Theory for the optimal control of time-averaged quantities in open quantum systems

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed

On the problem of Plasma Sheet Boundary Layer identification from plasma moments in Earth's magnetotail

The problem of identification of the interface region between the lobe and the Plasma Sheet (PS) – the Plasma Sheet Boundary Layer (PSBL) – using ion moments and magnetic field data often arises in works devoted to statistical studies of various PSBL phenomena. Our experience in the identification of this region based on the analysis of ion velocity distribution functions demonstrated that plasma parameters, such as the ion density and bulk velocity, the plasma beta or the dynamic pressure vary widely depending on the state of magnetotail activity. For example, while field-aligned beams of accelerated ions are often observed propagating along the lobeward edge of the PSBL there are times when no signatures of these beams could be observed. In the last case, a spacecraft moving from the lobe region to the PS registers almost isotropic PS-like ion velocity distribution. Such events may be classified as observations of the outer PS region. In this paper, we attempt to identify ion parameter ranges or their combinations that result in a clear distinction between the lobe, the PSBL and the adjacent PS or the outer PS regions. For this we used 100 crossings of the lobe-PSBL-PS regions by Cluster spacecraft (s/c) made in different periods of magnetotail activity. By eye inspection of the ion distribution functions we first identify and separate the lobe, the PSBL and the adjacent PS or outer PS regions and then perform a statistical study of plasma and magnetic field parameters in these regions. We found that the best results in the identification of the lobe-PSBL boundary are reached when one uses plasma moments, namely the ion bulk velocity and density calculated not for the entire energy range, but for the energies higher than 2 keV. In addition, we demonstrate that in many cases the plasma beta fails to correctly identify and separate the PSBL and the adjacent PS or the outer PS regions

Oxygen and hydrogen ion abundance in the near-Earth magnetosphere: Statistical results on the response to the geomagnetic and solar wind activity conditions

The composition of ions plays a crucial role for the fundamental plasma properties in the terrestrial magnetosphere. We investigate the oxygen-to-hydrogen ratio in the near-Earth magnetosphere from -10 RE<XGSE}< 10 RE. The results are based on seven years of ion flux measurements in the energy range ~10 keV to ~955 keV from the RAPID and CIS instruments on board the Cluster satellites. We find that (1) hydrogen ions at ~10 keV show only a slight correlation with the geomagnetic conditions and interplanetary magnetic field changes. They are best correlated with the solar wind dynamic pressure and density, which is an expected effect of the magnetospheric compression; (2) ~10 keV O+ ion intensities are more strongly affected during disturbed phase of a geomagnetic storm or substorm than >274 keV O+ ion intensities, relative to the corresponding hydrogen intensities; (3) In contrast to ~10 keV ions, the >274 keV O+ ions show the strongest acceleration during growth phase and not during the expansion phase itself. This suggests a connection between the energy input to the magnetosphere and the effective energization of energetic ions during growth phase; (4) The ratio between quiet and disturbed times for the intensities of ion ionospheric outflow is similar to those observed in the near-Earth magnetosphere at >274 keV. Therefore, the increase of the energetic ion intensity during disturbed time is more likely due to the intensification than to the more effective acceleration of the ionospheric source. In conclusion, the energization process in the near-Earth magnetosphere is mass dependent and it is more effective for the heavier ions

Spin-dependent effective interactions for halo nuclei

We discuss the spin-dependence of the effective two-body interactions appropriate for three-body computations. The only reasonable choice seems to be the fine and hyperfine interactions known for atomic electrons interacting with the nucleus. One exception is the nucleon-nucleon interaction imposing a different type of symmetry. We use the two-neutron halo nucleus 11Li as illustration. We demonstrate that models with the wrong spin-dependence are basically without predictive power. The Pauli forbidden core and valence states must be consistently treated.Comment: TeX file, 6 pages, 3 postscript figure

A multi-satellite study of accelerated ionospheric ion beams above the polar cap

This paper presents a study of nearly field-aligned outflowing ion beams observed on the Cluster satellites over the polar cap. Data are taken at geocentric radial distances of the order of 5&amp;ndash;9 &lt;i&gt;R&lt;sub&gt;E&lt;/sub&gt;&lt;/i&gt;. The distinction is made between ion beams originating from the polar cusp/cleft and beams accelerated almost along the magnetic field line passing by the spacecraft. Polar cusp beams are characterized by nearly field-aligned proton and oxygen ions with an energy ratio E&lt;sub&gt;O+&lt;/sub&gt; / E&lt;sub&gt;H+&lt;/sub&gt;, of the order of 3 to 4, due to the ion energy repartition inside the source and to the latitudinal extension of the source. Rapid variations in the outflowing ion energy are linked with pulses/modifications of the convection electric field. Cluster data allow one to show that these perturbations of the convection velocity and the associated ion structures propagate at the convection velocity. &lt;P style=&quot;line-height: 20px;&quot;&gt; In contrast, polar cap local ion beams are characterized by field-aligned proton and oxygen ions with similar energies. These beams show the typical inverted V structures usually observed in the auroral zone and are associated with a quasi-static converging electric field indicative of a field-aligned electric field. The field-aligned potential drop fits well the ion energy profile. The simultaneous observation of precipitating electrons and upflowing ions of similar energies at the Cluster orbit indicates that the spacecraft are crossing the mid-altitude part of the acceleration region. In the polar cap, the parallel electric field can thus extend to altitudes higher than 5&amp;nbsp;Earth radii. A detailed analysis of the distribution functions shows that the ions are heated during their parallel acceleration and that energy is exchanged between H&lt;sup&gt;+&lt;/sup&gt; and O&lt;sup&gt;+&lt;/sup&gt;. Furthermore, intense electrostatic waves are observed simultaneously. These observations could be due to an ion-ion two-stream instability

Molecular Structures in T=1 states of 10B

Multi-center (molecular) structures can play an important role in light nuclei. The highly deformed rotational band in 10Be with band head at 6.179 MeV has been observed recently and suggested to have an exotic alpha:2n:alpha configuration. A search for states with alpha:pn:alpha two-center molecular configurations in 10B that are analogous to the states with alpha:2n:alpha structure in 10Be has been performed. The T=1 isobaric analog states in 10B were studied in the excitation energy range of E=8.7-12.1 MeV using the reaction 1H(9Be,alpha)6Li*(T=1, 0+, 3.56 MeV). An R-matrix analysis was used to extract parameters for the states observed in the (p,alpha) excitation function. Five T=1 states in 10B have been identified. The known 2+ and 3- states at 8.9 MeV have been observed and their partial widths have been measured. The spin-parities and partial widths for three higher lying states were determined. Our data support theoretical predictions that the 2+ state at 8.9 MeV (isobaric analog of the 7.54 MeV state in 10Be) is a highly clustered state and can be identified as a member of the alpha:np:alpha rotational band. The next member of this band, the 4+ state, has not been found. A very broad 0+ state at 11 MeV that corresponds to pure alpha+6Li(0+,T=1) configuration is suggested and it might be related to similar structures found in 12C, 18O and 20Ne.Comment: 10 pages, 10 figures, accepted in Physical Review

Three-body structure of the low-lying 17^{17}Ne-states

The Borromean nucleus $^{17}$Ne ($^{15}$O$+ p + p$) is investigated by using the hyperspheric adiabatic expansion for a a three-body system. The measured size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O$+ p$) are first used as constraints to determine both central and spin-dependent two-body interactions. Then, the ground state structure of $^{17}$Ne is found to be an almost equal mixture of $s^2$ and $d^2$ proton-$^{15}$O relative states, the two lowest excited states have about 80% of $sd$-mixed components, and for the next two excited three-body states the proton-$^{15}$O relative s-states do not contribute. The spatial extension is as in ordinary nuclei. The widths of the resonances are estimated by the WKB transmission through the adiabatic potentials and found in agreement with the established experimental limits. We compare with experimental information and previous works.Comment: 29 pages, 7 postscript figures, to be published in Nuclear Physics

Analytical solution of the optimal laser control problem in two-level systems

The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or minimization of different physical quantities. We present solutions which reproduce and improve previous numerical results.Comment: 12 pages, 2 figure

Neutron-3^3H potentials and the 5^5H-properties

The continuum resonance spectrum of $^5$H ($^3$H+$n$+$n$) is investigated by use of the complex scaled hyperspherical adiabatic expansion method. The crucial $^3$H-neutron potential is obtained by switching off the Coulomb part from successful fits to $^3$He-proton experimental data. These two-body potentials must be expressed exclusively by operators conserving the nucleon-core mean field angular momentum quantum numbers. The energies $E_R$ and widths $\Gamma_R$ of the $1/2^+$ ground-state resonance and the lowest two excited $5/2^+$ and $3/2^+$-resonances are found to be $(1.6,1.5)$ MeV, $(2.8,2.5)$ MeV and $(3.2,3.9)$ MeV, respectively. These results agree with most of the experimental data. The energy distributions of the fragments after decay of the resonances are predicted.Comment: 26 pages, 8 tables, 7 figures. Accepted for publication in Nucl. Phys.