elements show lower magnetic flux density, they could carry the total magnetic flux in the order of magnitude close to 10^25 Mx to the solar surface each day.Comment: 10 figures, 25 pages. ApJ, in pres