New compact forms of the trigonometric Ruijsenaars-Schneider system

The reduction of the quasi-Hamiltonian double of ${\mathrm{SU}}(n)$ that has been shown to underlie Ruijsenaars' compactified trigonometric $n$-body system is studied in its natural generality. The constraints contain a parameter $y$, restricted in previous works to $0<y < \pi/n$ because Ruijsenaars' original compactification relies on an equivalent condition. It is found that allowing generic $0<y<\pi/2$ results in the appearance of new self-dual compact forms, of two qualitatively different types depending on the value of $y$. The type (i) cases are similar to the standard case in that the reduced phase space comes equipped with globally smooth action and position variables, and turns out to be symplectomorphic to ${\mathbb{C}P^{n-1}}$ as a Hamiltonian toric manifold. In the type (ii) cases both the position variables and the action variables develop singularities on a nowhere dense subset. A full classification is derived for the parameter $y$ according to the type (i) versus type (ii) dichotomy. The simplest new type (i) systems, for which $\pi/n < y < \pi/(n-1)$, are described in some detail as an illustration.Comment: 31 page

Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.Comment: Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 page

The Bacterial Photosynthetic Reaction Center as a Model for Membrane Proteins

Membrane proteins participate in many fundamental cellular processes. Until recently, an understanding of the function and properties of membrane proteins was hampered by an absence of structural information at the atomic level. A landmark achievement toward understanding the structure of membrane proteins was the crystallization (1) and structure determination (2-5) the photosynthetic reaction center (RC) from the purple bacteria Rhodopseudomonas viridis, followed by that of the RC from Rhodobacter sphaeroides (6-17). The RC is an integral membrane protein-pigment complex, which carries out the initial steps of photosynthesis (reviewed in 18). RCs from the purple bacteria Rps. viridis and Rb. sphaeroides are composed of three membrane-associated protein subunits (designated L, M, and H), and the following cofactors: four bacteriochlorophylls (Bchl or B), two bacteriopheophytins (Bphe or [phi]), two quinones, and a nonheme iron. The cofactors are organized into two symmetrical branches that are approximately related by a twofold rotation axis (2, 8). A central feature of the structural organization of the RC is the presence of 11 hydrophobic [alpha]-helixes, approximately 20-30 residues long, which are believed to represent the membrane-spanning portion of the RC (3, 9). Five membrane-spanning helixes are present in both the L and M subunits, while a single helix is in the H subunit. The folding of the L and M subunits is similar, consistent with significant sequence similarity between the two chains (19-25). The L and M subunits are approximately related by the same twofold rotation axis that relates the two cofactor branches. RCs are the first membrane proteins to be described at atomic resolution; consequently they provide an important model for discussing the folding of membrane proteins. The structure demonstrates that [alpha]-helical structures may be adopted by integral membrane proteins, and provides confirmation of the utility of hydropathy plots in identifying nonpolar membrane-spanning regions from sequence data. An important distinction between the folding environments of water-soluble proteins and membrane proteins is the large difference in water concentration surrounding the proteins. As a result, hydrophobic interactions (26) play very different roles in stabilizing the tertiary structures of these two classes of proteins; this has important structural consequences. There is a striking difference in surface polarity of membrane and water-soluble proteins. However, the characteristic atomic packing and surface area appear quite similar. A computational method is described for defining the position of the RC in the membrane (10). After localization of the RC structure in the membrane, surface residues in contact with the lipid bilayer were identified. As has been found for soluble globular proteins, surface residues are less well conserved in homologous membrane proteins than the buried, interior residues. Methods based on the variability of residues between homologous proteins are described (13); they are useful (a) in defining surface helical regions of membrane and water-soluble proteins and (b) in assigning the side of these helixes that are exposed to the solvent. A unifying view of protein structure suggests that water-soluble proteins may be considered as modified membrane proteins with covalently attached polar groups that solubilize the proteins in aqueous solution

Sine-Gordon multisoliton form factors in finite volume

Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.Comment: 24 pages, LaTeX2e file, 8 eps figures. v2: notations improved, some explanatory text and references adde

Simulation of the interaction between Alfvén waves and fast particles

There is a wide variety of Alfvén waves in tokamak and stellarator plasmas. While most of them are damped, some of the global eigenmodes can be driven unstable when they interact with energetic particles. By coupling the MHD code CKA with the gyrokinetic code EUTERPE, a hybrid kinetic-MHD model is created to describe this wave–particle interaction in stellarator geometry. In this thesis, the CKA-EUTERPE code package is presented. This numerical tool can be used for linear perturbative stability analysis of Alfvén waves in the presence of energetic particles. The equations for the hybrid model are based on the gyrokinetic equations. The fast particles are described with linearized gyrokinetic equations. The reduced MHD equations are derived by taking velocity moments of the gyrokinetic equations. An equation for describing the Alfvén waves is derived by combining the reduced MHD equations. The Alfvén wave equation can retain kinetic corrections. Considering the energy transfer between the particles and the waves, the stability of the waves can be calculated. Numerically, the Alfvén waves are calculated using the CKA code. The equations are solved as an eigenvalue problem to determine the frequency spectrum and the mode structure of the waves. The results of the MHD model are in good agreement with other sophisticated MHD codes. CKA results are shown for a JET and a W7-AS example. The linear version of the EUTERPE code is used to study the motion of energetic particles in the wavefield with fixed spatial structure, and harmonic oscillations in time. In EUTERPE, the gyrokinetic equations are discretized with a PIC scheme using the delta-f method, and both full orbit width and finite Larmor radius effects are included. The code is modified to be able to use the wavefield calculated externally by CKA. Different slowing-down distribution functions are also implemented. The work done by the electric field on the particles is measured to calculate the energy transfer between the particles and the wave and from that the growth rate is determined. The advantage of this approach is that the full magnetic geometry is retained without any limiting assumptions on guiding center orbits. Extensive benchmarks have been performed to test the new CKA-EUTERPE code. Three tokamak benchmarks are presented, where the stability of TAE modes are studied as a function of fast particle energy, or in one case as a function of the fast particle charge. The benchmarks show good agreement with other codes. Stellarator calculations were performed for Wendelstein 7-AS and the results demonstrate that the finite orbit width effects tend to be strongly stabilizing.Es gibt eine Vielzahl von Alfvén-Wellen in Tokamak und Stellarator Plasmen. Während die meisten dieser Wellen gedämpft sind, können einige globale Eigenmoden durch die Wechselwirkung mit schnellen Teilchen, die durch Fusions oder Heizungsprozesse im Plasma entstehen, instabil werden. Durch die Kopplung des MHD-Codes CKA mit dem gyrokinetischen Code EUTERPE wurde ein sogenanntes Hybridmodell zwischen kinetischer Theorie und MHD erstellt, um diese Welle-Teilchen Wechselwirkung in Stellaratorgeometrie beschreiben zu können. In dieser Arbeit wird das CKA-EUTERPE Codepaket vorgestellt. Dieses numerische Werkzeug kann für lineare störungstheoretische Stabilitätsanalyse der Alfvén-Wellen in Gegenwart von Teilchen mit sehr großer Energie verwendet werden. Die Gleichungen für das Hybridmodell wurden aus dem gyrokinetischen Vlasov-Maxwell-System hergeleitet. Dabei werden die schnellen Teilchen mit linearisierten gyrokinetischen Gleichungen beschrieben, während die reduzierten MHD Gleichungen für das Hauptplasma aus deren Geschwindigkeitsmomenten konstruiert sind. Daraus lässt sich eine Gleichung zur Beschreibung der Alfvén-Wellen ableiten, die auch kinetische Korrekturen beinhalten kann. Aus dem Energieübertrag zwischen den Teilchen und den Wellen kann schließlich die Stabilität der Wellen berechnet werden. Numerisch werden die Alfvén-Wellen mit dem CKA Code berechnet. Die Gleichungen werden als Eigenwertproblem gelöst, und das Frequenzspektrum und die Modenstruktur der Wellen bestimmt. Die Ergebnisse des MHD-Modell sind in guter Übereinstimmung mit anderen anspruchsvollen MHD-Codes. In der Arbeit werden Ergebnisse von CKA für eine JET Entladung und ein gut dokumentiertes Beispiel von Wendelstein 7-AS vorgestellt. Die lineare Version des EUTERPE Codes wird verwendet, um die Bewegung der energiereichen Teilchen in dem MHD Wellenfeld mit fester räumlicher Struktur und harmonischen Oszillationen in der Zeit zu untersuchen. Im EUTERPE-Code wurden die gyrokinetische Gleichungen mit der delta-f "particle-in-cell"- Methode diskretisiert. Dabei wurden sowohl die vollständige Bewegung des Gyrationszentrums als auch die endliche Größe des Gyrationsradius berücksichtigt. In der Arbeit wurde der Code geeignet angepasst, um das von CKA berechnete Wellenfeld nutzen zu können. Verschiedene "slowing down" Verteilungsfunktionen für die schnellen Teilchen wurden ebenfalls implementiert. Die Arbeit, die durch das elektrische Feld an den Teilchen oder von den Teilchen im Feld verrichtet wird, wird gemessen, um den Energieübertrag zwischen den Teilchen und der Welle zu bestimmen und die Wachstumsrate für die Amplitude der Welle zu berechnen. Der Vorteil dieses Ansatzes ist, dass die Probleme in voller magnetischer Geometrie betrachtet werden können, ohne durch zusätzliche Annahmen die Bewegung des Führungs- oder Gyrationszentrums der schnellen Teilchen zu vereinfachen. Umfangreiche Benchmarks wurden durchgeführt, um den neuen CKA-EUTERPE Code zu testen. Drei Tokamak Benchmarks werden vorgestellt, in denen die Stabilität der TAE-Moden als Funktion der Energie der schnellen Teilchen oder in einem Fall als Funktion der Ladung der schnellen Teilchen untersucht wird. Die Benchmarks zeigen eine gute Übereinstimmung mit anderen Codes. Stellarator-Rechnungen wurden für Wendelstein 7-AS durchgeführt, wobei die Ergebnisse zeigen, dass die Moden durch die vollständige Berücksichtigung der Bahnen der schnellen Teilchen stabilisiert werden

Cu NMR evidence for enhanced antiferromagnetic correlations around Zn impurities in YBa2Cu3O6.7

Doping the high-Tc superconductor YBa2Cu3O6.7 with 1.5 % of non-magnetic Zn impurities in CuO2 planes is shown to produce a considerable broadening of 63Cu NMR spectra, as well as an increase of low-energy magnetic fluctuations detected in 63Cu spin-lattice relaxation measurements. A model-independent analysis demonstrates that these effects are due to the development of staggered magnetic moments on many Cu sites around each Zn and that the Zn-induced moment in the bulk susceptibility might be explained by this staggered magnetization. Several implications of these enhanced antiferromagnetic correlations are discussed.Comment: 4 pages including 2 figure

Magnetic fullerenes inside single-wall carbon nanotubes

C59N magnetic fullerenes were formed inside single-wall carbon nanotubes by vacuum annealing functionalized C59N molecules encapsulated inside the tubes. A hindered, anisotropic rotation of C59N was deduced from the temperature dependence of the electron spin resonance spectra near room temperature. Shortening of spin-lattice relaxation time, T_1, of C59N indicates a reversible charge transfer toward the host nanotubes above $\sim 350$ K. Bound C59N-C60 heterodimers are formed at lower temperatures when C60 is co-encapsulated with the functionalized C59N. In the 10-300 K range, T_1 of the heterodimer shows a relaxation dominated by the conduction electrons on the nanotubes

Two-spin measurements in exchange interaction quantum computers

We propose and analyze a method for single shot measurement of the total spin of a two electron system in a coupled quantum dot or donor impurity structure, which can be used for readout in a quantum computer. The spin can be inferred by observing spin-dependent fluctuations of charge between the two sites, via a nearby electrometer. Realistic experimental parameters indicate that the fidelity of the measurement can be larger than 0.999 with existing or near-future technology. We also describe how our scheme can be used to implement various one- and two-qubit measurements, and hence to implement universal quantum computation

Optical Detection of a Single Nuclear Spin

We propose a method to optically detect the spin state of a 31-P nucleus embedded in a 28-Si matrix. The nuclear-electron hyperfine splitting of the 31-P neutral-donor ground state can be resolved via a direct frequency discrimination measurement of the 31-P bound exciton photoluminescence using single photon detectors. The measurement time is expected to be shorter than the lifetime of the nuclear spin at 4 K and 10 T.Comment: 4 pages, 3 figure